TSTP Solution File: SWV418-1.060 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV418-1.060 : TPTP v8.1.0. Released v3.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Thu Sep 29 15:11:43 EDT 2022
% Result : Unsatisfiable 11.99s 7.93s
% Output : Proof 12.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWV418-1.060 : TPTP v8.1.0. Released v3.5.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 03:07:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 11.99/7.93 % SZS status Unsatisfiable
% 11.99/7.93 % SZS output start Proof
% 11.99/7.93 tff(node3_type, type, (
% 11.99/7.93 node3: ( $i * $i * $i ) > $o)).
% 11.99/7.93 tff(s56_type, type, (
% 11.99/7.93 s56: $i)).
% 11.99/7.93 tff(s59_type, type, (
% 11.99/7.93 s59: $i)).
% 11.99/7.93 tff(c_bit2_type, type, (
% 11.99/7.93 c_bit2: $i)).
% 11.99/7.93 tff(trans_type, type, (
% 11.99/7.93 trans: ( $i * $i ) > $o)).
% 11.99/7.93 tff(s58_type, type, (
% 11.99/7.93 s58: $i)).
% 11.99/7.93 tff(m_counter_cell_v_value_type, type, (
% 11.99/7.93 m_counter_cell_v_value: ( $i * $i ) > $o)).
% 11.99/7.93 tff(node2_type, type, (
% 11.99/7.93 node2: ( $i * $i ) > $o)).
% 11.99/7.93 tff(c_bit1_type, type, (
% 11.99/7.93 c_bit1: $i)).
% 11.99/7.93 tff(node1_type, type, (
% 11.99/7.93 node1: ( $i * $i ) > $o)).
% 11.99/7.93 tff(s57_type, type, (
% 11.99/7.93 s57: $i)).
% 11.99/7.93 tff(s55_type, type, (
% 11.99/7.93 s55: $i)).
% 11.99/7.93 tff(s54_type, type, (
% 11.99/7.93 s54: $i)).
% 11.99/7.93 tff(s53_type, type, (
% 11.99/7.93 s53: $i)).
% 11.99/7.93 tff(s52_type, type, (
% 11.99/7.93 s52: $i)).
% 11.99/7.93 tff(s51_type, type, (
% 11.99/7.93 s51: $i)).
% 11.99/7.93 tff(s50_type, type, (
% 11.99/7.93 s50: $i)).
% 11.99/7.93 tff(s49_type, type, (
% 11.99/7.93 s49: $i)).
% 11.99/7.93 tff(s48_type, type, (
% 11.99/7.93 s48: $i)).
% 11.99/7.93 tff(s47_type, type, (
% 11.99/7.93 s47: $i)).
% 11.99/7.93 tff(node4_type, type, (
% 11.99/7.93 node4: ( $i * $i ) > $o)).
% 11.99/7.93 tff(m_counter_cell_v_carry_out_type, type, (
% 11.99/7.93 m_counter_cell_v_carry_out: ( $i * $i ) > $o)).
% 11.99/7.93 tff(s46_type, type, (
% 11.99/7.93 s46: $i)).
% 11.99/7.93 tff(s45_type, type, (
% 11.99/7.93 s45: $i)).
% 11.99/7.93 tff(s44_type, type, (
% 11.99/7.93 s44: $i)).
% 11.99/7.93 tff(s43_type, type, (
% 11.99/7.93 s43: $i)).
% 11.99/7.93 tff(s42_type, type, (
% 11.99/7.93 s42: $i)).
% 11.99/7.93 tff(s41_type, type, (
% 11.99/7.93 s41: $i)).
% 11.99/7.93 tff(s40_type, type, (
% 11.99/7.93 s40: $i)).
% 11.99/7.93 tff(m_counter_cell_v_carry_in_type, type, (
% 11.99/7.93 m_counter_cell_v_carry_in: ( $i * $i ) > $o)).
% 11.99/7.93 tff(c_bit0_type, type, (
% 11.99/7.93 c_bit0: $i)).
% 11.99/7.93 tff(s39_type, type, (
% 11.99/7.93 s39: $i)).
% 11.99/7.93 tff(s38_type, type, (
% 11.99/7.93 s38: $i)).
% 11.99/7.93 tff(s37_type, type, (
% 11.99/7.93 s37: $i)).
% 11.99/7.93 tff(s36_type, type, (
% 11.99/7.93 s36: $i)).
% 11.99/7.93 tff(s35_type, type, (
% 11.99/7.93 s35: $i)).
% 11.99/7.93 tff(s34_type, type, (
% 11.99/7.93 s34: $i)).
% 11.99/7.93 tff(s33_type, type, (
% 11.99/7.93 s33: $i)).
% 11.99/7.93 tff(s32_type, type, (
% 11.99/7.93 s32: $i)).
% 11.99/7.93 tff(s31_type, type, (
% 11.99/7.93 s31: $i)).
% 11.99/7.93 tff(s30_type, type, (
% 11.99/7.93 s30: $i)).
% 11.99/7.93 tff(s29_type, type, (
% 11.99/7.93 s29: $i)).
% 11.99/7.93 tff(s28_type, type, (
% 11.99/7.93 s28: $i)).
% 11.99/7.93 tff(s27_type, type, (
% 11.99/7.93 s27: $i)).
% 11.99/7.93 tff(s26_type, type, (
% 11.99/7.93 s26: $i)).
% 11.99/7.93 tff(s25_type, type, (
% 11.99/7.93 s25: $i)).
% 11.99/7.93 tff(s24_type, type, (
% 11.99/7.93 s24: $i)).
% 11.99/7.93 tff(s23_type, type, (
% 11.99/7.93 s23: $i)).
% 11.99/7.93 tff(s22_type, type, (
% 11.99/7.93 s22: $i)).
% 11.99/7.93 tff(s21_type, type, (
% 11.99/7.93 s21: $i)).
% 11.99/7.93 tff(s20_type, type, (
% 11.99/7.93 s20: $i)).
% 11.99/7.93 tff(s19_type, type, (
% 11.99/7.93 s19: $i)).
% 11.99/7.93 tff(s18_type, type, (
% 11.99/7.93 s18: $i)).
% 11.99/7.93 tff(s17_type, type, (
% 11.99/7.93 s17: $i)).
% 11.99/7.93 tff(s16_type, type, (
% 11.99/7.93 s16: $i)).
% 11.99/7.93 tff(s15_type, type, (
% 11.99/7.93 s15: $i)).
% 11.99/7.93 tff(s14_type, type, (
% 11.99/7.93 s14: $i)).
% 11.99/7.93 tff(s13_type, type, (
% 11.99/7.93 s13: $i)).
% 11.99/7.93 tff(s12_type, type, (
% 11.99/7.93 s12: $i)).
% 11.99/7.93 tff(succ_type, type, (
% 11.99/7.93 succ: ( $i * $i ) > $o)).
% 11.99/7.93 tff(s11_type, type, (
% 11.99/7.93 s11: $i)).
% 11.99/7.93 tff(s10_type, type, (
% 11.99/7.93 s10: $i)).
% 11.99/7.93 tff(s9_type, type, (
% 11.99/7.93 s9: $i)).
% 11.99/7.93 tff(s8_type, type, (
% 11.99/7.93 s8: $i)).
% 11.99/7.93 tff(s7_type, type, (
% 11.99/7.93 s7: $i)).
% 11.99/7.93 tff(s6_type, type, (
% 11.99/7.93 s6: $i)).
% 11.99/7.93 tff(s5_type, type, (
% 11.99/7.93 s5: $i)).
% 11.99/7.93 tff(s4_type, type, (
% 11.99/7.93 s4: $i)).
% 11.99/7.93 tff(s3_type, type, (
% 11.99/7.93 s3: $i)).
% 11.99/7.93 tff(s2_type, type, (
% 11.99/7.93 s2: $i)).
% 11.99/7.93 tff(s1_type, type, (
% 11.99/7.93 s1: $i)).
% 11.99/7.93 tff(s0_type, type, (
% 11.99/7.93 s0: $i)).
% 11.99/7.93 tff(always5_type, type, (
% 11.99/7.93 always5: $i > $o)).
% 11.99/7.93 tff(xuntil7_type, type, (
% 11.99/7.93 xuntil7: $i > $o)).
% 11.99/7.93 tff(until6_type, type, (
% 11.99/7.93 until6: $i > $o)).
% 11.99/7.93 tff(until2p8_type, type, (
% 11.99/7.93 until2p8: $i > $o)).
% 11.99/7.93 tff(xuntil2p9_type, type, (
% 11.99/7.93 xuntil2p9: $i > $o)).
% 11.99/7.93 tff(last_type, type, (
% 11.99/7.93 last: $i > $o)).
% 11.99/7.93 tff(loop_type, type, (
% 11.99/7.93 loop: $o)).
% 11.99/7.93 tff(1,plain,
% 11.99/7.93 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 11.99/7.93 inference(bind,[status(th)],[])).
% 11.99/7.93 tff(2,plain,
% 11.99/7.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.99/7.93 inference(quant_intro,[status(thm)],[1])).
% 11.99/7.93 tff(3,plain,
% 11.99/7.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(4,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound61')).
% 11.99/7.93 tff(5,plain,
% 11.99/7.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[4, 3])).
% 11.99/7.93 tff(6,plain,(
% 11.99/7.93 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.99/7.93 inference(skolemize,[status(sab)],[5])).
% 11.99/7.93 tff(7,plain,
% 11.99/7.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[6, 2])).
% 11.99/7.93 tff(8,plain,
% 11.99/7.93 (succ(s12, s13) <=> succ(s12, s13)),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(9,axiom,(succ(s12, s13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound13')).
% 11.99/7.93 tff(10,plain,
% 11.99/7.93 (succ(s12, s13)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[9, 8])).
% 11.99/7.93 tff(11,plain,
% 11.99/7.93 (((~![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))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(12,plain,
% 11.99/7.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 11.99/7.93 inference(quant_inst,[status(thm)],[])).
% 11.99/7.93 tff(13,plain,
% 11.99/7.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[12, 11])).
% 11.99/7.93 tff(14,plain,
% 11.99/7.93 (trans(s12, s13)),
% 11.99/7.93 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 11.99/7.93 tff(15,plain,
% 11.99/7.93 (^[Y: $i, I0: $i, X: $i] : refl(((~trans(X, Y)) | node3(I0, X, Y)) <=> ((~trans(X, Y)) | node3(I0, X, Y)))),
% 11.99/7.93 inference(bind,[status(th)],[])).
% 11.99/7.93 tff(16,plain,
% 11.99/7.93 (![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))),
% 11.99/7.93 inference(quant_intro,[status(thm)],[15])).
% 11.99/7.93 tff(17,plain,
% 11.99/7.93 (![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))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(18,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')).
% 11.99/7.93 tff(19,plain,
% 11.99/7.93 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[18, 17])).
% 11.99/7.93 tff(20,plain,(
% 11.99/7.93 ![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 11.99/7.93 inference(skolemize,[status(sab)],[19])).
% 11.99/7.93 tff(21,plain,
% 11.99/7.93 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[20, 16])).
% 11.99/7.93 tff(22,plain,
% 11.99/7.93 (((~![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))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(23,plain,
% 11.99/7.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit0, s12, s13))),
% 11.99/7.93 inference(quant_inst,[status(thm)],[])).
% 11.99/7.93 tff(24,plain,
% 11.99/7.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit0, s12, s13)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[23, 22])).
% 11.99/7.93 tff(25,plain,
% 11.99/7.93 (node3(c_bit0, s12, s13)),
% 11.99/7.93 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 11.99/7.93 tff(26,plain,
% 11.99/7.93 (succ(s7, s8) <=> succ(s7, s8)),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(27,axiom,(succ(s7, s8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound8')).
% 11.99/7.93 tff(28,plain,
% 11.99/7.93 (succ(s7, s8)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[27, 26])).
% 11.99/7.93 tff(29,plain,
% 11.99/7.93 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(30,plain,
% 11.99/7.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 11.99/7.93 inference(quant_inst,[status(thm)],[])).
% 11.99/7.93 tff(31,plain,
% 11.99/7.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[30, 29])).
% 11.99/7.93 tff(32,plain,
% 11.99/7.93 (trans(s7, s8)),
% 11.99/7.93 inference(unit_resolution,[status(thm)],[31, 28, 7])).
% 11.99/7.93 tff(33,plain,
% 11.99/7.93 (((~![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))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(34,plain,
% 11.99/7.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit0, s7, s8))),
% 11.99/7.93 inference(quant_inst,[status(thm)],[])).
% 11.99/7.93 tff(35,plain,
% 11.99/7.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit0, s7, s8)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[34, 33])).
% 11.99/7.93 tff(36,plain,
% 11.99/7.93 (node3(c_bit0, s7, s8)),
% 11.99/7.93 inference(unit_resolution,[status(thm)],[35, 21, 32])).
% 11.99/7.93 tff(37,plain,
% 11.99/7.93 (succ(s1, s2) <=> succ(s1, s2)),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(38,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 11.99/7.93 tff(39,plain,
% 11.99/7.93 (succ(s1, s2)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[38, 37])).
% 11.99/7.93 tff(40,plain,
% 11.99/7.93 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(41,plain,
% 11.99/7.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 11.99/7.93 inference(quant_inst,[status(thm)],[])).
% 11.99/7.93 tff(42,plain,
% 11.99/7.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[41, 40])).
% 11.99/7.93 tff(43,plain,
% 11.99/7.93 (trans(s1, s2)),
% 11.99/7.93 inference(unit_resolution,[status(thm)],[42, 39, 7])).
% 11.99/7.93 tff(44,plain,
% 11.99/7.93 (((~![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))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(45,plain,
% 11.99/7.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit0, s1, s2))),
% 11.99/7.93 inference(quant_inst,[status(thm)],[])).
% 11.99/7.93 tff(46,plain,
% 11.99/7.93 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit0, s1, s2)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[45, 44])).
% 11.99/7.93 tff(47,plain,
% 11.99/7.93 (node3(c_bit0, s1, s2)),
% 11.99/7.93 inference(unit_resolution,[status(thm)],[46, 21, 43])).
% 11.99/7.93 tff(48,assumption,(m_counter_cell_v_value(c_bit0, s0)), introduced(assumption)).
% 11.99/7.93 tff(49,plain,
% 11.99/7.93 (^[I0: $i] : refl((~m_counter_cell_v_value(I0, s0)) <=> (~m_counter_cell_v_value(I0, s0)))),
% 11.99/7.93 inference(bind,[status(th)],[])).
% 11.99/7.93 tff(50,plain,
% 11.99/7.93 (![I0: $i] : (~m_counter_cell_v_value(I0, s0)) <=> ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 11.99/7.93 inference(quant_intro,[status(thm)],[49])).
% 11.99/7.93 tff(51,plain,
% 11.99/7.93 (![I0: $i] : (~m_counter_cell_v_value(I0, s0)) <=> ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(52,axiom,(![I0: $i] : (~m_counter_cell_v_value(I0, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_1')).
% 11.99/7.93 tff(53,plain,
% 11.99/7.93 (![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[52, 51])).
% 11.99/7.93 tff(54,plain,(
% 11.99/7.93 ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 11.99/7.93 inference(skolemize,[status(sab)],[53])).
% 11.99/7.93 tff(55,plain,
% 11.99/7.93 (![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[54, 50])).
% 11.99/7.93 tff(56,plain,
% 11.99/7.93 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit0, s0))),
% 11.99/7.93 inference(quant_inst,[status(thm)],[])).
% 11.99/7.93 tff(57,plain,
% 11.99/7.93 ($false),
% 11.99/7.93 inference(unit_resolution,[status(thm)],[56, 55, 48])).
% 11.99/7.93 tff(58,plain,(~m_counter_cell_v_value(c_bit0, s0)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.93 tff(59,plain,
% 11.99/7.93 (^[X: $i] : refl(m_counter_cell_v_carry_in(c_bit0, X) <=> m_counter_cell_v_carry_in(c_bit0, X))),
% 11.99/7.93 inference(bind,[status(th)],[])).
% 11.99/7.93 tff(60,plain,
% 11.99/7.93 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X) <=> ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 11.99/7.93 inference(quant_intro,[status(thm)],[59])).
% 11.99/7.93 tff(61,plain,
% 11.99/7.93 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X) <=> ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(62,axiom,(![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_1')).
% 11.99/7.93 tff(63,plain,
% 11.99/7.93 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[62, 61])).
% 11.99/7.93 tff(64,plain,(
% 11.99/7.93 ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 11.99/7.93 inference(skolemize,[status(sab)],[63])).
% 11.99/7.93 tff(65,plain,
% 11.99/7.93 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[64, 60])).
% 11.99/7.93 tff(66,plain,
% 11.99/7.93 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s0)),
% 11.99/7.93 inference(quant_inst,[status(thm)],[])).
% 11.99/7.93 tff(67,plain,
% 11.99/7.93 (m_counter_cell_v_carry_in(c_bit0, s0)),
% 11.99/7.93 inference(unit_resolution,[status(thm)],[66, 65])).
% 11.99/7.93 tff(68,plain,
% 11.99/7.93 (^[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)))),
% 11.99/7.93 inference(bind,[status(th)],[])).
% 11.99/7.93 tff(69,plain,
% 11.99/7.93 (![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))),
% 11.99/7.93 inference(quant_intro,[status(thm)],[68])).
% 11.99/7.93 tff(70,plain,
% 11.99/7.93 (![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))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(71,plain,
% 11.99/7.93 (^[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))))),
% 11.99/7.93 inference(bind,[status(th)],[])).
% 11.99/7.93 tff(72,plain,
% 11.99/7.93 (![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))),
% 11.99/7.93 inference(quant_intro,[status(thm)],[71])).
% 11.99/7.93 tff(73,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')).
% 11.99/7.93 tff(74,plain,
% 11.99/7.93 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[73, 72])).
% 11.99/7.93 tff(75,plain,
% 11.99/7.93 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[74, 70])).
% 11.99/7.93 tff(76,plain,(
% 11.99/7.93 ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 11.99/7.93 inference(skolemize,[status(sab)],[75])).
% 11.99/7.93 tff(77,plain,
% 11.99/7.93 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 11.99/7.93 inference(modus_ponens,[status(thm)],[76, 69])).
% 11.99/7.93 tff(78,plain,
% 11.99/7.93 (((~![I0: $i, 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, s0) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(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_value(c_bit0, s0) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)))),
% 11.99/7.93 inference(rewrite,[status(thm)],[])).
% 11.99/7.93 tff(79,plain,
% 11.99/7.94 (((~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_value(c_bit0, s0) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(80,plain,
% 11.99/7.94 (((~![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_value(c_bit0, s0) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0))))),
% 11.99/7.94 inference(monotonicity,[status(thm)],[79])).
% 11.99/7.94 tff(81,plain,
% 11.99/7.94 (((~![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_value(c_bit0, s0) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)))),
% 11.99/7.94 inference(transitivity,[status(thm)],[80, 78])).
% 11.99/7.94 tff(82,plain,
% 11.99/7.94 ((~![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))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(83,plain,
% 11.99/7.94 ((~![I0: $i, 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, s0) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[82, 81])).
% 11.99/7.94 tff(84,plain,
% 11.99/7.94 (m_counter_cell_v_value(c_bit0, s0) | (~node1(c_bit0, s0))),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[83, 77, 67])).
% 11.99/7.94 tff(85,plain,
% 11.99/7.94 (~node1(c_bit0, s0)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[84, 58])).
% 11.99/7.94 tff(86,plain,
% 11.99/7.94 (succ(s0, s1) <=> succ(s0, s1)),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(87,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 11.99/7.94 tff(88,plain,
% 11.99/7.94 (succ(s0, s1)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[87, 86])).
% 11.99/7.94 tff(89,plain,
% 11.99/7.94 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(90,plain,
% 11.99/7.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(91,plain,
% 11.99/7.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[90, 89])).
% 11.99/7.94 tff(92,plain,
% 11.99/7.94 (trans(s0, s1)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[91, 88, 7])).
% 11.99/7.94 tff(93,plain,
% 11.99/7.94 (((~![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))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(94,plain,
% 11.99/7.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit0, s0, s1))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(95,plain,
% 11.99/7.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit0, s0, s1)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[94, 93])).
% 11.99/7.94 tff(96,plain,
% 11.99/7.94 (node3(c_bit0, s0, s1)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[95, 21, 92])).
% 11.99/7.94 tff(97,plain,
% 11.99/7.94 (^[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)))),
% 11.99/7.94 inference(bind,[status(th)],[])).
% 11.99/7.94 tff(98,plain,
% 11.99/7.94 (![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))),
% 11.99/7.94 inference(quant_intro,[status(thm)],[97])).
% 11.99/7.94 tff(99,plain,
% 11.99/7.94 (![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))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(100,plain,
% 11.99/7.94 (^[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)))),
% 11.99/7.94 inference(bind,[status(th)],[])).
% 11.99/7.94 tff(101,plain,
% 11.99/7.94 (![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))),
% 11.99/7.94 inference(quant_intro,[status(thm)],[100])).
% 11.99/7.94 tff(102,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')).
% 11.99/7.94 tff(103,plain,
% 11.99/7.94 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[102, 101])).
% 11.99/7.94 tff(104,plain,
% 11.99/7.94 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[103, 99])).
% 11.99/7.94 tff(105,plain,(
% 11.99/7.94 ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 11.99/7.94 inference(skolemize,[status(sab)],[104])).
% 11.99/7.94 tff(106,plain,
% 11.99/7.94 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[105, 98])).
% 11.99/7.94 tff(107,plain,
% 11.99/7.94 (((~![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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(108,plain,
% 11.99/7.94 ((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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(109,plain,
% 11.99/7.94 (((~![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))))),
% 11.99/7.94 inference(monotonicity,[status(thm)],[108])).
% 11.99/7.94 tff(110,plain,
% 11.99/7.94 (((~![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)))),
% 11.99/7.94 inference(transitivity,[status(thm)],[109, 107])).
% 11.99/7.94 tff(111,plain,
% 11.99/7.94 ((~![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))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(112,plain,
% 11.99/7.94 ((~![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))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[111, 110])).
% 11.99/7.94 tff(113,plain,
% 11.99/7.94 (node1(c_bit0, s0) | m_counter_cell_v_value(c_bit0, s1)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[112, 106, 96])).
% 11.99/7.94 tff(114,plain,
% 11.99/7.94 (m_counter_cell_v_value(c_bit0, s1)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[113, 85])).
% 11.99/7.94 tff(115,plain,
% 11.99/7.94 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s1)),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(116,plain,
% 11.99/7.94 (m_counter_cell_v_carry_in(c_bit0, s1)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[115, 65])).
% 11.99/7.94 tff(117,plain,
% 11.99/7.94 (^[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))))),
% 11.99/7.94 inference(bind,[status(th)],[])).
% 11.99/7.94 tff(118,plain,
% 11.99/7.94 (![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)))),
% 11.99/7.94 inference(quant_intro,[status(thm)],[117])).
% 11.99/7.94 tff(119,plain,
% 11.99/7.94 (![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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(120,plain,
% 11.99/7.94 (^[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)))))),
% 11.99/7.94 inference(bind,[status(th)],[])).
% 11.99/7.94 tff(121,plain,
% 11.99/7.94 (![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)))),
% 11.99/7.94 inference(quant_intro,[status(thm)],[120])).
% 11.99/7.94 tff(122,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')).
% 11.99/7.94 tff(123,plain,
% 11.99/7.94 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[122, 121])).
% 11.99/7.94 tff(124,plain,
% 11.99/7.94 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[123, 119])).
% 11.99/7.94 tff(125,plain,(
% 11.99/7.94 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 11.99/7.94 inference(skolemize,[status(sab)],[124])).
% 11.99/7.94 tff(126,plain,
% 11.99/7.94 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[125, 118])).
% 11.99/7.94 tff(127,plain,
% 11.99/7.94 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(128,plain,
% 11.99/7.94 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(129,plain,
% 11.99/7.94 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[128, 127])).
% 11.99/7.94 tff(130,plain,
% 11.99/7.94 ((~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1))),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[129, 126, 116])).
% 11.99/7.94 tff(131,plain,
% 11.99/7.94 (~node2(c_bit0, s1)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[130, 114])).
% 11.99/7.94 tff(132,plain,
% 11.99/7.94 (^[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))))),
% 11.99/7.94 inference(bind,[status(th)],[])).
% 11.99/7.94 tff(133,plain,
% 11.99/7.94 (![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)))),
% 11.99/7.94 inference(quant_intro,[status(thm)],[132])).
% 11.99/7.94 tff(134,plain,
% 11.99/7.94 (![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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(135,plain,
% 11.99/7.94 (^[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))))),
% 11.99/7.94 inference(bind,[status(th)],[])).
% 11.99/7.94 tff(136,plain,
% 11.99/7.94 (![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)))),
% 11.99/7.94 inference(quant_intro,[status(thm)],[135])).
% 11.99/7.94 tff(137,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')).
% 11.99/7.94 tff(138,plain,
% 11.99/7.94 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[137, 136])).
% 11.99/7.94 tff(139,plain,
% 11.99/7.94 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[138, 134])).
% 11.99/7.94 tff(140,plain,(
% 11.99/7.94 ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 11.99/7.94 inference(skolemize,[status(sab)],[139])).
% 11.99/7.94 tff(141,plain,
% 11.99/7.94 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[140, 133])).
% 11.99/7.94 tff(142,plain,
% 11.99/7.94 (((~![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, 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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(143,plain,
% 11.99/7.94 ((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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(144,plain,
% 11.99/7.94 (((~![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))))),
% 11.99/7.94 inference(monotonicity,[status(thm)],[143])).
% 11.99/7.94 tff(145,plain,
% 11.99/7.94 (((~![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)))),
% 11.99/7.94 inference(transitivity,[status(thm)],[144, 142])).
% 11.99/7.94 tff(146,plain,
% 11.99/7.94 ((~![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)))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(147,plain,
% 11.99/7.94 ((~![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, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[146, 145])).
% 11.99/7.94 tff(148,plain,
% 11.99/7.94 (~m_counter_cell_v_value(c_bit0, s2)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[147, 141, 131, 47])).
% 11.99/7.94 tff(149,plain,
% 11.99/7.94 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s2)),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(150,plain,
% 11.99/7.94 (m_counter_cell_v_carry_in(c_bit0, s2)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[149, 65])).
% 11.99/7.94 tff(151,plain,
% 11.99/7.94 (((~![I0: $i, 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, s2) | (~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(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))) | m_counter_cell_v_value(c_bit0, s2) | (~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(152,plain,
% 11.99/7.94 (((~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2)) <=> (m_counter_cell_v_value(c_bit0, s2) | (~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(153,plain,
% 11.99/7.94 (((~![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))) | (m_counter_cell_v_value(c_bit0, s2) | (~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2))))),
% 11.99/7.94 inference(monotonicity,[status(thm)],[152])).
% 11.99/7.94 tff(154,plain,
% 11.99/7.94 (((~![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))) | m_counter_cell_v_value(c_bit0, s2) | (~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)))),
% 11.99/7.94 inference(transitivity,[status(thm)],[153, 151])).
% 11.99/7.94 tff(155,plain,
% 11.99/7.94 ((~![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))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(156,plain,
% 11.99/7.94 ((~![I0: $i, 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, s2) | (~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[155, 154])).
% 11.99/7.94 tff(157,plain,
% 11.99/7.94 (m_counter_cell_v_value(c_bit0, s2) | (~node1(c_bit0, s2))),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[156, 77, 150])).
% 11.99/7.94 tff(158,plain,
% 11.99/7.94 (~node1(c_bit0, s2)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[157, 148])).
% 11.99/7.94 tff(159,plain,
% 11.99/7.94 (succ(s2, s3) <=> succ(s2, s3)),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(160,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 11.99/7.94 tff(161,plain,
% 11.99/7.94 (succ(s2, s3)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[160, 159])).
% 11.99/7.94 tff(162,plain,
% 11.99/7.94 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(163,plain,
% 11.99/7.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(164,plain,
% 11.99/7.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[163, 162])).
% 11.99/7.94 tff(165,plain,
% 11.99/7.94 (trans(s2, s3)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[164, 161, 7])).
% 11.99/7.94 tff(166,plain,
% 11.99/7.94 (((~![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))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(167,plain,
% 11.99/7.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit0, s2, s3))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(168,plain,
% 11.99/7.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit0, s2, s3)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[167, 166])).
% 11.99/7.94 tff(169,plain,
% 11.99/7.94 (node3(c_bit0, s2, s3)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[168, 21, 165])).
% 11.99/7.94 tff(170,plain,
% 11.99/7.94 (((~![Y: $i, 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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(171,plain,
% 11.99/7.94 ((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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(172,plain,
% 11.99/7.94 (((~![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))))),
% 11.99/7.94 inference(monotonicity,[status(thm)],[171])).
% 11.99/7.94 tff(173,plain,
% 11.99/7.94 (((~![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)))),
% 11.99/7.94 inference(transitivity,[status(thm)],[172, 170])).
% 11.99/7.94 tff(174,plain,
% 11.99/7.94 ((~![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))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(175,plain,
% 11.99/7.94 ((~![Y: $i, 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))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[174, 173])).
% 11.99/7.94 tff(176,plain,
% 11.99/7.94 (m_counter_cell_v_value(c_bit0, s3) | node1(c_bit0, s2)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[175, 106, 169])).
% 11.99/7.94 tff(177,plain,
% 11.99/7.94 (m_counter_cell_v_value(c_bit0, s3)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[176, 158])).
% 11.99/7.94 tff(178,plain,
% 11.99/7.94 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s3)),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(179,plain,
% 11.99/7.94 (m_counter_cell_v_carry_in(c_bit0, s3)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[178, 65])).
% 11.99/7.94 tff(180,plain,
% 11.99/7.94 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(181,plain,
% 11.99/7.94 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(182,plain,
% 11.99/7.94 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[181, 180])).
% 11.99/7.94 tff(183,plain,
% 11.99/7.94 ((~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3))),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[182, 126, 179])).
% 11.99/7.94 tff(184,plain,
% 11.99/7.94 (~node2(c_bit0, s3)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[183, 177])).
% 11.99/7.94 tff(185,plain,
% 11.99/7.94 (succ(s3, s4) <=> succ(s3, s4)),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(186,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 11.99/7.94 tff(187,plain,
% 11.99/7.94 (succ(s3, s4)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[186, 185])).
% 11.99/7.94 tff(188,plain,
% 11.99/7.94 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(189,plain,
% 11.99/7.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(190,plain,
% 11.99/7.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[189, 188])).
% 11.99/7.94 tff(191,plain,
% 11.99/7.94 (trans(s3, s4)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[190, 187, 7])).
% 11.99/7.94 tff(192,plain,
% 11.99/7.94 (((~![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))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(193,plain,
% 11.99/7.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit0, s3, s4))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(194,plain,
% 11.99/7.94 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit0, s3, s4)),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[193, 192])).
% 11.99/7.94 tff(195,plain,
% 11.99/7.94 (node3(c_bit0, s3, s4)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[194, 21, 191])).
% 11.99/7.94 tff(196,plain,
% 11.99/7.94 (((~![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, s4)) | node2(c_bit0, s3) | (~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)))) | (~m_counter_cell_v_value(c_bit0, s4)) | node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(197,plain,
% 11.99/7.94 ((node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)) | (~m_counter_cell_v_value(c_bit0, s4))) <=> ((~m_counter_cell_v_value(c_bit0, s4)) | node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(198,plain,
% 11.99/7.94 (((~![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)))) | ((~m_counter_cell_v_value(c_bit0, s4)) | node2(c_bit0, s3) | (~node3(c_bit0, s3, s4))))),
% 11.99/7.94 inference(monotonicity,[status(thm)],[197])).
% 11.99/7.94 tff(199,plain,
% 11.99/7.94 (((~![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)))) | (~m_counter_cell_v_value(c_bit0, s4)) | node2(c_bit0, s3) | (~node3(c_bit0, s3, s4)))),
% 11.99/7.94 inference(transitivity,[status(thm)],[198, 196])).
% 11.99/7.94 tff(200,plain,
% 11.99/7.94 ((~![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)))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(201,plain,
% 11.99/7.94 ((~![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, s4)) | node2(c_bit0, s3) | (~node3(c_bit0, s3, s4))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[200, 199])).
% 11.99/7.94 tff(202,plain,
% 11.99/7.94 ((~m_counter_cell_v_value(c_bit0, s4)) | node2(c_bit0, s3)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[201, 141, 195])).
% 11.99/7.94 tff(203,plain,
% 11.99/7.94 (~m_counter_cell_v_value(c_bit0, s4)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[202, 184])).
% 11.99/7.94 tff(204,plain,
% 11.99/7.94 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s4)),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(205,plain,
% 11.99/7.94 (m_counter_cell_v_carry_in(c_bit0, s4)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[204, 65])).
% 11.99/7.94 tff(206,plain,
% 11.99/7.94 (((~![I0: $i, 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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(207,plain,
% 11.99/7.94 (((~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)))),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.94 tff(208,plain,
% 11.99/7.94 (((~![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))))),
% 11.99/7.94 inference(monotonicity,[status(thm)],[207])).
% 11.99/7.94 tff(209,plain,
% 11.99/7.94 (((~![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)))),
% 11.99/7.94 inference(transitivity,[status(thm)],[208, 206])).
% 11.99/7.94 tff(210,plain,
% 11.99/7.94 ((~![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))),
% 11.99/7.94 inference(quant_inst,[status(thm)],[])).
% 11.99/7.94 tff(211,plain,
% 11.99/7.94 ((~![I0: $i, 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))),
% 11.99/7.94 inference(modus_ponens,[status(thm)],[210, 209])).
% 11.99/7.94 tff(212,plain,
% 11.99/7.94 (m_counter_cell_v_value(c_bit0, s4) | (~node1(c_bit0, s4))),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[211, 77, 205])).
% 11.99/7.94 tff(213,plain,
% 11.99/7.94 (~node1(c_bit0, s4)),
% 11.99/7.94 inference(unit_resolution,[status(thm)],[212, 203])).
% 11.99/7.94 tff(214,plain,
% 11.99/7.94 (succ(s4, s5) <=> succ(s4, s5)),
% 11.99/7.94 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(215,axiom,(succ(s4, s5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 11.99/7.95 tff(216,plain,
% 11.99/7.95 (succ(s4, s5)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[215, 214])).
% 11.99/7.95 tff(217,plain,
% 11.99/7.95 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(218,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(219,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[218, 217])).
% 11.99/7.95 tff(220,plain,
% 11.99/7.95 (trans(s4, s5)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[219, 216, 7])).
% 11.99/7.95 tff(221,plain,
% 11.99/7.95 (((~![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))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(222,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit0, s4, s5))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(223,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit0, s4, s5)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[222, 221])).
% 11.99/7.95 tff(224,plain,
% 11.99/7.95 (node3(c_bit0, s4, s5)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[223, 21, 220])).
% 11.99/7.95 tff(225,plain,
% 11.99/7.95 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | m_counter_cell_v_value(c_bit0, s5) | (~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))) | node1(c_bit0, s4) | m_counter_cell_v_value(c_bit0, s5) | (~node3(c_bit0, s4, s5)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(226,plain,
% 11.99/7.95 ((node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5)) <=> (node1(c_bit0, s4) | m_counter_cell_v_value(c_bit0, s5) | (~node3(c_bit0, s4, s5)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(227,plain,
% 11.99/7.95 (((~![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))) | (node1(c_bit0, s4) | m_counter_cell_v_value(c_bit0, s5) | (~node3(c_bit0, s4, s5))))),
% 11.99/7.95 inference(monotonicity,[status(thm)],[226])).
% 11.99/7.95 tff(228,plain,
% 11.99/7.95 (((~![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))) | node1(c_bit0, s4) | m_counter_cell_v_value(c_bit0, s5) | (~node3(c_bit0, s4, s5)))),
% 11.99/7.95 inference(transitivity,[status(thm)],[227, 225])).
% 11.99/7.95 tff(229,plain,
% 11.99/7.95 ((~![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))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(230,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s4) | m_counter_cell_v_value(c_bit0, s5) | (~node3(c_bit0, s4, s5))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[229, 228])).
% 11.99/7.95 tff(231,plain,
% 11.99/7.95 (node1(c_bit0, s4) | m_counter_cell_v_value(c_bit0, s5)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[230, 106, 224])).
% 11.99/7.95 tff(232,plain,
% 11.99/7.95 (m_counter_cell_v_value(c_bit0, s5)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[231, 213])).
% 11.99/7.95 tff(233,plain,
% 11.99/7.95 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s5)),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(234,plain,
% 11.99/7.95 (m_counter_cell_v_carry_in(c_bit0, s5)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[233, 65])).
% 11.99/7.95 tff(235,plain,
% 11.99/7.95 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(236,plain,
% 11.99/7.95 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(237,plain,
% 11.99/7.95 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[236, 235])).
% 11.99/7.95 tff(238,plain,
% 11.99/7.95 ((~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5))),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[237, 126, 234])).
% 11.99/7.95 tff(239,plain,
% 11.99/7.95 (~node2(c_bit0, s5)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[238, 232])).
% 11.99/7.95 tff(240,plain,
% 11.99/7.95 (succ(s5, s6) <=> succ(s5, s6)),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(241,axiom,(succ(s5, s6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 11.99/7.95 tff(242,plain,
% 11.99/7.95 (succ(s5, s6)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[241, 240])).
% 11.99/7.95 tff(243,plain,
% 11.99/7.95 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(244,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(245,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[244, 243])).
% 11.99/7.95 tff(246,plain,
% 11.99/7.95 (trans(s5, s6)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[245, 242, 7])).
% 11.99/7.95 tff(247,plain,
% 11.99/7.95 (((~![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))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(248,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit0, s5, s6))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(249,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit0, s5, s6)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[248, 247])).
% 11.99/7.95 tff(250,plain,
% 11.99/7.95 (node3(c_bit0, s5, s6)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[249, 21, 246])).
% 11.99/7.95 tff(251,plain,
% 11.99/7.95 (((~![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, s6)) | node2(c_bit0, s5) | (~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)))) | (~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(252,plain,
% 11.99/7.95 ((node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)) | (~m_counter_cell_v_value(c_bit0, s6))) <=> ((~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(253,plain,
% 11.99/7.95 (((~![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)))) | ((~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6))))),
% 11.99/7.95 inference(monotonicity,[status(thm)],[252])).
% 11.99/7.95 tff(254,plain,
% 11.99/7.95 (((~![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)))) | (~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6)))),
% 11.99/7.95 inference(transitivity,[status(thm)],[253, 251])).
% 11.99/7.95 tff(255,plain,
% 11.99/7.95 ((~![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)))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(256,plain,
% 11.99/7.95 ((~![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, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[255, 254])).
% 11.99/7.95 tff(257,plain,
% 11.99/7.95 ((~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[256, 141, 250])).
% 11.99/7.95 tff(258,plain,
% 11.99/7.95 (~m_counter_cell_v_value(c_bit0, s6)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[257, 239])).
% 11.99/7.95 tff(259,plain,
% 11.99/7.95 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s6)),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(260,plain,
% 11.99/7.95 (m_counter_cell_v_carry_in(c_bit0, s6)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[259, 65])).
% 11.99/7.95 tff(261,plain,
% 11.99/7.95 (((~![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))) | (~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(262,plain,
% 11.99/7.95 ((~![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))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(263,plain,
% 11.99/7.95 ((~![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)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[262, 261])).
% 11.99/7.95 tff(264,plain,
% 11.99/7.95 ((~node1(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[263, 77, 260])).
% 11.99/7.95 tff(265,plain,
% 11.99/7.95 (~node1(c_bit0, s6)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[264, 258])).
% 11.99/7.95 tff(266,plain,
% 11.99/7.95 (succ(s6, s7) <=> succ(s6, s7)),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(267,axiom,(succ(s6, s7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 11.99/7.95 tff(268,plain,
% 11.99/7.95 (succ(s6, s7)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[267, 266])).
% 11.99/7.95 tff(269,plain,
% 11.99/7.95 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(270,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(271,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[270, 269])).
% 11.99/7.95 tff(272,plain,
% 11.99/7.95 (trans(s6, s7)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[271, 268, 7])).
% 11.99/7.95 tff(273,plain,
% 11.99/7.95 (((~![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))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(274,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit0, s6, s7))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(275,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit0, s6, s7)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[274, 273])).
% 11.99/7.95 tff(276,plain,
% 11.99/7.95 (node3(c_bit0, s6, s7)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[275, 21, 272])).
% 11.99/7.95 tff(277,plain,
% 11.99/7.95 (((~![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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(278,plain,
% 11.99/7.95 ((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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(279,plain,
% 11.99/7.95 (((~![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))))),
% 11.99/7.95 inference(monotonicity,[status(thm)],[278])).
% 11.99/7.95 tff(280,plain,
% 11.99/7.95 (((~![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)))),
% 11.99/7.95 inference(transitivity,[status(thm)],[279, 277])).
% 11.99/7.95 tff(281,plain,
% 11.99/7.95 ((~![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))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(282,plain,
% 11.99/7.95 ((~![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))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[281, 280])).
% 11.99/7.95 tff(283,plain,
% 11.99/7.95 (node1(c_bit0, s6) | m_counter_cell_v_value(c_bit0, s7)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[282, 106, 276])).
% 11.99/7.95 tff(284,plain,
% 11.99/7.95 (m_counter_cell_v_value(c_bit0, s7)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[283, 265])).
% 11.99/7.95 tff(285,plain,
% 11.99/7.95 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s7)),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(286,plain,
% 11.99/7.95 (m_counter_cell_v_carry_in(c_bit0, s7)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[285, 65])).
% 11.99/7.95 tff(287,plain,
% 11.99/7.95 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(288,plain,
% 11.99/7.95 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(289,plain,
% 11.99/7.95 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[288, 287])).
% 11.99/7.95 tff(290,plain,
% 11.99/7.95 ((~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7))),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[289, 126, 286])).
% 11.99/7.95 tff(291,plain,
% 11.99/7.95 (~node2(c_bit0, s7)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[290, 284])).
% 11.99/7.95 tff(292,plain,
% 11.99/7.95 (((~![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, 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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(293,plain,
% 11.99/7.95 ((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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(294,plain,
% 11.99/7.95 (((~![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))))),
% 11.99/7.95 inference(monotonicity,[status(thm)],[293])).
% 11.99/7.95 tff(295,plain,
% 11.99/7.95 (((~![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)))),
% 11.99/7.95 inference(transitivity,[status(thm)],[294, 292])).
% 11.99/7.95 tff(296,plain,
% 11.99/7.95 ((~![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)))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(297,plain,
% 11.99/7.95 ((~![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, s8)) | node2(c_bit0, s7) | (~node3(c_bit0, s7, s8))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[296, 295])).
% 11.99/7.95 tff(298,plain,
% 11.99/7.95 (~m_counter_cell_v_value(c_bit0, s8)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[297, 141, 291, 36])).
% 11.99/7.95 tff(299,plain,
% 11.99/7.95 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s8)),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(300,plain,
% 11.99/7.95 (m_counter_cell_v_carry_in(c_bit0, s8)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[299, 65])).
% 11.99/7.95 tff(301,plain,
% 11.99/7.95 (((~![I0: $i, X: $i] : ((~node1(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)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(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)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(302,plain,
% 11.99/7.95 (((~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)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(303,plain,
% 11.99/7.95 (((~![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)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8))))),
% 11.99/7.95 inference(monotonicity,[status(thm)],[302])).
% 11.99/7.95 tff(304,plain,
% 11.99/7.95 (((~![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)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8)))),
% 11.99/7.95 inference(transitivity,[status(thm)],[303, 301])).
% 11.99/7.95 tff(305,plain,
% 11.99/7.95 ((~![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))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(306,plain,
% 11.99/7.95 ((~![I0: $i, X: $i] : ((~node1(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)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[305, 304])).
% 11.99/7.95 tff(307,plain,
% 11.99/7.95 (m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8))),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[306, 77, 300])).
% 11.99/7.95 tff(308,plain,
% 11.99/7.95 (~node1(c_bit0, s8)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[307, 298])).
% 11.99/7.95 tff(309,plain,
% 11.99/7.95 (succ(s8, s9) <=> succ(s8, s9)),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(310,axiom,(succ(s8, s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound9')).
% 11.99/7.95 tff(311,plain,
% 11.99/7.95 (succ(s8, s9)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[310, 309])).
% 11.99/7.95 tff(312,plain,
% 11.99/7.95 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(313,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(314,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[313, 312])).
% 11.99/7.95 tff(315,plain,
% 11.99/7.95 (trans(s8, s9)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[314, 311, 7])).
% 11.99/7.95 tff(316,plain,
% 11.99/7.95 (((~![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))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(317,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit0, s8, s9))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(318,plain,
% 11.99/7.95 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit0, s8, s9)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[317, 316])).
% 11.99/7.95 tff(319,plain,
% 11.99/7.95 (node3(c_bit0, s8, s9)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[318, 21, 315])).
% 11.99/7.95 tff(320,plain,
% 11.99/7.95 (((~![Y: $i, 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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(321,plain,
% 11.99/7.95 ((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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(322,plain,
% 11.99/7.95 (((~![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))))),
% 11.99/7.95 inference(monotonicity,[status(thm)],[321])).
% 11.99/7.95 tff(323,plain,
% 11.99/7.95 (((~![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)))),
% 11.99/7.95 inference(transitivity,[status(thm)],[322, 320])).
% 11.99/7.95 tff(324,plain,
% 11.99/7.95 ((~![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))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(325,plain,
% 11.99/7.95 ((~![Y: $i, 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))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[324, 323])).
% 11.99/7.95 tff(326,plain,
% 11.99/7.95 (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[325, 106, 319])).
% 11.99/7.95 tff(327,plain,
% 11.99/7.95 (m_counter_cell_v_value(c_bit0, s9)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[326, 308])).
% 11.99/7.95 tff(328,plain,
% 11.99/7.95 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s9)),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(329,plain,
% 11.99/7.95 (m_counter_cell_v_carry_in(c_bit0, s9)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[328, 65])).
% 11.99/7.95 tff(330,plain,
% 11.99/7.95 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(331,plain,
% 11.99/7.95 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(332,plain,
% 11.99/7.95 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[331, 330])).
% 11.99/7.95 tff(333,plain,
% 11.99/7.95 ((~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9))),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[332, 126, 329])).
% 11.99/7.95 tff(334,plain,
% 11.99/7.95 (~node2(c_bit0, s9)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[333, 327])).
% 11.99/7.95 tff(335,plain,
% 11.99/7.95 (succ(s9, s10) <=> succ(s9, s10)),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(336,axiom,(succ(s9, s10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound10')).
% 11.99/7.95 tff(337,plain,
% 11.99/7.95 (succ(s9, s10)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[336, 335])).
% 11.99/7.95 tff(338,plain,
% 11.99/7.95 (((~![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))),
% 11.99/7.95 inference(rewrite,[status(thm)],[])).
% 11.99/7.95 tff(339,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 11.99/7.95 inference(quant_inst,[status(thm)],[])).
% 11.99/7.95 tff(340,plain,
% 11.99/7.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 11.99/7.95 inference(modus_ponens,[status(thm)],[339, 338])).
% 11.99/7.95 tff(341,plain,
% 11.99/7.95 (trans(s9, s10)),
% 11.99/7.95 inference(unit_resolution,[status(thm)],[340, 337, 7])).
% 11.99/7.95 tff(342,plain,
% 11.99/7.95 (((~![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))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(343,plain,
% 11.99/7.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit0, s9, s10))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(344,plain,
% 11.99/7.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit0, s9, s10)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[343, 342])).
% 11.99/7.96 tff(345,plain,
% 11.99/7.96 (node3(c_bit0, s9, s10)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[344, 21, 341])).
% 11.99/7.96 tff(346,plain,
% 11.99/7.96 (((~![Y: $i, 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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(347,plain,
% 11.99/7.96 ((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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(348,plain,
% 11.99/7.96 (((~![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))))),
% 11.99/7.96 inference(monotonicity,[status(thm)],[347])).
% 11.99/7.96 tff(349,plain,
% 11.99/7.96 (((~![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)))),
% 11.99/7.96 inference(transitivity,[status(thm)],[348, 346])).
% 11.99/7.96 tff(350,plain,
% 11.99/7.96 ((~![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)))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(351,plain,
% 11.99/7.96 ((~![Y: $i, 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))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[350, 349])).
% 11.99/7.96 tff(352,plain,
% 11.99/7.96 ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[351, 141, 345])).
% 11.99/7.96 tff(353,plain,
% 11.99/7.96 (~m_counter_cell_v_value(c_bit0, s10)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[352, 334])).
% 11.99/7.96 tff(354,plain,
% 11.99/7.96 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s10)),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(355,plain,
% 11.99/7.96 (m_counter_cell_v_carry_in(c_bit0, s10)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[354, 65])).
% 11.99/7.96 tff(356,plain,
% 11.99/7.96 (((~![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_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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(357,plain,
% 11.99/7.96 (((~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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(358,plain,
% 11.99/7.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 11.99/7.96 inference(monotonicity,[status(thm)],[357])).
% 11.99/7.96 tff(359,plain,
% 11.99/7.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 11.99/7.96 inference(transitivity,[status(thm)],[358, 356])).
% 11.99/7.96 tff(360,plain,
% 11.99/7.96 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(361,plain,
% 11.99/7.96 ((~![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_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[360, 359])).
% 11.99/7.96 tff(362,plain,
% 11.99/7.96 (m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[361, 77, 355])).
% 11.99/7.96 tff(363,plain,
% 11.99/7.96 (~node1(c_bit0, s10)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[362, 353])).
% 11.99/7.96 tff(364,plain,
% 11.99/7.96 (succ(s10, s11) <=> succ(s10, s11)),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(365,axiom,(succ(s10, s11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound11')).
% 11.99/7.96 tff(366,plain,
% 11.99/7.96 (succ(s10, s11)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[365, 364])).
% 11.99/7.96 tff(367,plain,
% 11.99/7.96 (((~![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))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(368,plain,
% 11.99/7.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(369,plain,
% 11.99/7.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[368, 367])).
% 11.99/7.96 tff(370,plain,
% 11.99/7.96 (trans(s10, s11)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[369, 366, 7])).
% 11.99/7.96 tff(371,plain,
% 11.99/7.96 (((~![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))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(372,plain,
% 11.99/7.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit0, s10, s11))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(373,plain,
% 11.99/7.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit0, s10, s11)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[372, 371])).
% 11.99/7.96 tff(374,plain,
% 11.99/7.96 (node3(c_bit0, s10, s11)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[373, 21, 370])).
% 11.99/7.96 tff(375,plain,
% 11.99/7.96 (((~![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_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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(376,plain,
% 11.99/7.96 ((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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(377,plain,
% 11.99/7.96 (((~![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))))),
% 11.99/7.96 inference(monotonicity,[status(thm)],[376])).
% 11.99/7.96 tff(378,plain,
% 11.99/7.96 (((~![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)))),
% 11.99/7.96 inference(transitivity,[status(thm)],[377, 375])).
% 11.99/7.96 tff(379,plain,
% 11.99/7.96 ((~![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))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(380,plain,
% 11.99/7.96 ((~![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_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[379, 378])).
% 11.99/7.96 tff(381,plain,
% 11.99/7.96 (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[380, 106, 374])).
% 11.99/7.96 tff(382,plain,
% 11.99/7.96 (m_counter_cell_v_value(c_bit0, s11)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[381, 363])).
% 11.99/7.96 tff(383,plain,
% 11.99/7.96 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s11)),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(384,plain,
% 11.99/7.96 (m_counter_cell_v_carry_in(c_bit0, s11)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[383, 65])).
% 11.99/7.96 tff(385,plain,
% 11.99/7.96 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(386,plain,
% 11.99/7.96 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(387,plain,
% 11.99/7.96 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[386, 385])).
% 11.99/7.96 tff(388,plain,
% 11.99/7.96 ((~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11))),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[387, 126, 384])).
% 11.99/7.96 tff(389,plain,
% 11.99/7.96 (~node2(c_bit0, s11)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[388, 382])).
% 11.99/7.96 tff(390,plain,
% 11.99/7.96 (succ(s11, s12) <=> succ(s11, s12)),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(391,axiom,(succ(s11, s12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound12')).
% 11.99/7.96 tff(392,plain,
% 11.99/7.96 (succ(s11, s12)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[391, 390])).
% 11.99/7.96 tff(393,plain,
% 11.99/7.96 (((~![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))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(394,plain,
% 11.99/7.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(395,plain,
% 11.99/7.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[394, 393])).
% 11.99/7.96 tff(396,plain,
% 11.99/7.96 (trans(s11, s12)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[395, 392, 7])).
% 11.99/7.96 tff(397,plain,
% 11.99/7.96 (((~![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))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(398,plain,
% 11.99/7.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit0, s11, s12))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(399,plain,
% 11.99/7.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit0, s11, s12)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[398, 397])).
% 11.99/7.96 tff(400,plain,
% 11.99/7.96 (node3(c_bit0, s11, s12)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[399, 21, 396])).
% 11.99/7.96 tff(401,plain,
% 11.99/7.96 (((~![Y: $i, 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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(402,plain,
% 11.99/7.96 ((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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(403,plain,
% 11.99/7.96 (((~![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))))),
% 11.99/7.96 inference(monotonicity,[status(thm)],[402])).
% 11.99/7.96 tff(404,plain,
% 11.99/7.96 (((~![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)))),
% 11.99/7.96 inference(transitivity,[status(thm)],[403, 401])).
% 11.99/7.96 tff(405,plain,
% 11.99/7.96 ((~![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)))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(406,plain,
% 11.99/7.96 ((~![Y: $i, 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))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[405, 404])).
% 11.99/7.96 tff(407,plain,
% 11.99/7.96 ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[406, 141, 400])).
% 11.99/7.96 tff(408,plain,
% 11.99/7.96 (~m_counter_cell_v_value(c_bit0, s12)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[407, 389])).
% 11.99/7.96 tff(409,plain,
% 11.99/7.96 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s12)),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(410,plain,
% 11.99/7.96 (m_counter_cell_v_carry_in(c_bit0, s12)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[409, 65])).
% 11.99/7.96 tff(411,plain,
% 11.99/7.96 (((~![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_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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(412,plain,
% 11.99/7.96 (((~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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(413,plain,
% 11.99/7.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 11.99/7.96 inference(monotonicity,[status(thm)],[412])).
% 11.99/7.96 tff(414,plain,
% 11.99/7.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 11.99/7.96 inference(transitivity,[status(thm)],[413, 411])).
% 11.99/7.96 tff(415,plain,
% 11.99/7.96 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(416,plain,
% 11.99/7.96 ((~![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_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[415, 414])).
% 11.99/7.96 tff(417,plain,
% 11.99/7.96 (m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[416, 77, 410])).
% 11.99/7.96 tff(418,plain,
% 11.99/7.96 (~node1(c_bit0, s12)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[417, 408])).
% 11.99/7.96 tff(419,plain,
% 11.99/7.96 (((~![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_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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(420,plain,
% 11.99/7.96 ((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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(421,plain,
% 11.99/7.96 (((~![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))))),
% 11.99/7.96 inference(monotonicity,[status(thm)],[420])).
% 11.99/7.96 tff(422,plain,
% 11.99/7.96 (((~![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)))),
% 11.99/7.96 inference(transitivity,[status(thm)],[421, 419])).
% 11.99/7.96 tff(423,plain,
% 11.99/7.96 ((~![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))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(424,plain,
% 11.99/7.96 ((~![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_bit0, s13) | node1(c_bit0, s12) | (~node3(c_bit0, s12, s13))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[423, 422])).
% 11.99/7.96 tff(425,plain,
% 11.99/7.96 (m_counter_cell_v_value(c_bit0, s13)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[424, 106, 418, 25])).
% 11.99/7.96 tff(426,plain,
% 11.99/7.96 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s13)),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(427,plain,
% 11.99/7.96 (m_counter_cell_v_carry_in(c_bit0, s13)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[426, 65])).
% 11.99/7.96 tff(428,plain,
% 11.99/7.96 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(429,plain,
% 11.99/7.96 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(430,plain,
% 11.99/7.96 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[429, 428])).
% 11.99/7.96 tff(431,plain,
% 11.99/7.96 ((~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13))),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[430, 126, 427])).
% 11.99/7.96 tff(432,plain,
% 11.99/7.96 (~node2(c_bit0, s13)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[431, 425])).
% 11.99/7.96 tff(433,plain,
% 11.99/7.96 (succ(s13, s14) <=> succ(s13, s14)),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(434,axiom,(succ(s13, s14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound14')).
% 11.99/7.96 tff(435,plain,
% 11.99/7.96 (succ(s13, s14)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[434, 433])).
% 11.99/7.96 tff(436,plain,
% 11.99/7.96 (((~![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))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(437,plain,
% 11.99/7.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(438,plain,
% 11.99/7.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[437, 436])).
% 11.99/7.96 tff(439,plain,
% 11.99/7.96 (trans(s13, s14)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[438, 435, 7])).
% 11.99/7.96 tff(440,plain,
% 11.99/7.96 (((~![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))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(441,plain,
% 11.99/7.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit0, s13, s14))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(442,plain,
% 11.99/7.96 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit0, s13, s14)),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[441, 440])).
% 11.99/7.96 tff(443,plain,
% 11.99/7.96 (node3(c_bit0, s13, s14)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[442, 21, 439])).
% 11.99/7.96 tff(444,plain,
% 11.99/7.96 (((~![Y: $i, 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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(445,plain,
% 11.99/7.96 ((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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(446,plain,
% 11.99/7.96 (((~![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))))),
% 11.99/7.96 inference(monotonicity,[status(thm)],[445])).
% 11.99/7.96 tff(447,plain,
% 11.99/7.96 (((~![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)))),
% 11.99/7.96 inference(transitivity,[status(thm)],[446, 444])).
% 11.99/7.96 tff(448,plain,
% 11.99/7.96 ((~![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)))),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(449,plain,
% 11.99/7.96 ((~![Y: $i, 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))),
% 11.99/7.96 inference(modus_ponens,[status(thm)],[448, 447])).
% 11.99/7.96 tff(450,plain,
% 11.99/7.96 ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[449, 141, 443])).
% 11.99/7.96 tff(451,plain,
% 11.99/7.96 (~m_counter_cell_v_value(c_bit0, s14)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[450, 432])).
% 11.99/7.96 tff(452,plain,
% 11.99/7.96 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s14)),
% 11.99/7.96 inference(quant_inst,[status(thm)],[])).
% 11.99/7.96 tff(453,plain,
% 11.99/7.96 (m_counter_cell_v_carry_in(c_bit0, s14)),
% 11.99/7.96 inference(unit_resolution,[status(thm)],[452, 65])).
% 11.99/7.96 tff(454,plain,
% 11.99/7.96 (((~![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_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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(455,plain,
% 11.99/7.96 (((~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)))),
% 11.99/7.96 inference(rewrite,[status(thm)],[])).
% 11.99/7.96 tff(456,plain,
% 11.99/7.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 11.99/7.96 inference(monotonicity,[status(thm)],[455])).
% 11.99/7.96 tff(457,plain,
% 11.99/7.96 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 11.99/7.97 inference(transitivity,[status(thm)],[456, 454])).
% 11.99/7.97 tff(458,plain,
% 11.99/7.97 ((~![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))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(459,plain,
% 11.99/7.97 ((~![I0: $i, X: $i] : ((~node1(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))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[458, 457])).
% 11.99/7.97 tff(460,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[459, 77, 453])).
% 11.99/7.97 tff(461,plain,
% 11.99/7.97 (~node1(c_bit0, s14)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[460, 451])).
% 11.99/7.97 tff(462,plain,
% 11.99/7.97 (succ(s14, s15) <=> succ(s14, s15)),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(463,axiom,(succ(s14, s15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound15')).
% 11.99/7.97 tff(464,plain,
% 11.99/7.97 (succ(s14, s15)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[463, 462])).
% 11.99/7.97 tff(465,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(466,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(467,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[466, 465])).
% 11.99/7.97 tff(468,plain,
% 11.99/7.97 (trans(s14, s15)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[467, 464, 7])).
% 11.99/7.97 tff(469,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(470,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit0, s14, s15))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(471,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit0, s14, s15)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[470, 469])).
% 11.99/7.97 tff(472,plain,
% 11.99/7.97 (node3(c_bit0, s14, s15)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[471, 21, 468])).
% 11.99/7.97 tff(473,plain,
% 11.99/7.97 (((~![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_bit0, s15) | node1(c_bit0, s14) | (~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))) | m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(474,plain,
% 11.99/7.97 ((node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)) | m_counter_cell_v_value(c_bit0, s15)) <=> (m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(475,plain,
% 11.99/7.97 (((~![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))) | (m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15))))),
% 11.99/7.97 inference(monotonicity,[status(thm)],[474])).
% 11.99/7.97 tff(476,plain,
% 11.99/7.97 (((~![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))) | m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15)))),
% 11.99/7.97 inference(transitivity,[status(thm)],[475, 473])).
% 11.99/7.97 tff(477,plain,
% 11.99/7.97 ((~![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))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(478,plain,
% 11.99/7.97 ((~![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_bit0, s15) | node1(c_bit0, s14) | (~node3(c_bit0, s14, s15))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[477, 476])).
% 11.99/7.97 tff(479,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[478, 106, 472])).
% 11.99/7.97 tff(480,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s15)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[479, 461])).
% 11.99/7.97 tff(481,plain,
% 11.99/7.97 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s15)),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(482,plain,
% 11.99/7.97 (m_counter_cell_v_carry_in(c_bit0, s15)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[481, 65])).
% 11.99/7.97 tff(483,plain,
% 11.99/7.97 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(484,plain,
% 11.99/7.97 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(485,plain,
% 11.99/7.97 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[484, 483])).
% 11.99/7.97 tff(486,plain,
% 11.99/7.97 ((~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15))),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[485, 126, 482])).
% 11.99/7.97 tff(487,plain,
% 11.99/7.97 (~node2(c_bit0, s15)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[486, 480])).
% 11.99/7.97 tff(488,plain,
% 11.99/7.97 (succ(s15, s16) <=> succ(s15, s16)),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(489,axiom,(succ(s15, s16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound16')).
% 11.99/7.97 tff(490,plain,
% 11.99/7.97 (succ(s15, s16)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[489, 488])).
% 11.99/7.97 tff(491,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(492,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(493,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[492, 491])).
% 11.99/7.97 tff(494,plain,
% 11.99/7.97 (trans(s15, s16)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[493, 490, 7])).
% 11.99/7.97 tff(495,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(496,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit0, s15, s16))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(497,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit0, s15, s16)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[496, 495])).
% 11.99/7.97 tff(498,plain,
% 11.99/7.97 (node3(c_bit0, s15, s16)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[497, 21, 494])).
% 11.99/7.97 tff(499,plain,
% 11.99/7.97 (((~![Y: $i, 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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(500,plain,
% 11.99/7.97 ((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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(501,plain,
% 11.99/7.97 (((~![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))))),
% 11.99/7.97 inference(monotonicity,[status(thm)],[500])).
% 11.99/7.97 tff(502,plain,
% 11.99/7.97 (((~![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)))),
% 11.99/7.97 inference(transitivity,[status(thm)],[501, 499])).
% 11.99/7.97 tff(503,plain,
% 11.99/7.97 ((~![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)))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(504,plain,
% 11.99/7.97 ((~![Y: $i, 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))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[503, 502])).
% 11.99/7.97 tff(505,plain,
% 11.99/7.97 ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[504, 141, 498])).
% 11.99/7.97 tff(506,plain,
% 11.99/7.97 (~m_counter_cell_v_value(c_bit0, s16)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[505, 487])).
% 11.99/7.97 tff(507,plain,
% 11.99/7.97 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s16)),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(508,plain,
% 11.99/7.97 (m_counter_cell_v_carry_in(c_bit0, s16)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[507, 65])).
% 11.99/7.97 tff(509,plain,
% 11.99/7.97 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(510,plain,
% 11.99/7.97 (((~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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(511,plain,
% 11.99/7.97 (((~![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))))),
% 11.99/7.97 inference(monotonicity,[status(thm)],[510])).
% 11.99/7.97 tff(512,plain,
% 11.99/7.97 (((~![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)))),
% 11.99/7.97 inference(transitivity,[status(thm)],[511, 509])).
% 11.99/7.97 tff(513,plain,
% 11.99/7.97 ((~![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))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(514,plain,
% 11.99/7.97 ((~![I0: $i, X: $i] : ((~node1(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))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[513, 512])).
% 11.99/7.97 tff(515,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[514, 77, 508])).
% 11.99/7.97 tff(516,plain,
% 11.99/7.97 (~node1(c_bit0, s16)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[515, 506])).
% 11.99/7.97 tff(517,plain,
% 11.99/7.97 (succ(s16, s17) <=> succ(s16, s17)),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(518,axiom,(succ(s16, s17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound17')).
% 11.99/7.97 tff(519,plain,
% 11.99/7.97 (succ(s16, s17)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[518, 517])).
% 11.99/7.97 tff(520,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(521,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(522,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[521, 520])).
% 11.99/7.97 tff(523,plain,
% 11.99/7.97 (trans(s16, s17)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[522, 519, 7])).
% 11.99/7.97 tff(524,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(525,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit0, s16, s17))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(526,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit0, s16, s17)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[525, 524])).
% 11.99/7.97 tff(527,plain,
% 11.99/7.97 (node3(c_bit0, s16, s17)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[526, 21, 523])).
% 11.99/7.97 tff(528,plain,
% 11.99/7.97 (((~![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_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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(529,plain,
% 11.99/7.97 ((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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(530,plain,
% 11.99/7.97 (((~![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))))),
% 11.99/7.97 inference(monotonicity,[status(thm)],[529])).
% 11.99/7.97 tff(531,plain,
% 11.99/7.97 (((~![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)))),
% 11.99/7.97 inference(transitivity,[status(thm)],[530, 528])).
% 11.99/7.97 tff(532,plain,
% 11.99/7.97 ((~![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))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(533,plain,
% 11.99/7.97 ((~![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_bit0, s17) | node1(c_bit0, s16) | (~node3(c_bit0, s16, s17))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[532, 531])).
% 11.99/7.97 tff(534,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[533, 106, 527])).
% 11.99/7.97 tff(535,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s17)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[534, 516])).
% 11.99/7.97 tff(536,assumption,(~m_counter_cell_v_carry_in(c_bit0, s17)), introduced(assumption)).
% 11.99/7.97 tff(537,plain,
% 11.99/7.97 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s17)),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(538,plain,
% 11.99/7.97 ($false),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[537, 65, 536])).
% 11.99/7.97 tff(539,plain,(m_counter_cell_v_carry_in(c_bit0, s17)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.97 tff(540,plain,
% 11.99/7.97 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(541,plain,
% 11.99/7.97 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(542,plain,
% 11.99/7.97 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[541, 540])).
% 11.99/7.97 tff(543,plain,
% 11.99/7.97 ((~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17))),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[542, 126, 539])).
% 11.99/7.97 tff(544,plain,
% 11.99/7.97 (~node2(c_bit0, s17)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[543, 535])).
% 11.99/7.97 tff(545,plain,
% 11.99/7.97 (succ(s17, s18) <=> succ(s17, s18)),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(546,axiom,(succ(s17, s18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound18')).
% 11.99/7.97 tff(547,plain,
% 11.99/7.97 (succ(s17, s18)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[546, 545])).
% 11.99/7.97 tff(548,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(549,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(550,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[549, 548])).
% 11.99/7.97 tff(551,plain,
% 11.99/7.97 (trans(s17, s18)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[550, 547, 7])).
% 11.99/7.97 tff(552,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(553,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit0, s17, s18))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(554,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit0, s17, s18)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[553, 552])).
% 11.99/7.97 tff(555,plain,
% 11.99/7.97 (node3(c_bit0, s17, s18)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[554, 21, 551])).
% 11.99/7.97 tff(556,plain,
% 11.99/7.97 (((~![Y: $i, 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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(557,plain,
% 11.99/7.97 ((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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(558,plain,
% 11.99/7.97 (((~![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))))),
% 11.99/7.97 inference(monotonicity,[status(thm)],[557])).
% 11.99/7.97 tff(559,plain,
% 11.99/7.97 (((~![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)))),
% 11.99/7.97 inference(transitivity,[status(thm)],[558, 556])).
% 11.99/7.97 tff(560,plain,
% 11.99/7.97 ((~![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)))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(561,plain,
% 11.99/7.97 ((~![Y: $i, 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))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[560, 559])).
% 11.99/7.97 tff(562,plain,
% 11.99/7.97 ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[561, 141, 555])).
% 11.99/7.97 tff(563,plain,
% 11.99/7.97 (~m_counter_cell_v_value(c_bit0, s18)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[562, 544])).
% 11.99/7.97 tff(564,assumption,(~m_counter_cell_v_carry_in(c_bit0, s18)), introduced(assumption)).
% 11.99/7.97 tff(565,plain,
% 11.99/7.97 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s18)),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(566,plain,
% 11.99/7.97 ($false),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[565, 65, 564])).
% 11.99/7.97 tff(567,plain,(m_counter_cell_v_carry_in(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.97 tff(568,plain,
% 11.99/7.97 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(569,plain,
% 11.99/7.97 (((~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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(570,plain,
% 11.99/7.97 (((~![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))))),
% 11.99/7.97 inference(monotonicity,[status(thm)],[569])).
% 11.99/7.97 tff(571,plain,
% 11.99/7.97 (((~![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)))),
% 11.99/7.97 inference(transitivity,[status(thm)],[570, 568])).
% 11.99/7.97 tff(572,plain,
% 11.99/7.97 ((~![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))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(573,plain,
% 11.99/7.97 ((~![I0: $i, X: $i] : ((~node1(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))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[572, 571])).
% 11.99/7.97 tff(574,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[573, 77, 567])).
% 11.99/7.97 tff(575,plain,
% 11.99/7.97 (~node1(c_bit0, s18)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[574, 563])).
% 11.99/7.97 tff(576,plain,
% 11.99/7.97 (succ(s18, s19) <=> succ(s18, s19)),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(577,axiom,(succ(s18, s19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound19')).
% 11.99/7.97 tff(578,plain,
% 11.99/7.97 (succ(s18, s19)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[577, 576])).
% 11.99/7.97 tff(579,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(580,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(581,plain,
% 11.99/7.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[580, 579])).
% 11.99/7.97 tff(582,plain,
% 11.99/7.97 (trans(s18, s19)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[581, 578, 7])).
% 11.99/7.97 tff(583,plain,
% 11.99/7.97 (((~![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))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(584,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit0, s18, s19))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(585,plain,
% 11.99/7.97 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit0, s18, s19)),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[584, 583])).
% 11.99/7.97 tff(586,plain,
% 11.99/7.97 (node3(c_bit0, s18, s19)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[585, 21, 582])).
% 11.99/7.97 tff(587,plain,
% 11.99/7.97 (((~![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_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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(588,plain,
% 11.99/7.97 ((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)))),
% 11.99/7.97 inference(rewrite,[status(thm)],[])).
% 11.99/7.97 tff(589,plain,
% 11.99/7.97 (((~![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))))),
% 11.99/7.97 inference(monotonicity,[status(thm)],[588])).
% 11.99/7.97 tff(590,plain,
% 11.99/7.97 (((~![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)))),
% 11.99/7.97 inference(transitivity,[status(thm)],[589, 587])).
% 11.99/7.97 tff(591,plain,
% 11.99/7.97 ((~![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))),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(592,plain,
% 11.99/7.97 ((~![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_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19))),
% 11.99/7.97 inference(modus_ponens,[status(thm)],[591, 590])).
% 11.99/7.97 tff(593,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[592, 106, 586])).
% 11.99/7.97 tff(594,plain,
% 11.99/7.97 (m_counter_cell_v_value(c_bit0, s19)),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[593, 575])).
% 11.99/7.97 tff(595,assumption,(~m_counter_cell_v_carry_in(c_bit0, s19)), introduced(assumption)).
% 11.99/7.97 tff(596,plain,
% 11.99/7.97 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s19)),
% 11.99/7.97 inference(quant_inst,[status(thm)],[])).
% 11.99/7.97 tff(597,plain,
% 11.99/7.97 ($false),
% 11.99/7.97 inference(unit_resolution,[status(thm)],[596, 65, 595])).
% 11.99/7.97 tff(598,plain,(m_counter_cell_v_carry_in(c_bit0, s19)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.97 tff(599,plain,
% 11.99/7.97 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(600,plain,
% 11.99/7.98 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(601,plain,
% 11.99/7.98 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[600, 599])).
% 11.99/7.98 tff(602,plain,
% 11.99/7.98 ((~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19))),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[601, 126, 598])).
% 11.99/7.98 tff(603,plain,
% 11.99/7.98 (~node2(c_bit0, s19)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[602, 594])).
% 11.99/7.98 tff(604,plain,
% 11.99/7.98 (succ(s19, s20) <=> succ(s19, s20)),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(605,axiom,(succ(s19, s20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound20')).
% 11.99/7.98 tff(606,plain,
% 11.99/7.98 (succ(s19, s20)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[605, 604])).
% 11.99/7.98 tff(607,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(608,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(609,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[608, 607])).
% 11.99/7.98 tff(610,plain,
% 11.99/7.98 (trans(s19, s20)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[609, 606, 7])).
% 11.99/7.98 tff(611,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(612,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit0, s19, s20))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(613,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit0, s19, s20)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[612, 611])).
% 11.99/7.98 tff(614,plain,
% 11.99/7.98 (node3(c_bit0, s19, s20)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[613, 21, 610])).
% 11.99/7.98 tff(615,plain,
% 11.99/7.98 (((~![Y: $i, 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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(616,plain,
% 11.99/7.98 ((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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(617,plain,
% 11.99/7.98 (((~![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))))),
% 11.99/7.98 inference(monotonicity,[status(thm)],[616])).
% 11.99/7.98 tff(618,plain,
% 11.99/7.98 (((~![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)))),
% 11.99/7.98 inference(transitivity,[status(thm)],[617, 615])).
% 11.99/7.98 tff(619,plain,
% 11.99/7.98 ((~![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)))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(620,plain,
% 11.99/7.98 ((~![Y: $i, 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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[619, 618])).
% 11.99/7.98 tff(621,plain,
% 11.99/7.98 ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[620, 141, 614])).
% 11.99/7.98 tff(622,plain,
% 11.99/7.98 (~m_counter_cell_v_value(c_bit0, s20)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[621, 603])).
% 11.99/7.98 tff(623,assumption,(~m_counter_cell_v_carry_in(c_bit0, s20)), introduced(assumption)).
% 11.99/7.98 tff(624,plain,
% 11.99/7.98 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s20)),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(625,plain,
% 11.99/7.98 ($false),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[624, 65, 623])).
% 11.99/7.98 tff(626,plain,(m_counter_cell_v_carry_in(c_bit0, s20)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.98 tff(627,plain,
% 11.99/7.98 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(628,plain,
% 11.99/7.98 (((~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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(629,plain,
% 11.99/7.98 (((~![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))))),
% 11.99/7.98 inference(monotonicity,[status(thm)],[628])).
% 11.99/7.98 tff(630,plain,
% 11.99/7.98 (((~![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)))),
% 11.99/7.98 inference(transitivity,[status(thm)],[629, 627])).
% 11.99/7.98 tff(631,plain,
% 11.99/7.98 ((~![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))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(632,plain,
% 11.99/7.98 ((~![I0: $i, X: $i] : ((~node1(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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[631, 630])).
% 11.99/7.98 tff(633,plain,
% 11.99/7.98 (m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[632, 77, 626])).
% 11.99/7.98 tff(634,plain,
% 11.99/7.98 (~node1(c_bit0, s20)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[633, 622])).
% 11.99/7.98 tff(635,plain,
% 11.99/7.98 (succ(s20, s21) <=> succ(s20, s21)),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(636,axiom,(succ(s20, s21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound21')).
% 11.99/7.98 tff(637,plain,
% 11.99/7.98 (succ(s20, s21)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[636, 635])).
% 11.99/7.98 tff(638,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(639,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(640,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[639, 638])).
% 11.99/7.98 tff(641,plain,
% 11.99/7.98 (trans(s20, s21)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[640, 637, 7])).
% 11.99/7.98 tff(642,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(643,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit0, s20, s21))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(644,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit0, s20, s21)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[643, 642])).
% 11.99/7.98 tff(645,plain,
% 11.99/7.98 (node3(c_bit0, s20, s21)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[644, 21, 641])).
% 11.99/7.98 tff(646,plain,
% 11.99/7.98 (((~![Y: $i, 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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(647,plain,
% 11.99/7.98 ((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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(648,plain,
% 11.99/7.98 (((~![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))))),
% 11.99/7.98 inference(monotonicity,[status(thm)],[647])).
% 11.99/7.98 tff(649,plain,
% 11.99/7.98 (((~![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)))),
% 11.99/7.98 inference(transitivity,[status(thm)],[648, 646])).
% 11.99/7.98 tff(650,plain,
% 11.99/7.98 ((~![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))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(651,plain,
% 11.99/7.98 ((~![Y: $i, 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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[650, 649])).
% 11.99/7.98 tff(652,plain,
% 11.99/7.98 (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[651, 106, 645])).
% 11.99/7.98 tff(653,plain,
% 11.99/7.98 (m_counter_cell_v_value(c_bit0, s21)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[652, 634])).
% 11.99/7.98 tff(654,assumption,(~m_counter_cell_v_carry_in(c_bit0, s21)), introduced(assumption)).
% 11.99/7.98 tff(655,plain,
% 11.99/7.98 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s21)),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(656,plain,
% 11.99/7.98 ($false),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[655, 65, 654])).
% 11.99/7.98 tff(657,plain,(m_counter_cell_v_carry_in(c_bit0, s21)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.98 tff(658,plain,
% 11.99/7.98 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(659,plain,
% 11.99/7.98 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(660,plain,
% 11.99/7.98 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[659, 658])).
% 11.99/7.98 tff(661,plain,
% 11.99/7.98 ((~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21))),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[660, 126, 657])).
% 11.99/7.98 tff(662,plain,
% 11.99/7.98 (~node2(c_bit0, s21)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[661, 653])).
% 11.99/7.98 tff(663,plain,
% 11.99/7.98 (succ(s21, s22) <=> succ(s21, s22)),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(664,axiom,(succ(s21, s22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound22')).
% 11.99/7.98 tff(665,plain,
% 11.99/7.98 (succ(s21, s22)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[664, 663])).
% 11.99/7.98 tff(666,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(667,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(668,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[667, 666])).
% 11.99/7.98 tff(669,plain,
% 11.99/7.98 (trans(s21, s22)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[668, 665, 7])).
% 11.99/7.98 tff(670,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(671,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit0, s21, s22))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(672,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit0, s21, s22)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[671, 670])).
% 11.99/7.98 tff(673,plain,
% 11.99/7.98 (node3(c_bit0, s21, s22)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[672, 21, 669])).
% 11.99/7.98 tff(674,plain,
% 11.99/7.98 (((~![Y: $i, 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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(675,plain,
% 11.99/7.98 ((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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(676,plain,
% 11.99/7.98 (((~![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))))),
% 11.99/7.98 inference(monotonicity,[status(thm)],[675])).
% 11.99/7.98 tff(677,plain,
% 11.99/7.98 (((~![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)))),
% 11.99/7.98 inference(transitivity,[status(thm)],[676, 674])).
% 11.99/7.98 tff(678,plain,
% 11.99/7.98 ((~![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)))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(679,plain,
% 11.99/7.98 ((~![Y: $i, 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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[678, 677])).
% 11.99/7.98 tff(680,plain,
% 11.99/7.98 ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[679, 141, 673])).
% 11.99/7.98 tff(681,plain,
% 11.99/7.98 (~m_counter_cell_v_value(c_bit0, s22)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[680, 662])).
% 11.99/7.98 tff(682,assumption,(~m_counter_cell_v_carry_in(c_bit0, s22)), introduced(assumption)).
% 11.99/7.98 tff(683,plain,
% 11.99/7.98 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s22)),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(684,plain,
% 11.99/7.98 ($false),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[683, 65, 682])).
% 11.99/7.98 tff(685,plain,(m_counter_cell_v_carry_in(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.98 tff(686,plain,
% 11.99/7.98 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(687,plain,
% 11.99/7.98 (((~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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(688,plain,
% 11.99/7.98 (((~![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))))),
% 11.99/7.98 inference(monotonicity,[status(thm)],[687])).
% 11.99/7.98 tff(689,plain,
% 11.99/7.98 (((~![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)))),
% 11.99/7.98 inference(transitivity,[status(thm)],[688, 686])).
% 11.99/7.98 tff(690,plain,
% 11.99/7.98 ((~![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))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(691,plain,
% 11.99/7.98 ((~![I0: $i, X: $i] : ((~node1(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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[690, 689])).
% 11.99/7.98 tff(692,plain,
% 11.99/7.98 (m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[691, 77, 685])).
% 11.99/7.98 tff(693,plain,
% 11.99/7.98 (~node1(c_bit0, s22)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[692, 681])).
% 11.99/7.98 tff(694,plain,
% 11.99/7.98 (succ(s22, s23) <=> succ(s22, s23)),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(695,axiom,(succ(s22, s23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound23')).
% 11.99/7.98 tff(696,plain,
% 11.99/7.98 (succ(s22, s23)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[695, 694])).
% 11.99/7.98 tff(697,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(698,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(699,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[698, 697])).
% 11.99/7.98 tff(700,plain,
% 11.99/7.98 (trans(s22, s23)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[699, 696, 7])).
% 11.99/7.98 tff(701,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(702,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit0, s22, s23))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(703,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit0, s22, s23)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[702, 701])).
% 11.99/7.98 tff(704,plain,
% 11.99/7.98 (node3(c_bit0, s22, s23)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[703, 21, 700])).
% 11.99/7.98 tff(705,plain,
% 11.99/7.98 (((~![Y: $i, 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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(706,plain,
% 11.99/7.98 ((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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(707,plain,
% 11.99/7.98 (((~![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))))),
% 11.99/7.98 inference(monotonicity,[status(thm)],[706])).
% 11.99/7.98 tff(708,plain,
% 11.99/7.98 (((~![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)))),
% 11.99/7.98 inference(transitivity,[status(thm)],[707, 705])).
% 11.99/7.98 tff(709,plain,
% 11.99/7.98 ((~![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))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(710,plain,
% 11.99/7.98 ((~![Y: $i, 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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[709, 708])).
% 11.99/7.98 tff(711,plain,
% 11.99/7.98 (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[710, 106, 704])).
% 11.99/7.98 tff(712,plain,
% 11.99/7.98 (m_counter_cell_v_value(c_bit0, s23)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[711, 693])).
% 11.99/7.98 tff(713,assumption,(~m_counter_cell_v_carry_in(c_bit0, s23)), introduced(assumption)).
% 11.99/7.98 tff(714,plain,
% 11.99/7.98 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s23)),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(715,plain,
% 11.99/7.98 ($false),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[714, 65, 713])).
% 11.99/7.98 tff(716,plain,(m_counter_cell_v_carry_in(c_bit0, s23)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.98 tff(717,plain,
% 11.99/7.98 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(718,plain,
% 11.99/7.98 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(719,plain,
% 11.99/7.98 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[718, 717])).
% 11.99/7.98 tff(720,plain,
% 11.99/7.98 ((~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23))),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[719, 126, 716])).
% 11.99/7.98 tff(721,plain,
% 11.99/7.98 (~node2(c_bit0, s23)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[720, 712])).
% 11.99/7.98 tff(722,plain,
% 11.99/7.98 (succ(s23, s24) <=> succ(s23, s24)),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(723,axiom,(succ(s23, s24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound24')).
% 11.99/7.98 tff(724,plain,
% 11.99/7.98 (succ(s23, s24)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[723, 722])).
% 11.99/7.98 tff(725,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(726,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(727,plain,
% 11.99/7.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[726, 725])).
% 11.99/7.98 tff(728,plain,
% 11.99/7.98 (trans(s23, s24)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[727, 724, 7])).
% 11.99/7.98 tff(729,plain,
% 11.99/7.98 (((~![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))),
% 11.99/7.98 inference(rewrite,[status(thm)],[])).
% 11.99/7.98 tff(730,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit0, s23, s24))),
% 11.99/7.98 inference(quant_inst,[status(thm)],[])).
% 11.99/7.98 tff(731,plain,
% 11.99/7.98 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit0, s23, s24)),
% 11.99/7.98 inference(modus_ponens,[status(thm)],[730, 729])).
% 11.99/7.98 tff(732,plain,
% 11.99/7.98 (node3(c_bit0, s23, s24)),
% 11.99/7.98 inference(unit_resolution,[status(thm)],[731, 21, 728])).
% 11.99/7.98 tff(733,plain,
% 11.99/7.98 (((~![Y: $i, 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)) | (~node3(c_bit0, s23, s24)) | node2(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, s24)) | (~node3(c_bit0, s23, s24)) | node2(c_bit0, s23))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(734,plain,
% 11.99/7.99 ((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)) | (~node3(c_bit0, s23, s24)) | node2(c_bit0, s23))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(735,plain,
% 11.99/7.99 (((~![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)) | (~node3(c_bit0, s23, s24)) | node2(c_bit0, s23)))),
% 11.99/7.99 inference(monotonicity,[status(thm)],[734])).
% 11.99/7.99 tff(736,plain,
% 11.99/7.99 (((~![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)) | (~node3(c_bit0, s23, s24)) | node2(c_bit0, s23))),
% 11.99/7.99 inference(transitivity,[status(thm)],[735, 733])).
% 11.99/7.99 tff(737,plain,
% 11.99/7.99 ((~![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)))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(738,plain,
% 11.99/7.99 ((~![Y: $i, 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)) | (~node3(c_bit0, s23, s24)) | node2(c_bit0, s23)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[737, 736])).
% 11.99/7.99 tff(739,plain,
% 11.99/7.99 ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[738, 141, 732])).
% 11.99/7.99 tff(740,plain,
% 11.99/7.99 (~m_counter_cell_v_value(c_bit0, s24)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[739, 721])).
% 11.99/7.99 tff(741,assumption,(~m_counter_cell_v_carry_in(c_bit0, s24)), introduced(assumption)).
% 11.99/7.99 tff(742,plain,
% 11.99/7.99 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s24)),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(743,plain,
% 11.99/7.99 ($false),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[742, 65, 741])).
% 11.99/7.99 tff(744,plain,(m_counter_cell_v_carry_in(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.99 tff(745,plain,
% 11.99/7.99 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(746,plain,
% 11.99/7.99 (((~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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(747,plain,
% 11.99/7.99 (((~![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))))),
% 11.99/7.99 inference(monotonicity,[status(thm)],[746])).
% 11.99/7.99 tff(748,plain,
% 11.99/7.99 (((~![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)))),
% 11.99/7.99 inference(transitivity,[status(thm)],[747, 745])).
% 11.99/7.99 tff(749,plain,
% 11.99/7.99 ((~![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))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(750,plain,
% 11.99/7.99 ((~![I0: $i, X: $i] : ((~node1(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))),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[749, 748])).
% 11.99/7.99 tff(751,plain,
% 11.99/7.99 (m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[750, 77, 744])).
% 11.99/7.99 tff(752,plain,
% 11.99/7.99 (~node1(c_bit0, s24)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[751, 740])).
% 11.99/7.99 tff(753,plain,
% 11.99/7.99 (succ(s24, s25) <=> succ(s24, s25)),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(754,axiom,(succ(s24, s25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound25')).
% 11.99/7.99 tff(755,plain,
% 11.99/7.99 (succ(s24, s25)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[754, 753])).
% 11.99/7.99 tff(756,plain,
% 11.99/7.99 (((~![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))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(757,plain,
% 11.99/7.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(758,plain,
% 11.99/7.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[757, 756])).
% 11.99/7.99 tff(759,plain,
% 11.99/7.99 (trans(s24, s25)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[758, 755, 7])).
% 11.99/7.99 tff(760,plain,
% 11.99/7.99 (((~![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))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(761,plain,
% 11.99/7.99 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit0, s24, s25))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(762,plain,
% 11.99/7.99 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit0, s24, s25)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[761, 760])).
% 11.99/7.99 tff(763,plain,
% 11.99/7.99 (node3(c_bit0, s24, s25)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[762, 21, 759])).
% 11.99/7.99 tff(764,plain,
% 11.99/7.99 (((~![Y: $i, 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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(765,plain,
% 11.99/7.99 ((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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(766,plain,
% 11.99/7.99 (((~![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))))),
% 11.99/7.99 inference(monotonicity,[status(thm)],[765])).
% 11.99/7.99 tff(767,plain,
% 11.99/7.99 (((~![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)))),
% 11.99/7.99 inference(transitivity,[status(thm)],[766, 764])).
% 11.99/7.99 tff(768,plain,
% 11.99/7.99 ((~![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))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(769,plain,
% 11.99/7.99 ((~![Y: $i, 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))),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[768, 767])).
% 11.99/7.99 tff(770,plain,
% 11.99/7.99 (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[769, 106, 763])).
% 11.99/7.99 tff(771,plain,
% 11.99/7.99 (m_counter_cell_v_value(c_bit0, s25)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[770, 752])).
% 11.99/7.99 tff(772,assumption,(~m_counter_cell_v_carry_in(c_bit0, s25)), introduced(assumption)).
% 11.99/7.99 tff(773,plain,
% 11.99/7.99 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s25)),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(774,plain,
% 11.99/7.99 ($false),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[773, 65, 772])).
% 11.99/7.99 tff(775,plain,(m_counter_cell_v_carry_in(c_bit0, s25)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.99 tff(776,plain,
% 11.99/7.99 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(777,plain,
% 11.99/7.99 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(778,plain,
% 11.99/7.99 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[777, 776])).
% 11.99/7.99 tff(779,plain,
% 11.99/7.99 ((~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25))),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[778, 126, 775])).
% 11.99/7.99 tff(780,plain,
% 11.99/7.99 (~node2(c_bit0, s25)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[779, 771])).
% 11.99/7.99 tff(781,plain,
% 11.99/7.99 (succ(s25, s26) <=> succ(s25, s26)),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(782,axiom,(succ(s25, s26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound26')).
% 11.99/7.99 tff(783,plain,
% 11.99/7.99 (succ(s25, s26)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[782, 781])).
% 11.99/7.99 tff(784,plain,
% 11.99/7.99 (((~![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))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(785,plain,
% 11.99/7.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(786,plain,
% 11.99/7.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[785, 784])).
% 11.99/7.99 tff(787,plain,
% 11.99/7.99 (trans(s25, s26)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[786, 783, 7])).
% 11.99/7.99 tff(788,plain,
% 11.99/7.99 (((~![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))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(789,plain,
% 11.99/7.99 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit0, s25, s26))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(790,plain,
% 11.99/7.99 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit0, s25, s26)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[789, 788])).
% 11.99/7.99 tff(791,plain,
% 11.99/7.99 (node3(c_bit0, s25, s26)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[790, 21, 787])).
% 11.99/7.99 tff(792,plain,
% 11.99/7.99 (((~![Y: $i, 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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(793,plain,
% 11.99/7.99 ((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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(794,plain,
% 11.99/7.99 (((~![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))))),
% 11.99/7.99 inference(monotonicity,[status(thm)],[793])).
% 11.99/7.99 tff(795,plain,
% 11.99/7.99 (((~![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)))),
% 11.99/7.99 inference(transitivity,[status(thm)],[794, 792])).
% 11.99/7.99 tff(796,plain,
% 11.99/7.99 ((~![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)))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(797,plain,
% 11.99/7.99 ((~![Y: $i, 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))),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[796, 795])).
% 11.99/7.99 tff(798,plain,
% 11.99/7.99 ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[797, 141, 791])).
% 11.99/7.99 tff(799,plain,
% 11.99/7.99 (~m_counter_cell_v_value(c_bit0, s26)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[798, 780])).
% 11.99/7.99 tff(800,assumption,(~m_counter_cell_v_carry_in(c_bit0, s26)), introduced(assumption)).
% 11.99/7.99 tff(801,plain,
% 11.99/7.99 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s26)),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(802,plain,
% 11.99/7.99 ($false),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[801, 65, 800])).
% 11.99/7.99 tff(803,plain,(m_counter_cell_v_carry_in(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.99 tff(804,plain,
% 11.99/7.99 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(805,plain,
% 11.99/7.99 (((~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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(806,plain,
% 11.99/7.99 (((~![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))))),
% 11.99/7.99 inference(monotonicity,[status(thm)],[805])).
% 11.99/7.99 tff(807,plain,
% 11.99/7.99 (((~![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)))),
% 11.99/7.99 inference(transitivity,[status(thm)],[806, 804])).
% 11.99/7.99 tff(808,plain,
% 11.99/7.99 ((~![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))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(809,plain,
% 11.99/7.99 ((~![I0: $i, X: $i] : ((~node1(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))),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[808, 807])).
% 11.99/7.99 tff(810,plain,
% 11.99/7.99 (m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[809, 77, 803])).
% 11.99/7.99 tff(811,plain,
% 11.99/7.99 (~node1(c_bit0, s26)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[810, 799])).
% 11.99/7.99 tff(812,plain,
% 11.99/7.99 (succ(s26, s27) <=> succ(s26, s27)),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(813,axiom,(succ(s26, s27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound27')).
% 11.99/7.99 tff(814,plain,
% 11.99/7.99 (succ(s26, s27)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[813, 812])).
% 11.99/7.99 tff(815,plain,
% 11.99/7.99 (((~![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))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(816,plain,
% 11.99/7.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(817,plain,
% 11.99/7.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[816, 815])).
% 11.99/7.99 tff(818,plain,
% 11.99/7.99 (trans(s26, s27)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[817, 814, 7])).
% 11.99/7.99 tff(819,plain,
% 11.99/7.99 (((~![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))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(820,plain,
% 11.99/7.99 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit0, s26, s27))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(821,plain,
% 11.99/7.99 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit0, s26, s27)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[820, 819])).
% 11.99/7.99 tff(822,plain,
% 11.99/7.99 (node3(c_bit0, s26, s27)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[821, 21, 818])).
% 11.99/7.99 tff(823,plain,
% 11.99/7.99 (((~![Y: $i, 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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(824,plain,
% 11.99/7.99 ((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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(825,plain,
% 11.99/7.99 (((~![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))))),
% 11.99/7.99 inference(monotonicity,[status(thm)],[824])).
% 11.99/7.99 tff(826,plain,
% 11.99/7.99 (((~![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)))),
% 11.99/7.99 inference(transitivity,[status(thm)],[825, 823])).
% 11.99/7.99 tff(827,plain,
% 11.99/7.99 ((~![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))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(828,plain,
% 11.99/7.99 ((~![Y: $i, 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))),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[827, 826])).
% 11.99/7.99 tff(829,plain,
% 11.99/7.99 (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[828, 106, 822])).
% 11.99/7.99 tff(830,plain,
% 11.99/7.99 (m_counter_cell_v_value(c_bit0, s27)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[829, 811])).
% 11.99/7.99 tff(831,assumption,(~m_counter_cell_v_carry_in(c_bit0, s27)), introduced(assumption)).
% 11.99/7.99 tff(832,plain,
% 11.99/7.99 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s27)),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(833,plain,
% 11.99/7.99 ($false),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[832, 65, 831])).
% 11.99/7.99 tff(834,plain,(m_counter_cell_v_carry_in(c_bit0, s27)), inference(lemma,lemma(discharge,[]))).
% 11.99/7.99 tff(835,plain,
% 11.99/7.99 (((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(836,plain,
% 11.99/7.99 ((~![I0: $i, X: $i] : ((~m_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)))),
% 11.99/7.99 inference(quant_inst,[status(thm)],[])).
% 11.99/7.99 tff(837,plain,
% 11.99/7.99 ((~![I0: $i, X: $i] : ((~m_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))),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[836, 835])).
% 11.99/7.99 tff(838,plain,
% 11.99/7.99 ((~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27))),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[837, 126, 834])).
% 11.99/7.99 tff(839,plain,
% 11.99/7.99 (~node2(c_bit0, s27)),
% 11.99/7.99 inference(unit_resolution,[status(thm)],[838, 830])).
% 11.99/7.99 tff(840,plain,
% 11.99/7.99 (succ(s27, s28) <=> succ(s27, s28)),
% 11.99/7.99 inference(rewrite,[status(thm)],[])).
% 11.99/7.99 tff(841,axiom,(succ(s27, s28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound28')).
% 11.99/7.99 tff(842,plain,
% 11.99/7.99 (succ(s27, s28)),
% 11.99/7.99 inference(modus_ponens,[status(thm)],[841, 840])).
% 11.99/7.99 tff(843,plain,
% 11.99/7.99 (((~![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))),
% 12.07/7.99 inference(rewrite,[status(thm)],[])).
% 12.07/7.99 tff(844,plain,
% 12.07/7.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))),
% 12.07/7.99 inference(quant_inst,[status(thm)],[])).
% 12.07/7.99 tff(845,plain,
% 12.07/7.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28)),
% 12.07/7.99 inference(modus_ponens,[status(thm)],[844, 843])).
% 12.07/7.99 tff(846,plain,
% 12.07/7.99 (trans(s27, s28)),
% 12.07/7.99 inference(unit_resolution,[status(thm)],[845, 842, 7])).
% 12.07/7.99 tff(847,plain,
% 12.07/7.99 (((~![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))),
% 12.07/7.99 inference(rewrite,[status(thm)],[])).
% 12.07/7.99 tff(848,plain,
% 12.07/7.99 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit0, s27, s28))),
% 12.07/7.99 inference(quant_inst,[status(thm)],[])).
% 12.07/7.99 tff(849,plain,
% 12.07/7.99 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit0, s27, s28)),
% 12.07/7.99 inference(modus_ponens,[status(thm)],[848, 847])).
% 12.07/7.99 tff(850,plain,
% 12.07/7.99 (node3(c_bit0, s27, s28)),
% 12.07/7.99 inference(unit_resolution,[status(thm)],[849, 21, 846])).
% 12.07/7.99 tff(851,plain,
% 12.07/7.99 (((~![Y: $i, 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)) | (~node3(c_bit0, s27, s28)) | node2(c_bit0, s27))) <=> ((~![Y: $i, 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)) | (~node3(c_bit0, s27, s28)) | node2(c_bit0, s27))),
% 12.07/7.99 inference(rewrite,[status(thm)],[])).
% 12.07/7.99 tff(852,plain,
% 12.07/7.99 ((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)) | (~node3(c_bit0, s27, s28)) | node2(c_bit0, s27))),
% 12.07/7.99 inference(rewrite,[status(thm)],[])).
% 12.07/7.99 tff(853,plain,
% 12.07/7.99 (((~![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)) | (~node3(c_bit0, s27, s28)) | node2(c_bit0, s27)))),
% 12.07/7.99 inference(monotonicity,[status(thm)],[852])).
% 12.07/7.99 tff(854,plain,
% 12.07/7.99 (((~![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)) | (~node3(c_bit0, s27, s28)) | node2(c_bit0, s27))),
% 12.07/7.99 inference(transitivity,[status(thm)],[853, 851])).
% 12.07/7.99 tff(855,plain,
% 12.07/7.99 ((~![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)))),
% 12.07/7.99 inference(quant_inst,[status(thm)],[])).
% 12.07/7.99 tff(856,plain,
% 12.07/7.99 ((~![Y: $i, 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)) | (~node3(c_bit0, s27, s28)) | node2(c_bit0, s27)),
% 12.07/7.99 inference(modus_ponens,[status(thm)],[855, 854])).
% 12.07/7.99 tff(857,plain,
% 12.07/7.99 ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27)),
% 12.07/7.99 inference(unit_resolution,[status(thm)],[856, 141, 850])).
% 12.07/7.99 tff(858,plain,
% 12.07/7.99 (~m_counter_cell_v_value(c_bit0, s28)),
% 12.07/7.99 inference(unit_resolution,[status(thm)],[857, 839])).
% 12.07/7.99 tff(859,assumption,(~m_counter_cell_v_carry_in(c_bit0, s28)), introduced(assumption)).
% 12.07/7.99 tff(860,plain,
% 12.07/7.99 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s28)),
% 12.07/7.99 inference(quant_inst,[status(thm)],[])).
% 12.07/7.99 tff(861,plain,
% 12.07/7.99 ($false),
% 12.07/7.99 inference(unit_resolution,[status(thm)],[860, 65, 859])).
% 12.07/8.00 tff(862,plain,(m_counter_cell_v_carry_in(c_bit0, s28)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.00 tff(863,plain,
% 12.07/8.00 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(864,plain,
% 12.07/8.00 (((~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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(865,plain,
% 12.07/8.00 (((~![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))))),
% 12.07/8.00 inference(monotonicity,[status(thm)],[864])).
% 12.07/8.00 tff(866,plain,
% 12.07/8.00 (((~![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)))),
% 12.07/8.00 inference(transitivity,[status(thm)],[865, 863])).
% 12.07/8.00 tff(867,plain,
% 12.07/8.00 ((~![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))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(868,plain,
% 12.07/8.00 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[867, 866])).
% 12.07/8.00 tff(869,plain,
% 12.07/8.00 (m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[868, 77, 862])).
% 12.07/8.00 tff(870,plain,
% 12.07/8.00 (~node1(c_bit0, s28)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[869, 858])).
% 12.07/8.00 tff(871,plain,
% 12.07/8.00 (succ(s28, s29) <=> succ(s28, s29)),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(872,axiom,(succ(s28, s29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound29')).
% 12.07/8.00 tff(873,plain,
% 12.07/8.00 (succ(s28, s29)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[872, 871])).
% 12.07/8.00 tff(874,plain,
% 12.07/8.00 (((~![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))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(875,plain,
% 12.07/8.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(876,plain,
% 12.07/8.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[875, 874])).
% 12.07/8.00 tff(877,plain,
% 12.07/8.00 (trans(s28, s29)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[876, 873, 7])).
% 12.07/8.00 tff(878,plain,
% 12.07/8.00 (((~![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))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(879,plain,
% 12.07/8.00 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit0, s28, s29))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(880,plain,
% 12.07/8.00 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit0, s28, s29)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[879, 878])).
% 12.07/8.00 tff(881,plain,
% 12.07/8.00 (node3(c_bit0, s28, s29)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[880, 21, 877])).
% 12.07/8.00 tff(882,plain,
% 12.07/8.00 (((~![Y: $i, 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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(883,plain,
% 12.07/8.00 ((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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(884,plain,
% 12.07/8.00 (((~![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))))),
% 12.07/8.00 inference(monotonicity,[status(thm)],[883])).
% 12.07/8.00 tff(885,plain,
% 12.07/8.00 (((~![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)))),
% 12.07/8.00 inference(transitivity,[status(thm)],[884, 882])).
% 12.07/8.00 tff(886,plain,
% 12.07/8.00 ((~![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))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(887,plain,
% 12.07/8.00 ((~![Y: $i, 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))),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[886, 885])).
% 12.07/8.00 tff(888,plain,
% 12.07/8.00 (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[887, 106, 881])).
% 12.07/8.00 tff(889,plain,
% 12.07/8.00 (m_counter_cell_v_value(c_bit0, s29)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[888, 870])).
% 12.07/8.00 tff(890,assumption,(~m_counter_cell_v_carry_in(c_bit0, s29)), introduced(assumption)).
% 12.07/8.00 tff(891,plain,
% 12.07/8.00 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s29)),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(892,plain,
% 12.07/8.00 ($false),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[891, 65, 890])).
% 12.07/8.00 tff(893,plain,(m_counter_cell_v_carry_in(c_bit0, s29)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.00 tff(894,plain,
% 12.07/8.00 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(895,plain,
% 12.07/8.00 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(896,plain,
% 12.07/8.00 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[895, 894])).
% 12.07/8.00 tff(897,plain,
% 12.07/8.00 ((~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29))),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[896, 126, 893])).
% 12.07/8.00 tff(898,plain,
% 12.07/8.00 (~node2(c_bit0, s29)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[897, 889])).
% 12.07/8.00 tff(899,plain,
% 12.07/8.00 (succ(s29, s30) <=> succ(s29, s30)),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(900,axiom,(succ(s29, s30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound30')).
% 12.07/8.00 tff(901,plain,
% 12.07/8.00 (succ(s29, s30)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[900, 899])).
% 12.07/8.00 tff(902,plain,
% 12.07/8.00 (((~![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))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(903,plain,
% 12.07/8.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(904,plain,
% 12.07/8.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[903, 902])).
% 12.07/8.00 tff(905,plain,
% 12.07/8.00 (trans(s29, s30)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[904, 901, 7])).
% 12.07/8.00 tff(906,plain,
% 12.07/8.00 (((~![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))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(907,plain,
% 12.07/8.00 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit0, s29, s30))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(908,plain,
% 12.07/8.00 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit0, s29, s30)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[907, 906])).
% 12.07/8.00 tff(909,plain,
% 12.07/8.00 (node3(c_bit0, s29, s30)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[908, 21, 905])).
% 12.07/8.00 tff(910,plain,
% 12.07/8.00 (((~![Y: $i, 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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(911,plain,
% 12.07/8.00 ((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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(912,plain,
% 12.07/8.00 (((~![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))))),
% 12.07/8.00 inference(monotonicity,[status(thm)],[911])).
% 12.07/8.00 tff(913,plain,
% 12.07/8.00 (((~![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)))),
% 12.07/8.00 inference(transitivity,[status(thm)],[912, 910])).
% 12.07/8.00 tff(914,plain,
% 12.07/8.00 ((~![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)))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(915,plain,
% 12.07/8.00 ((~![Y: $i, 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))),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[914, 913])).
% 12.07/8.00 tff(916,plain,
% 12.07/8.00 ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[915, 141, 909])).
% 12.07/8.00 tff(917,plain,
% 12.07/8.00 (~m_counter_cell_v_value(c_bit0, s30)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[916, 898])).
% 12.07/8.00 tff(918,assumption,(~m_counter_cell_v_carry_in(c_bit0, s30)), introduced(assumption)).
% 12.07/8.00 tff(919,plain,
% 12.07/8.00 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s30)),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(920,plain,
% 12.07/8.00 ($false),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[919, 65, 918])).
% 12.07/8.00 tff(921,plain,(m_counter_cell_v_carry_in(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.00 tff(922,plain,
% 12.07/8.00 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(923,plain,
% 12.07/8.00 (((~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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(924,plain,
% 12.07/8.00 (((~![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))))),
% 12.07/8.00 inference(monotonicity,[status(thm)],[923])).
% 12.07/8.00 tff(925,plain,
% 12.07/8.00 (((~![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)))),
% 12.07/8.00 inference(transitivity,[status(thm)],[924, 922])).
% 12.07/8.00 tff(926,plain,
% 12.07/8.00 ((~![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))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(927,plain,
% 12.07/8.00 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[926, 925])).
% 12.07/8.00 tff(928,plain,
% 12.07/8.00 (m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[927, 77, 921])).
% 12.07/8.00 tff(929,plain,
% 12.07/8.00 (~node1(c_bit0, s30)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[928, 917])).
% 12.07/8.00 tff(930,plain,
% 12.07/8.00 (succ(s30, s31) <=> succ(s30, s31)),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(931,axiom,(succ(s30, s31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound31')).
% 12.07/8.00 tff(932,plain,
% 12.07/8.00 (succ(s30, s31)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[931, 930])).
% 12.07/8.00 tff(933,plain,
% 12.07/8.00 (((~![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))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(934,plain,
% 12.07/8.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(935,plain,
% 12.07/8.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[934, 933])).
% 12.07/8.00 tff(936,plain,
% 12.07/8.00 (trans(s30, s31)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[935, 932, 7])).
% 12.07/8.00 tff(937,plain,
% 12.07/8.00 (((~![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))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(938,plain,
% 12.07/8.00 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit0, s30, s31))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(939,plain,
% 12.07/8.00 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit0, s30, s31)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[938, 937])).
% 12.07/8.00 tff(940,plain,
% 12.07/8.00 (node3(c_bit0, s30, s31)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[939, 21, 936])).
% 12.07/8.00 tff(941,plain,
% 12.07/8.00 (((~![Y: $i, 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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(942,plain,
% 12.07/8.00 ((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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(943,plain,
% 12.07/8.00 (((~![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))))),
% 12.07/8.00 inference(monotonicity,[status(thm)],[942])).
% 12.07/8.00 tff(944,plain,
% 12.07/8.00 (((~![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)))),
% 12.07/8.00 inference(transitivity,[status(thm)],[943, 941])).
% 12.07/8.00 tff(945,plain,
% 12.07/8.00 ((~![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))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(946,plain,
% 12.07/8.00 ((~![Y: $i, 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))),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[945, 944])).
% 12.07/8.00 tff(947,plain,
% 12.07/8.00 (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[946, 106, 940])).
% 12.07/8.00 tff(948,plain,
% 12.07/8.00 (m_counter_cell_v_value(c_bit0, s31)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[947, 929])).
% 12.07/8.00 tff(949,assumption,(~m_counter_cell_v_carry_in(c_bit0, s31)), introduced(assumption)).
% 12.07/8.00 tff(950,plain,
% 12.07/8.00 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s31)),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(951,plain,
% 12.07/8.00 ($false),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[950, 65, 949])).
% 12.07/8.00 tff(952,plain,(m_counter_cell_v_carry_in(c_bit0, s31)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.00 tff(953,plain,
% 12.07/8.00 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(954,plain,
% 12.07/8.00 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(955,plain,
% 12.07/8.00 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[954, 953])).
% 12.07/8.00 tff(956,plain,
% 12.07/8.00 ((~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31))),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[955, 126, 952])).
% 12.07/8.00 tff(957,plain,
% 12.07/8.00 (~node2(c_bit0, s31)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[956, 948])).
% 12.07/8.00 tff(958,plain,
% 12.07/8.00 (succ(s31, s32) <=> succ(s31, s32)),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(959,axiom,(succ(s31, s32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound32')).
% 12.07/8.00 tff(960,plain,
% 12.07/8.00 (succ(s31, s32)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[959, 958])).
% 12.07/8.00 tff(961,plain,
% 12.07/8.00 (((~![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))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(962,plain,
% 12.07/8.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(963,plain,
% 12.07/8.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[962, 961])).
% 12.07/8.00 tff(964,plain,
% 12.07/8.00 (trans(s31, s32)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[963, 960, 7])).
% 12.07/8.00 tff(965,plain,
% 12.07/8.00 (((~![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))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(966,plain,
% 12.07/8.00 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit0, s31, s32))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(967,plain,
% 12.07/8.00 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit0, s31, s32)),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[966, 965])).
% 12.07/8.00 tff(968,plain,
% 12.07/8.00 (node3(c_bit0, s31, s32)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[967, 21, 964])).
% 12.07/8.00 tff(969,plain,
% 12.07/8.00 (((~![Y: $i, 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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(970,plain,
% 12.07/8.00 ((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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(971,plain,
% 12.07/8.00 (((~![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))))),
% 12.07/8.00 inference(monotonicity,[status(thm)],[970])).
% 12.07/8.00 tff(972,plain,
% 12.07/8.00 (((~![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)))),
% 12.07/8.00 inference(transitivity,[status(thm)],[971, 969])).
% 12.07/8.00 tff(973,plain,
% 12.07/8.00 ((~![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)))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(974,plain,
% 12.07/8.00 ((~![Y: $i, 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))),
% 12.07/8.00 inference(modus_ponens,[status(thm)],[973, 972])).
% 12.07/8.00 tff(975,plain,
% 12.07/8.00 ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[974, 141, 968])).
% 12.07/8.00 tff(976,plain,
% 12.07/8.00 (~m_counter_cell_v_value(c_bit0, s32)),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[975, 957])).
% 12.07/8.00 tff(977,assumption,(~m_counter_cell_v_carry_in(c_bit0, s32)), introduced(assumption)).
% 12.07/8.00 tff(978,plain,
% 12.07/8.00 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s32)),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(979,plain,
% 12.07/8.00 ($false),
% 12.07/8.00 inference(unit_resolution,[status(thm)],[978, 65, 977])).
% 12.07/8.00 tff(980,plain,(m_counter_cell_v_carry_in(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.00 tff(981,plain,
% 12.07/8.00 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(982,plain,
% 12.07/8.00 (((~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)))),
% 12.07/8.00 inference(rewrite,[status(thm)],[])).
% 12.07/8.00 tff(983,plain,
% 12.07/8.00 (((~![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))))),
% 12.07/8.00 inference(monotonicity,[status(thm)],[982])).
% 12.07/8.00 tff(984,plain,
% 12.07/8.00 (((~![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)))),
% 12.07/8.00 inference(transitivity,[status(thm)],[983, 981])).
% 12.07/8.00 tff(985,plain,
% 12.07/8.00 ((~![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))),
% 12.07/8.00 inference(quant_inst,[status(thm)],[])).
% 12.07/8.00 tff(986,plain,
% 12.07/8.00 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[985, 984])).
% 12.07/8.01 tff(987,plain,
% 12.07/8.01 (m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[986, 77, 980])).
% 12.07/8.01 tff(988,plain,
% 12.07/8.01 (~node1(c_bit0, s32)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[987, 976])).
% 12.07/8.01 tff(989,plain,
% 12.07/8.01 (succ(s32, s33) <=> succ(s32, s33)),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(990,axiom,(succ(s32, s33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound33')).
% 12.07/8.01 tff(991,plain,
% 12.07/8.01 (succ(s32, s33)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[990, 989])).
% 12.07/8.01 tff(992,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(993,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(994,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[993, 992])).
% 12.07/8.01 tff(995,plain,
% 12.07/8.01 (trans(s32, s33)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[994, 991, 7])).
% 12.07/8.01 tff(996,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(997,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit0, s32, s33))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(998,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit0, s32, s33)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[997, 996])).
% 12.07/8.01 tff(999,plain,
% 12.07/8.01 (node3(c_bit0, s32, s33)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[998, 21, 995])).
% 12.07/8.01 tff(1000,plain,
% 12.07/8.01 (((~![Y: $i, 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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1001,plain,
% 12.07/8.01 ((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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1002,plain,
% 12.07/8.01 (((~![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))))),
% 12.07/8.01 inference(monotonicity,[status(thm)],[1001])).
% 12.07/8.01 tff(1003,plain,
% 12.07/8.01 (((~![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)))),
% 12.07/8.01 inference(transitivity,[status(thm)],[1002, 1000])).
% 12.07/8.01 tff(1004,plain,
% 12.07/8.01 ((~![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))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1005,plain,
% 12.07/8.01 ((~![Y: $i, 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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1004, 1003])).
% 12.07/8.01 tff(1006,plain,
% 12.07/8.01 (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1005, 106, 999])).
% 12.07/8.01 tff(1007,plain,
% 12.07/8.01 (m_counter_cell_v_value(c_bit0, s33)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1006, 988])).
% 12.07/8.01 tff(1008,assumption,(~m_counter_cell_v_carry_in(c_bit0, s33)), introduced(assumption)).
% 12.07/8.01 tff(1009,plain,
% 12.07/8.01 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s33)),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1010,plain,
% 12.07/8.01 ($false),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1009, 65, 1008])).
% 12.07/8.01 tff(1011,plain,(m_counter_cell_v_carry_in(c_bit0, s33)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.01 tff(1012,plain,
% 12.07/8.01 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1013,plain,
% 12.07/8.01 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1014,plain,
% 12.07/8.01 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 12.07/8.01 tff(1015,plain,
% 12.07/8.01 ((~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33))),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1014, 126, 1011])).
% 12.07/8.01 tff(1016,plain,
% 12.07/8.01 (~node2(c_bit0, s33)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1015, 1007])).
% 12.07/8.01 tff(1017,plain,
% 12.07/8.01 (succ(s33, s34) <=> succ(s33, s34)),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1018,axiom,(succ(s33, s34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound34')).
% 12.07/8.01 tff(1019,plain,
% 12.07/8.01 (succ(s33, s34)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1018, 1017])).
% 12.07/8.01 tff(1020,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1021,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1022,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1021, 1020])).
% 12.07/8.01 tff(1023,plain,
% 12.07/8.01 (trans(s33, s34)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1022, 1019, 7])).
% 12.07/8.01 tff(1024,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1025,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit0, s33, s34))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1026,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit0, s33, s34)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1025, 1024])).
% 12.07/8.01 tff(1027,plain,
% 12.07/8.01 (node3(c_bit0, s33, s34)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1026, 21, 1023])).
% 12.07/8.01 tff(1028,plain,
% 12.07/8.01 (((~![Y: $i, 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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1029,plain,
% 12.07/8.01 ((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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1030,plain,
% 12.07/8.01 (((~![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))))),
% 12.07/8.01 inference(monotonicity,[status(thm)],[1029])).
% 12.07/8.01 tff(1031,plain,
% 12.07/8.01 (((~![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)))),
% 12.07/8.01 inference(transitivity,[status(thm)],[1030, 1028])).
% 12.07/8.01 tff(1032,plain,
% 12.07/8.01 ((~![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)))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1033,plain,
% 12.07/8.01 ((~![Y: $i, 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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 12.07/8.01 tff(1034,plain,
% 12.07/8.01 ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1033, 141, 1027])).
% 12.07/8.01 tff(1035,plain,
% 12.07/8.01 (~m_counter_cell_v_value(c_bit0, s34)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1034, 1016])).
% 12.07/8.01 tff(1036,assumption,(~m_counter_cell_v_carry_in(c_bit0, s34)), introduced(assumption)).
% 12.07/8.01 tff(1037,plain,
% 12.07/8.01 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s34)),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1038,plain,
% 12.07/8.01 ($false),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1037, 65, 1036])).
% 12.07/8.01 tff(1039,plain,(m_counter_cell_v_carry_in(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.01 tff(1040,plain,
% 12.07/8.01 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1041,plain,
% 12.07/8.01 (((~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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1042,plain,
% 12.07/8.01 (((~![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))))),
% 12.07/8.01 inference(monotonicity,[status(thm)],[1041])).
% 12.07/8.01 tff(1043,plain,
% 12.07/8.01 (((~![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)))),
% 12.07/8.01 inference(transitivity,[status(thm)],[1042, 1040])).
% 12.07/8.01 tff(1044,plain,
% 12.07/8.01 ((~![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))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1045,plain,
% 12.07/8.01 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 12.07/8.01 tff(1046,plain,
% 12.07/8.01 (m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1045, 77, 1039])).
% 12.07/8.01 tff(1047,plain,
% 12.07/8.01 (~node1(c_bit0, s34)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1046, 1035])).
% 12.07/8.01 tff(1048,plain,
% 12.07/8.01 (succ(s34, s35) <=> succ(s34, s35)),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1049,axiom,(succ(s34, s35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound35')).
% 12.07/8.01 tff(1050,plain,
% 12.07/8.01 (succ(s34, s35)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 12.07/8.01 tff(1051,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1052,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1053,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1052, 1051])).
% 12.07/8.01 tff(1054,plain,
% 12.07/8.01 (trans(s34, s35)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1053, 1050, 7])).
% 12.07/8.01 tff(1055,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1056,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit0, s34, s35))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1057,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit0, s34, s35)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1056, 1055])).
% 12.07/8.01 tff(1058,plain,
% 12.07/8.01 (node3(c_bit0, s34, s35)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1057, 21, 1054])).
% 12.07/8.01 tff(1059,plain,
% 12.07/8.01 (((~![Y: $i, 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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1060,plain,
% 12.07/8.01 ((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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1061,plain,
% 12.07/8.01 (((~![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))))),
% 12.07/8.01 inference(monotonicity,[status(thm)],[1060])).
% 12.07/8.01 tff(1062,plain,
% 12.07/8.01 (((~![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)))),
% 12.07/8.01 inference(transitivity,[status(thm)],[1061, 1059])).
% 12.07/8.01 tff(1063,plain,
% 12.07/8.01 ((~![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))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1064,plain,
% 12.07/8.01 ((~![Y: $i, 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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 12.07/8.01 tff(1065,plain,
% 12.07/8.01 (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1064, 106, 1058])).
% 12.07/8.01 tff(1066,plain,
% 12.07/8.01 (m_counter_cell_v_value(c_bit0, s35)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1065, 1047])).
% 12.07/8.01 tff(1067,assumption,(~m_counter_cell_v_carry_in(c_bit0, s35)), introduced(assumption)).
% 12.07/8.01 tff(1068,plain,
% 12.07/8.01 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s35)),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1069,plain,
% 12.07/8.01 ($false),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1068, 65, 1067])).
% 12.07/8.01 tff(1070,plain,(m_counter_cell_v_carry_in(c_bit0, s35)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.01 tff(1071,plain,
% 12.07/8.01 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1072,plain,
% 12.07/8.01 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1073,plain,
% 12.07/8.01 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 12.07/8.01 tff(1074,plain,
% 12.07/8.01 ((~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35))),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1073, 126, 1070])).
% 12.07/8.01 tff(1075,plain,
% 12.07/8.01 (~node2(c_bit0, s35)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1074, 1066])).
% 12.07/8.01 tff(1076,plain,
% 12.07/8.01 (succ(s35, s36) <=> succ(s35, s36)),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1077,axiom,(succ(s35, s36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound36')).
% 12.07/8.01 tff(1078,plain,
% 12.07/8.01 (succ(s35, s36)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 12.07/8.01 tff(1079,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1080,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1081,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 12.07/8.01 tff(1082,plain,
% 12.07/8.01 (trans(s35, s36)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1081, 1078, 7])).
% 12.07/8.01 tff(1083,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1084,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit0, s35, s36))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1085,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit0, s35, s36)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1084, 1083])).
% 12.07/8.01 tff(1086,plain,
% 12.07/8.01 (node3(c_bit0, s35, s36)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1085, 21, 1082])).
% 12.07/8.01 tff(1087,plain,
% 12.07/8.01 (((~![Y: $i, 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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1088,plain,
% 12.07/8.01 ((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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1089,plain,
% 12.07/8.01 (((~![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))))),
% 12.07/8.01 inference(monotonicity,[status(thm)],[1088])).
% 12.07/8.01 tff(1090,plain,
% 12.07/8.01 (((~![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)))),
% 12.07/8.01 inference(transitivity,[status(thm)],[1089, 1087])).
% 12.07/8.01 tff(1091,plain,
% 12.07/8.01 ((~![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)))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1092,plain,
% 12.07/8.01 ((~![Y: $i, 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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 12.07/8.01 tff(1093,plain,
% 12.07/8.01 ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1092, 141, 1086])).
% 12.07/8.01 tff(1094,plain,
% 12.07/8.01 (~m_counter_cell_v_value(c_bit0, s36)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1093, 1075])).
% 12.07/8.01 tff(1095,assumption,(~m_counter_cell_v_carry_in(c_bit0, s36)), introduced(assumption)).
% 12.07/8.01 tff(1096,plain,
% 12.07/8.01 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s36)),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1097,plain,
% 12.07/8.01 ($false),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1096, 65, 1095])).
% 12.07/8.01 tff(1098,plain,(m_counter_cell_v_carry_in(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.01 tff(1099,plain,
% 12.07/8.01 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1100,plain,
% 12.07/8.01 (((~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)))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1101,plain,
% 12.07/8.01 (((~![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))))),
% 12.07/8.01 inference(monotonicity,[status(thm)],[1100])).
% 12.07/8.01 tff(1102,plain,
% 12.07/8.01 (((~![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)))),
% 12.07/8.01 inference(transitivity,[status(thm)],[1101, 1099])).
% 12.07/8.01 tff(1103,plain,
% 12.07/8.01 ((~![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))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1104,plain,
% 12.07/8.01 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 12.07/8.01 tff(1105,plain,
% 12.07/8.01 (m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1104, 77, 1098])).
% 12.07/8.01 tff(1106,plain,
% 12.07/8.01 (~node1(c_bit0, s36)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1105, 1094])).
% 12.07/8.01 tff(1107,plain,
% 12.07/8.01 (succ(s36, s37) <=> succ(s36, s37)),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1108,axiom,(succ(s36, s37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound37')).
% 12.07/8.01 tff(1109,plain,
% 12.07/8.01 (succ(s36, s37)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 12.07/8.01 tff(1110,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1111,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1112,plain,
% 12.07/8.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1111, 1110])).
% 12.07/8.01 tff(1113,plain,
% 12.07/8.01 (trans(s36, s37)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1112, 1109, 7])).
% 12.07/8.01 tff(1114,plain,
% 12.07/8.01 (((~![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))),
% 12.07/8.01 inference(rewrite,[status(thm)],[])).
% 12.07/8.01 tff(1115,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit0, s36, s37))),
% 12.07/8.01 inference(quant_inst,[status(thm)],[])).
% 12.07/8.01 tff(1116,plain,
% 12.07/8.01 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit0, s36, s37)),
% 12.07/8.01 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 12.07/8.01 tff(1117,plain,
% 12.07/8.01 (node3(c_bit0, s36, s37)),
% 12.07/8.01 inference(unit_resolution,[status(thm)],[1116, 21, 1113])).
% 12.07/8.01 tff(1118,plain,
% 12.07/8.01 (((~![Y: $i, 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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1119,plain,
% 12.07/8.02 ((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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1120,plain,
% 12.07/8.02 (((~![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))))),
% 12.07/8.02 inference(monotonicity,[status(thm)],[1119])).
% 12.07/8.02 tff(1121,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.02 inference(transitivity,[status(thm)],[1120, 1118])).
% 12.07/8.02 tff(1122,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1123,plain,
% 12.07/8.02 ((~![Y: $i, 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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 12.07/8.02 tff(1124,plain,
% 12.07/8.02 (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1123, 106, 1117])).
% 12.07/8.02 tff(1125,plain,
% 12.07/8.02 (m_counter_cell_v_value(c_bit0, s37)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1124, 1106])).
% 12.07/8.02 tff(1126,assumption,(~m_counter_cell_v_carry_in(c_bit0, s37)), introduced(assumption)).
% 12.07/8.02 tff(1127,plain,
% 12.07/8.02 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s37)),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1128,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1127, 65, 1126])).
% 12.07/8.02 tff(1129,plain,(m_counter_cell_v_carry_in(c_bit0, s37)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1130,plain,
% 12.07/8.02 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1131,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1132,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1131, 1130])).
% 12.07/8.02 tff(1133,plain,
% 12.07/8.02 ((~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37))),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1132, 126, 1129])).
% 12.07/8.02 tff(1134,plain,
% 12.07/8.02 (~node2(c_bit0, s37)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1133, 1125])).
% 12.07/8.02 tff(1135,plain,
% 12.07/8.02 (succ(s37, s38) <=> succ(s37, s38)),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1136,axiom,(succ(s37, s38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound38')).
% 12.07/8.02 tff(1137,plain,
% 12.07/8.02 (succ(s37, s38)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1136, 1135])).
% 12.07/8.02 tff(1138,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1139,plain,
% 12.07/8.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1140,plain,
% 12.07/8.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1139, 1138])).
% 12.07/8.02 tff(1141,plain,
% 12.07/8.02 (trans(s37, s38)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1140, 1137, 7])).
% 12.07/8.02 tff(1142,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1143,plain,
% 12.07/8.02 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit0, s37, s38))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1144,plain,
% 12.07/8.02 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit0, s37, s38)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 12.07/8.02 tff(1145,plain,
% 12.07/8.02 (node3(c_bit0, s37, s38)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1144, 21, 1141])).
% 12.07/8.02 tff(1146,plain,
% 12.07/8.02 (((~![Y: $i, 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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1147,plain,
% 12.07/8.02 ((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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1148,plain,
% 12.07/8.02 (((~![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))))),
% 12.07/8.02 inference(monotonicity,[status(thm)],[1147])).
% 12.07/8.02 tff(1149,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.02 inference(transitivity,[status(thm)],[1148, 1146])).
% 12.07/8.02 tff(1150,plain,
% 12.07/8.02 ((~![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)))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1151,plain,
% 12.07/8.02 ((~![Y: $i, 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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 12.07/8.02 tff(1152,plain,
% 12.07/8.02 ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1151, 141, 1145])).
% 12.07/8.02 tff(1153,plain,
% 12.07/8.02 (~m_counter_cell_v_value(c_bit0, s38)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1152, 1134])).
% 12.07/8.02 tff(1154,assumption,(~m_counter_cell_v_carry_in(c_bit0, s38)), introduced(assumption)).
% 12.07/8.02 tff(1155,plain,
% 12.07/8.02 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s38)),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1156,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1155, 65, 1154])).
% 12.07/8.02 tff(1157,plain,(m_counter_cell_v_carry_in(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1158,plain,
% 12.07/8.02 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1159,plain,
% 12.07/8.02 (((~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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1160,plain,
% 12.07/8.02 (((~![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))))),
% 12.07/8.02 inference(monotonicity,[status(thm)],[1159])).
% 12.07/8.02 tff(1161,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.02 inference(transitivity,[status(thm)],[1160, 1158])).
% 12.07/8.02 tff(1162,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1163,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 12.07/8.02 tff(1164,plain,
% 12.07/8.02 (m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1163, 77, 1157])).
% 12.07/8.02 tff(1165,plain,
% 12.07/8.02 (~node1(c_bit0, s38)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1164, 1153])).
% 12.07/8.02 tff(1166,plain,
% 12.07/8.02 (succ(s38, s39) <=> succ(s38, s39)),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1167,axiom,(succ(s38, s39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound39')).
% 12.07/8.02 tff(1168,plain,
% 12.07/8.02 (succ(s38, s39)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1167, 1166])).
% 12.07/8.02 tff(1169,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1170,plain,
% 12.07/8.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1171,plain,
% 12.07/8.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 12.07/8.02 tff(1172,plain,
% 12.07/8.02 (trans(s38, s39)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1171, 1168, 7])).
% 12.07/8.02 tff(1173,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1174,plain,
% 12.07/8.02 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit0, s38, s39))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1175,plain,
% 12.07/8.02 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit0, s38, s39)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 12.07/8.02 tff(1176,plain,
% 12.07/8.02 (node3(c_bit0, s38, s39)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1175, 21, 1172])).
% 12.07/8.02 tff(1177,plain,
% 12.07/8.02 (((~![Y: $i, 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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1178,plain,
% 12.07/8.02 ((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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1179,plain,
% 12.07/8.02 (((~![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))))),
% 12.07/8.02 inference(monotonicity,[status(thm)],[1178])).
% 12.07/8.02 tff(1180,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.02 inference(transitivity,[status(thm)],[1179, 1177])).
% 12.07/8.02 tff(1181,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1182,plain,
% 12.07/8.02 ((~![Y: $i, 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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 12.07/8.02 tff(1183,plain,
% 12.07/8.02 (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1182, 106, 1176])).
% 12.07/8.02 tff(1184,plain,
% 12.07/8.02 (m_counter_cell_v_value(c_bit0, s39)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1183, 1165])).
% 12.07/8.02 tff(1185,assumption,(~m_counter_cell_v_carry_in(c_bit0, s39)), introduced(assumption)).
% 12.07/8.02 tff(1186,plain,
% 12.07/8.02 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s39)),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1187,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1186, 65, 1185])).
% 12.07/8.02 tff(1188,plain,(m_counter_cell_v_carry_in(c_bit0, s39)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1189,plain,
% 12.07/8.02 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1190,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1191,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1190, 1189])).
% 12.07/8.02 tff(1192,plain,
% 12.07/8.02 ((~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39))),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1191, 126, 1188])).
% 12.07/8.02 tff(1193,plain,
% 12.07/8.02 (~node2(c_bit0, s39)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1192, 1184])).
% 12.07/8.02 tff(1194,plain,
% 12.07/8.02 (succ(s39, s40) <=> succ(s39, s40)),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1195,axiom,(succ(s39, s40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound40')).
% 12.07/8.02 tff(1196,plain,
% 12.07/8.02 (succ(s39, s40)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 12.07/8.02 tff(1197,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1198,plain,
% 12.07/8.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1199,plain,
% 12.07/8.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 12.07/8.02 tff(1200,plain,
% 12.07/8.02 (trans(s39, s40)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1199, 1196, 7])).
% 12.07/8.02 tff(1201,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1202,plain,
% 12.07/8.02 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit0, s39, s40))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1203,plain,
% 12.07/8.02 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit0, s39, s40)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 12.07/8.02 tff(1204,plain,
% 12.07/8.02 (node3(c_bit0, s39, s40)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1203, 21, 1200])).
% 12.07/8.02 tff(1205,plain,
% 12.07/8.02 (((~![Y: $i, 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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1206,plain,
% 12.07/8.02 ((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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1207,plain,
% 12.07/8.02 (((~![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))))),
% 12.07/8.02 inference(monotonicity,[status(thm)],[1206])).
% 12.07/8.02 tff(1208,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.02 inference(transitivity,[status(thm)],[1207, 1205])).
% 12.07/8.02 tff(1209,plain,
% 12.07/8.02 ((~![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)))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1210,plain,
% 12.07/8.02 ((~![Y: $i, 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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 12.07/8.02 tff(1211,plain,
% 12.07/8.02 ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1210, 141, 1204])).
% 12.07/8.02 tff(1212,plain,
% 12.07/8.02 (~m_counter_cell_v_value(c_bit0, s40)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1211, 1193])).
% 12.07/8.02 tff(1213,assumption,(node4(c_bit0, s40)), introduced(assumption)).
% 12.07/8.02 tff(1214,assumption,(~m_counter_cell_v_value(c_bit0, s40)), introduced(assumption)).
% 12.07/8.02 tff(1215,plain,
% 12.07/8.02 (^[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))))),
% 12.07/8.02 inference(bind,[status(th)],[])).
% 12.07/8.02 tff(1216,plain,
% 12.07/8.02 (![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)))),
% 12.07/8.02 inference(quant_intro,[status(thm)],[1215])).
% 12.07/8.02 tff(1217,plain,
% 12.07/8.02 (![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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1218,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')).
% 12.07/8.02 tff(1219,plain,
% 12.07/8.02 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 12.07/8.02 tff(1220,plain,(
% 12.07/8.02 ![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 12.07/8.02 inference(skolemize,[status(sab)],[1219])).
% 12.07/8.02 tff(1221,plain,
% 12.07/8.02 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1220, 1216])).
% 12.07/8.02 tff(1222,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1223,plain,
% 12.07/8.02 ((~![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)))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1224,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1223, 1222])).
% 12.07/8.02 tff(1225,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1224, 1221, 1214, 1213])).
% 12.07/8.02 tff(1226,plain,(m_counter_cell_v_value(c_bit0, s40) | (~node4(c_bit0, s40))), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1227,plain,
% 12.07/8.02 (~node4(c_bit0, s40)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1226, 1212])).
% 12.07/8.02 tff(1228,assumption,(m_counter_cell_v_carry_out(c_bit0, s40)), introduced(assumption)).
% 12.07/8.02 tff(1229,plain,
% 12.07/8.02 (^[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)))),
% 12.07/8.02 inference(bind,[status(th)],[])).
% 12.07/8.02 tff(1230,plain,
% 12.07/8.02 (![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))),
% 12.07/8.02 inference(quant_intro,[status(thm)],[1229])).
% 12.07/8.02 tff(1231,plain,
% 12.07/8.02 (![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1232,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')).
% 12.07/8.02 tff(1233,plain,
% 12.07/8.02 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 12.07/8.02 tff(1234,plain,(
% 12.07/8.02 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 12.07/8.02 inference(skolemize,[status(sab)],[1233])).
% 12.07/8.02 tff(1235,plain,
% 12.07/8.02 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1234, 1230])).
% 12.07/8.02 tff(1236,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1237,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1238,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 12.07/8.02 tff(1239,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1238, 1235, 1228, 1227])).
% 12.07/8.02 tff(1240,plain,(~m_counter_cell_v_carry_out(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1241,assumption,(m_counter_cell_v_carry_in(c_bit1, s40)), introduced(assumption)).
% 12.07/8.02 tff(1242,assumption,(~m_counter_cell_v_carry_out(c_bit0, s40)), introduced(assumption)).
% 12.07/8.02 tff(1243,plain,
% 12.07/8.02 (^[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)))),
% 12.07/8.02 inference(bind,[status(th)],[])).
% 12.07/8.02 tff(1244,plain,
% 12.07/8.02 (![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))),
% 12.07/8.02 inference(quant_intro,[status(thm)],[1243])).
% 12.07/8.02 tff(1245,plain,
% 12.07/8.02 (![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1246,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')).
% 12.07/8.02 tff(1247,plain,
% 12.07/8.02 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1246, 1245])).
% 12.07/8.02 tff(1248,plain,(
% 12.07/8.02 ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 12.07/8.02 inference(skolemize,[status(sab)],[1247])).
% 12.07/8.02 tff(1249,plain,
% 12.07/8.02 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1248, 1244])).
% 12.07/8.02 tff(1250,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1251,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1252,plain,
% 12.07/8.02 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s40)) | m_counter_cell_v_carry_out(c_bit0, s40)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 12.07/8.02 tff(1253,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1252, 1249, 1242, 1241])).
% 12.07/8.02 tff(1254,plain,(m_counter_cell_v_carry_out(c_bit0, s40) | (~m_counter_cell_v_carry_in(c_bit1, s40))), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1255,plain,
% 12.07/8.02 (~m_counter_cell_v_carry_in(c_bit1, s40)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1254, 1240])).
% 12.07/8.02 tff(1256,assumption,(node2(c_bit1, s40)), introduced(assumption)).
% 12.07/8.02 tff(1257,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1258,plain,
% 12.07/8.02 ((~![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)))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1259,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 12.07/8.02 tff(1260,plain,
% 12.07/8.02 (~node4(c_bit0, s38)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1259, 1221, 1153])).
% 12.07/8.02 tff(1261,assumption,(~node4(c_bit0, s38)), introduced(assumption)).
% 12.07/8.02 tff(1262,assumption,(m_counter_cell_v_carry_out(c_bit0, s38)), introduced(assumption)).
% 12.07/8.02 tff(1263,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1264,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1265,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1264, 1263])).
% 12.07/8.02 tff(1266,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1265, 1235, 1262, 1261])).
% 12.07/8.02 tff(1267,plain,((~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1268,plain,
% 12.07/8.02 (~m_counter_cell_v_carry_out(c_bit0, s38)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1267, 1260])).
% 12.07/8.02 tff(1269,assumption,(m_counter_cell_v_carry_in(c_bit1, s38)), introduced(assumption)).
% 12.07/8.02 tff(1270,assumption,(~m_counter_cell_v_carry_out(c_bit0, s38)), introduced(assumption)).
% 12.07/8.02 tff(1271,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1272,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1273,plain,
% 12.07/8.02 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1272, 1271])).
% 12.07/8.02 tff(1274,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1273, 1249, 1270, 1269])).
% 12.07/8.02 tff(1275,plain,((~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1276,plain,
% 12.07/8.02 (~m_counter_cell_v_carry_in(c_bit1, s38)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1275, 1268])).
% 12.07/8.02 tff(1277,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1278,plain,
% 12.07/8.02 ((~![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)))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1279,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 12.07/8.02 tff(1280,plain,
% 12.07/8.02 (~node4(c_bit0, s22)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1279, 1221, 681])).
% 12.07/8.02 tff(1281,assumption,(m_counter_cell_v_carry_out(c_bit0, s22)), introduced(assumption)).
% 12.07/8.02 tff(1282,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1283,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1284,plain,
% 12.07/8.02 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 12.07/8.02 tff(1285,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1284, 1235, 1281, 1280])).
% 12.07/8.02 tff(1286,plain,(~m_counter_cell_v_carry_out(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1287,assumption,(m_counter_cell_v_carry_in(c_bit1, s22)), introduced(assumption)).
% 12.07/8.02 tff(1288,assumption,(~m_counter_cell_v_carry_out(c_bit0, s22)), introduced(assumption)).
% 12.07/8.02 tff(1289,plain,
% 12.07/8.02 (((~![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))),
% 12.07/8.02 inference(rewrite,[status(thm)],[])).
% 12.07/8.02 tff(1290,plain,
% 12.07/8.02 ((~![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))),
% 12.07/8.02 inference(quant_inst,[status(thm)],[])).
% 12.07/8.02 tff(1291,plain,
% 12.07/8.02 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22)),
% 12.07/8.02 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 12.07/8.02 tff(1292,plain,
% 12.07/8.02 ($false),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1291, 1249, 1288, 1287])).
% 12.07/8.02 tff(1293,plain,(m_counter_cell_v_carry_out(c_bit0, s22) | (~m_counter_cell_v_carry_in(c_bit1, s22))), inference(lemma,lemma(discharge,[]))).
% 12.07/8.02 tff(1294,plain,
% 12.07/8.02 (~m_counter_cell_v_carry_in(c_bit1, s22)),
% 12.07/8.02 inference(unit_resolution,[status(thm)],[1293, 1286])).
% 12.07/8.02 tff(1295,assumption,(node4(c_bit0, s20)), introduced(assumption)).
% 12.07/8.02 tff(1296,assumption,(~m_counter_cell_v_value(c_bit0, s20)), introduced(assumption)).
% 12.07/8.02 tff(1297,plain,
% 12.07/8.02 (((~![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)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1298,plain,
% 12.07/8.03 ((~![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)))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1299,plain,
% 12.07/8.03 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 12.07/8.03 tff(1300,plain,
% 12.07/8.03 ($false),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1299, 1221, 1296, 1295])).
% 12.07/8.03 tff(1301,plain,(m_counter_cell_v_value(c_bit0, s20) | (~node4(c_bit0, s20))), inference(lemma,lemma(discharge,[]))).
% 12.07/8.03 tff(1302,plain,
% 12.07/8.03 (~node4(c_bit0, s20)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1301, 622])).
% 12.07/8.03 tff(1303,assumption,(m_counter_cell_v_carry_out(c_bit0, s20)), introduced(assumption)).
% 12.07/8.03 tff(1304,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1305,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1306,plain,
% 12.07/8.03 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s20)) | node4(c_bit0, s20)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 12.07/8.03 tff(1307,plain,
% 12.07/8.03 ($false),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1306, 1235, 1303, 1302])).
% 12.07/8.03 tff(1308,plain,(~m_counter_cell_v_carry_out(c_bit0, s20)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.03 tff(1309,assumption,(m_counter_cell_v_carry_in(c_bit1, s20)), introduced(assumption)).
% 12.07/8.03 tff(1310,assumption,(~m_counter_cell_v_carry_out(c_bit0, s20)), introduced(assumption)).
% 12.07/8.03 tff(1311,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1312,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1313,plain,
% 12.07/8.03 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s20)) | m_counter_cell_v_carry_out(c_bit0, s20)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1312, 1311])).
% 12.07/8.03 tff(1314,plain,
% 12.07/8.03 ($false),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1313, 1249, 1310, 1309])).
% 12.07/8.03 tff(1315,plain,(m_counter_cell_v_carry_out(c_bit0, s20) | (~m_counter_cell_v_carry_in(c_bit1, s20))), inference(lemma,lemma(discharge,[]))).
% 12.07/8.03 tff(1316,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_in(c_bit1, s20)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1315, 1308])).
% 12.07/8.03 tff(1317,plain,
% 12.07/8.03 (((~![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)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1318,plain,
% 12.07/8.03 ((~![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)))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1319,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 12.07/8.03 tff(1320,plain,
% 12.07/8.03 (~node4(c_bit0, s18)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1319, 1221, 563])).
% 12.07/8.03 tff(1321,assumption,(m_counter_cell_v_carry_out(c_bit0, s18)), introduced(assumption)).
% 12.07/8.03 tff(1322,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1323,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1324,plain,
% 12.07/8.03 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 12.07/8.03 tff(1325,plain,
% 12.07/8.03 ($false),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1324, 1235, 1321, 1320])).
% 12.07/8.03 tff(1326,plain,(~m_counter_cell_v_carry_out(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.03 tff(1327,assumption,(m_counter_cell_v_carry_in(c_bit1, s18)), introduced(assumption)).
% 12.07/8.03 tff(1328,assumption,(~m_counter_cell_v_carry_out(c_bit0, s18)), introduced(assumption)).
% 12.07/8.03 tff(1329,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1330,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1331,plain,
% 12.07/8.03 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 12.07/8.03 tff(1332,plain,
% 12.07/8.03 ($false),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1331, 1249, 1328, 1327])).
% 12.07/8.03 tff(1333,plain,((~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.03 tff(1334,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_in(c_bit1, s18)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1333, 1326])).
% 12.07/8.03 tff(1335,plain,
% 12.07/8.03 (((~![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)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1336,plain,
% 12.07/8.03 ((~![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)))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1337,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 12.07/8.03 tff(1338,plain,
% 12.07/8.03 (~node4(c_bit0, s16)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1337, 1221, 506])).
% 12.07/8.03 tff(1339,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1340,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1341,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1340, 1339])).
% 12.07/8.03 tff(1342,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_out(c_bit0, s16)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1341, 1235, 1338])).
% 12.07/8.03 tff(1343,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1344,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1345,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1344, 1343])).
% 12.07/8.03 tff(1346,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_in(c_bit1, s16)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1345, 1249, 1342])).
% 12.07/8.03 tff(1347,plain,
% 12.07/8.03 (((~![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)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1348,plain,
% 12.07/8.03 ((~![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)))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1349,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1348, 1347])).
% 12.07/8.03 tff(1350,plain,
% 12.07/8.03 (~node4(c_bit0, s14)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1349, 1221, 451])).
% 12.07/8.03 tff(1351,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1352,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1353,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1352, 1351])).
% 12.07/8.03 tff(1354,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_out(c_bit0, s14)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1353, 1235, 1350])).
% 12.07/8.03 tff(1355,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1356,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1357,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 12.07/8.03 tff(1358,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_in(c_bit1, s14)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1357, 1249, 1354])).
% 12.07/8.03 tff(1359,plain,
% 12.07/8.03 (^[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)))),
% 12.07/8.03 inference(bind,[status(th)],[])).
% 12.07/8.03 tff(1360,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(quant_intro,[status(thm)],[1359])).
% 12.07/8.03 tff(1361,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1362,plain,
% 12.07/8.03 (^[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))))),
% 12.07/8.03 inference(bind,[status(th)],[])).
% 12.07/8.03 tff(1363,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(quant_intro,[status(thm)],[1362])).
% 12.07/8.03 tff(1364,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')).
% 12.07/8.03 tff(1365,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1364, 1363])).
% 12.07/8.03 tff(1366,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1365, 1361])).
% 12.07/8.03 tff(1367,plain,(
% 12.07/8.03 ![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))),
% 12.07/8.03 inference(skolemize,[status(sab)],[1366])).
% 12.07/8.03 tff(1368,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1367, 1360])).
% 12.07/8.03 tff(1369,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1370,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1371,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 12.07/8.03 tff(1372,plain,
% 12.07/8.03 ((~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1371, 1368, 427])).
% 12.07/8.03 tff(1373,plain,
% 12.07/8.03 (m_counter_cell_v_carry_out(c_bit0, s13)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1372, 425])).
% 12.07/8.03 tff(1374,plain,
% 12.07/8.03 (^[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)))),
% 12.07/8.03 inference(bind,[status(th)],[])).
% 12.07/8.03 tff(1375,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(quant_intro,[status(thm)],[1374])).
% 12.07/8.03 tff(1376,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1377,plain,
% 12.07/8.03 (^[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)))),
% 12.07/8.03 inference(bind,[status(th)],[])).
% 12.07/8.03 tff(1378,plain,
% 12.07/8.03 (![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))),
% 12.07/8.03 inference(quant_intro,[status(thm)],[1377])).
% 12.07/8.03 tff(1379,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')).
% 12.07/8.03 tff(1380,plain,
% 12.07/8.03 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 12.07/8.03 tff(1381,plain,
% 12.07/8.03 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1380, 1376])).
% 12.07/8.03 tff(1382,plain,(
% 12.07/8.03 ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 12.07/8.03 inference(skolemize,[status(sab)],[1381])).
% 12.07/8.03 tff(1383,plain,
% 12.07/8.03 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1382, 1375])).
% 12.07/8.03 tff(1384,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1385,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1386,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 12.07/8.03 tff(1387,plain,
% 12.07/8.03 (m_counter_cell_v_carry_in(c_bit1, s13)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1386, 1383, 1373])).
% 12.07/8.03 tff(1388,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1389,plain,
% 12.07/8.03 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit1, s12, s13))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1390,plain,
% 12.07/8.03 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit1, s12, s13)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 12.07/8.03 tff(1391,plain,
% 12.07/8.03 (node3(c_bit1, s12, s13)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1390, 21, 14])).
% 12.07/8.03 tff(1392,plain,
% 12.07/8.03 (((~![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)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1393,plain,
% 12.07/8.03 ((~![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)))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1394,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 12.07/8.03 tff(1395,plain,
% 12.07/8.03 (~node4(c_bit0, s10)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1394, 1221, 353])).
% 12.07/8.03 tff(1396,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1397,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1398,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 12.07/8.03 tff(1399,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_out(c_bit0, s10)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1398, 1235, 1395])).
% 12.07/8.03 tff(1400,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1401,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1402,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 12.07/8.03 tff(1403,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_in(c_bit1, s10)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1402, 1249, 1399])).
% 12.07/8.03 tff(1404,plain,
% 12.07/8.03 (((~![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)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1405,plain,
% 12.07/8.03 ((~![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)))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1406,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 12.07/8.03 tff(1407,plain,
% 12.07/8.03 (~node4(c_bit0, s8)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1406, 1221, 298])).
% 12.07/8.03 tff(1408,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1409,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1410,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1409, 1408])).
% 12.07/8.03 tff(1411,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_out(c_bit0, s8)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1410, 1235, 1407])).
% 12.07/8.03 tff(1412,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1413,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1414,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1413, 1412])).
% 12.07/8.03 tff(1415,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_in(c_bit1, s8)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1414, 1249, 1411])).
% 12.07/8.03 tff(1416,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1417,plain,
% 12.07/8.03 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit1, s7, s8))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1418,plain,
% 12.07/8.03 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit1, s7, s8)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 12.07/8.03 tff(1419,plain,
% 12.07/8.03 (node3(c_bit1, s7, s8)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1418, 21, 32])).
% 12.07/8.03 tff(1420,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1421,plain,
% 12.07/8.03 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit1, s5, s6))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1422,plain,
% 12.07/8.03 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit1, s5, s6)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 12.07/8.03 tff(1423,plain,
% 12.07/8.03 (node3(c_bit1, s5, s6)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1422, 21, 246])).
% 12.07/8.03 tff(1424,assumption,(m_counter_cell_v_value(c_bit1, s0)), introduced(assumption)).
% 12.07/8.03 tff(1425,plain,
% 12.07/8.03 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit1, s0))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1426,plain,
% 12.07/8.03 ($false),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1425, 55, 1424])).
% 12.07/8.03 tff(1427,plain,(~m_counter_cell_v_value(c_bit1, s0)), inference(lemma,lemma(discharge,[]))).
% 12.07/8.03 tff(1428,plain,
% 12.07/8.03 (((~![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)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1429,plain,
% 12.07/8.03 ((~![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)))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1430,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1429, 1428])).
% 12.07/8.03 tff(1431,plain,
% 12.07/8.03 (~node4(c_bit0, s0)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1430, 1221, 58])).
% 12.07/8.03 tff(1432,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1433,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1434,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1433, 1432])).
% 12.07/8.03 tff(1435,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_out(c_bit0, s0)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1434, 1235, 1431])).
% 12.07/8.03 tff(1436,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1437,plain,
% 12.07/8.03 ((~![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))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1438,plain,
% 12.07/8.03 ((~![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)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 12.07/8.03 tff(1439,plain,
% 12.07/8.03 (~m_counter_cell_v_carry_in(c_bit1, s0)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1438, 1249, 1435])).
% 12.07/8.03 tff(1440,plain,
% 12.07/8.03 (^[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))))),
% 12.07/8.03 inference(bind,[status(th)],[])).
% 12.07/8.03 tff(1441,plain,
% 12.07/8.03 (![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)))),
% 12.07/8.03 inference(quant_intro,[status(thm)],[1440])).
% 12.07/8.03 tff(1442,plain,
% 12.07/8.03 (![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)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1443,plain,
% 12.07/8.03 (^[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)))))),
% 12.07/8.03 inference(bind,[status(th)],[])).
% 12.07/8.03 tff(1444,plain,
% 12.07/8.03 (![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)))),
% 12.07/8.03 inference(quant_intro,[status(thm)],[1443])).
% 12.07/8.03 tff(1445,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')).
% 12.07/8.03 tff(1446,plain,
% 12.07/8.03 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1445, 1444])).
% 12.07/8.03 tff(1447,plain,
% 12.07/8.03 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1446, 1442])).
% 12.07/8.03 tff(1448,plain,(
% 12.07/8.03 ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 12.07/8.03 inference(skolemize,[status(sab)],[1447])).
% 12.07/8.03 tff(1449,plain,
% 12.07/8.03 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1448, 1441])).
% 12.07/8.03 tff(1450,plain,
% 12.07/8.03 (((~![I0: $i, X: $i] : (m_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_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1451,plain,
% 12.07/8.03 ((~![I0: $i, X: $i] : (m_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)))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1452,plain,
% 12.07/8.03 ((~![I0: $i, X: $i] : (m_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))),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 12.07/8.03 tff(1453,plain,
% 12.07/8.03 (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0))),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1452, 1449, 1439])).
% 12.07/8.03 tff(1454,plain,
% 12.07/8.03 (~node2(c_bit1, s0)),
% 12.07/8.03 inference(unit_resolution,[status(thm)],[1453, 1427])).
% 12.07/8.03 tff(1455,plain,
% 12.07/8.03 (((~![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))),
% 12.07/8.03 inference(rewrite,[status(thm)],[])).
% 12.07/8.03 tff(1456,plain,
% 12.07/8.03 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit1, s0, s1))),
% 12.07/8.03 inference(quant_inst,[status(thm)],[])).
% 12.07/8.03 tff(1457,plain,
% 12.07/8.03 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit1, s0, s1)),
% 12.07/8.03 inference(modus_ponens,[status(thm)],[1456, 1455])).
% 12.07/8.03 tff(1458,plain,
% 12.07/8.03 (node3(c_bit1, s0, s1)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1457, 21, 92])).
% 12.07/8.04 tff(1459,plain,
% 12.07/8.04 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~node3(c_bit1, s0, s1)) | node2(c_bit1, s0) | (~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)))) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1460,plain,
% 12.07/8.04 ((node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1))) <=> ((~node3(c_bit1, s0, s1)) | node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1461,plain,
% 12.07/8.04 (((~![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)))) | ((~node3(c_bit1, s0, s1)) | node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1))))),
% 12.07/8.04 inference(monotonicity,[status(thm)],[1460])).
% 12.07/8.04 tff(1462,plain,
% 12.07/8.04 (((~![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)))) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1)))),
% 12.07/8.04 inference(transitivity,[status(thm)],[1461, 1459])).
% 12.07/8.04 tff(1463,plain,
% 12.07/8.04 ((~![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)))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1464,plain,
% 12.07/8.04 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit1, s0, s1)) | node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1463, 1462])).
% 12.07/8.04 tff(1465,plain,
% 12.07/8.04 (node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1))),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1464, 141, 1458])).
% 12.07/8.04 tff(1466,plain,
% 12.07/8.04 (~m_counter_cell_v_value(c_bit1, s1)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1465, 1454])).
% 12.07/8.04 tff(1467,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1468,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1469,plain,
% 12.07/8.04 ((~![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)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1468, 1467])).
% 12.07/8.04 tff(1470,plain,
% 12.07/8.04 ((~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1469, 1368, 116])).
% 12.07/8.04 tff(1471,plain,
% 12.07/8.04 (m_counter_cell_v_carry_out(c_bit0, s1)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1470, 114])).
% 12.07/8.04 tff(1472,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1473,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1474,plain,
% 12.07/8.04 ((~![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)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1473, 1472])).
% 12.07/8.04 tff(1475,plain,
% 12.07/8.04 (m_counter_cell_v_carry_in(c_bit1, s1)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1474, 1383, 1471])).
% 12.07/8.04 tff(1476,plain,
% 12.07/8.04 (((~![I0: $i, 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)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1477,plain,
% 12.07/8.04 (((~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)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1478,plain,
% 12.07/8.04 (((~![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))))),
% 12.07/8.04 inference(monotonicity,[status(thm)],[1477])).
% 12.07/8.04 tff(1479,plain,
% 12.07/8.04 (((~![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)))),
% 12.07/8.04 inference(transitivity,[status(thm)],[1478, 1476])).
% 12.07/8.04 tff(1480,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1481,plain,
% 12.07/8.04 ((~![I0: $i, 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))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1480, 1479])).
% 12.07/8.04 tff(1482,plain,
% 12.07/8.04 (m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1))),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1481, 77, 1475])).
% 12.07/8.04 tff(1483,plain,
% 12.07/8.04 (~node1(c_bit1, s1)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1482, 1466])).
% 12.07/8.04 tff(1484,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1485,plain,
% 12.07/8.04 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit1, s1, s2))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1486,plain,
% 12.07/8.04 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit1, s1, s2)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 12.07/8.04 tff(1487,plain,
% 12.07/8.04 (node3(c_bit1, s1, s2)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1486, 21, 43])).
% 12.07/8.04 tff(1488,plain,
% 12.07/8.04 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | ((~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1489,plain,
% 12.07/8.04 ((node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2)) <=> ((~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1490,plain,
% 12.07/8.04 (((~![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))) | ((~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1)))),
% 12.07/8.04 inference(monotonicity,[status(thm)],[1489])).
% 12.07/8.04 tff(1491,plain,
% 12.07/8.04 (((~![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))) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1))),
% 12.07/8.04 inference(transitivity,[status(thm)],[1490, 1488])).
% 12.07/8.04 tff(1492,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1493,plain,
% 12.07/8.04 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 12.07/8.04 tff(1494,plain,
% 12.07/8.04 (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1493, 106, 1487])).
% 12.07/8.04 tff(1495,plain,
% 12.07/8.04 (m_counter_cell_v_value(c_bit1, s2)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1494, 1483])).
% 12.07/8.04 tff(1496,plain,
% 12.07/8.04 (((~![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)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1497,plain,
% 12.07/8.04 ((~![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)))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1498,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1497, 1496])).
% 12.07/8.04 tff(1499,plain,
% 12.07/8.04 (~node4(c_bit0, s2)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1498, 1221, 148])).
% 12.07/8.04 tff(1500,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1501,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1502,plain,
% 12.07/8.04 ((~![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)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 12.07/8.04 tff(1503,plain,
% 12.07/8.04 (~m_counter_cell_v_carry_out(c_bit0, s2)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1502, 1235, 1499])).
% 12.07/8.04 tff(1504,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1505,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1506,plain,
% 12.07/8.04 ((~![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)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 12.07/8.04 tff(1507,plain,
% 12.07/8.04 (~m_counter_cell_v_carry_in(c_bit1, s2)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1506, 1249, 1503])).
% 12.07/8.04 tff(1508,plain,
% 12.07/8.04 (^[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))))),
% 12.07/8.04 inference(bind,[status(th)],[])).
% 12.07/8.04 tff(1509,plain,
% 12.07/8.04 (![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)))),
% 12.07/8.04 inference(quant_intro,[status(thm)],[1508])).
% 12.07/8.04 tff(1510,plain,
% 12.07/8.04 (![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)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1511,plain,
% 12.07/8.04 (^[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))))),
% 12.07/8.04 inference(bind,[status(th)],[])).
% 12.07/8.04 tff(1512,plain,
% 12.07/8.04 (![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)))),
% 12.07/8.04 inference(quant_intro,[status(thm)],[1511])).
% 12.07/8.04 tff(1513,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')).
% 12.07/8.04 tff(1514,plain,
% 12.07/8.04 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 12.07/8.04 tff(1515,plain,
% 12.07/8.04 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1514, 1510])).
% 12.07/8.04 tff(1516,plain,(
% 12.07/8.04 ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 12.07/8.04 inference(skolemize,[status(sab)],[1515])).
% 12.07/8.04 tff(1517,plain,
% 12.07/8.04 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1516, 1509])).
% 12.07/8.04 tff(1518,plain,
% 12.07/8.04 (((~![I0: $i, X: $i] : ((~node1(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) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(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) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1519,plain,
% 12.07/8.04 (((~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) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1520,plain,
% 12.07/8.04 (((~![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) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2))))),
% 12.07/8.04 inference(monotonicity,[status(thm)],[1519])).
% 12.07/8.04 tff(1521,plain,
% 12.07/8.04 (((~![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) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2)))),
% 12.07/8.04 inference(transitivity,[status(thm)],[1520, 1518])).
% 12.07/8.04 tff(1522,plain,
% 12.07/8.04 ((~![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)))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1523,plain,
% 12.07/8.04 ((~![I0: $i, X: $i] : ((~node1(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) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 12.07/8.04 tff(1524,plain,
% 12.07/8.04 ((~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2))),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1523, 1517, 1507])).
% 12.07/8.04 tff(1525,plain,
% 12.07/8.04 (~node1(c_bit1, s2)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1524, 1495])).
% 12.07/8.04 tff(1526,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1527,plain,
% 12.07/8.04 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit1, s2, s3))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1528,plain,
% 12.07/8.04 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit1, s2, s3)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 12.07/8.04 tff(1529,plain,
% 12.07/8.04 (node3(c_bit1, s2, s3)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1528, 21, 165])).
% 12.07/8.04 tff(1530,plain,
% 12.07/8.04 (((~![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)) | m_counter_cell_v_value(c_bit1, s3) | node1(c_bit1, s2))) <=> ((~![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)) | m_counter_cell_v_value(c_bit1, s3) | node1(c_bit1, s2))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1531,plain,
% 12.07/8.04 ((node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3)) <=> ((~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3) | node1(c_bit1, s2))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1532,plain,
% 12.07/8.04 (((~![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)) | m_counter_cell_v_value(c_bit1, s3) | node1(c_bit1, s2)))),
% 12.07/8.04 inference(monotonicity,[status(thm)],[1531])).
% 12.07/8.04 tff(1533,plain,
% 12.07/8.04 (((~![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)) | m_counter_cell_v_value(c_bit1, s3) | node1(c_bit1, s2))),
% 12.07/8.04 inference(transitivity,[status(thm)],[1532, 1530])).
% 12.07/8.04 tff(1534,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1535,plain,
% 12.07/8.04 ((~![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)) | m_counter_cell_v_value(c_bit1, s3) | node1(c_bit1, s2)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1534, 1533])).
% 12.07/8.04 tff(1536,plain,
% 12.07/8.04 (m_counter_cell_v_value(c_bit1, s3) | node1(c_bit1, s2)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1535, 106, 1529])).
% 12.07/8.04 tff(1537,plain,
% 12.07/8.04 (m_counter_cell_v_value(c_bit1, s3)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1536, 1525])).
% 12.07/8.04 tff(1538,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1539,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1540,plain,
% 12.07/8.04 ((~![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)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 12.07/8.04 tff(1541,plain,
% 12.07/8.04 ((~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1540, 1368, 179])).
% 12.07/8.04 tff(1542,plain,
% 12.07/8.04 (m_counter_cell_v_carry_out(c_bit0, s3)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1541, 177])).
% 12.07/8.04 tff(1543,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1544,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1545,plain,
% 12.07/8.04 ((~![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)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 12.07/8.04 tff(1546,plain,
% 12.07/8.04 (m_counter_cell_v_carry_in(c_bit1, s3)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1545, 1383, 1542])).
% 12.07/8.04 tff(1547,plain,
% 12.07/8.04 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1548,plain,
% 12.07/8.04 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1549,plain,
% 12.07/8.04 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 12.07/8.04 tff(1550,plain,
% 12.07/8.04 ((~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3))),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1549, 126, 1546])).
% 12.07/8.04 tff(1551,plain,
% 12.07/8.04 (~node2(c_bit1, s3)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1550, 1537])).
% 12.07/8.04 tff(1552,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1553,plain,
% 12.07/8.04 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit1, s3, s4))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1554,plain,
% 12.07/8.04 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit1, s3, s4)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 12.07/8.04 tff(1555,plain,
% 12.07/8.04 (node3(c_bit1, s3, s4)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1554, 21, 191])).
% 12.07/8.04 tff(1556,plain,
% 12.07/8.04 (((~![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)) | node2(c_bit1, s3) | (~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)) | node2(c_bit1, s3) | (~m_counter_cell_v_value(c_bit1, s4)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1557,plain,
% 12.07/8.04 ((node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4))) <=> ((~node3(c_bit1, s3, s4)) | node2(c_bit1, s3) | (~m_counter_cell_v_value(c_bit1, s4)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1558,plain,
% 12.07/8.04 (((~![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)) | node2(c_bit1, s3) | (~m_counter_cell_v_value(c_bit1, s4))))),
% 12.07/8.04 inference(monotonicity,[status(thm)],[1557])).
% 12.07/8.04 tff(1559,plain,
% 12.07/8.04 (((~![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)) | node2(c_bit1, s3) | (~m_counter_cell_v_value(c_bit1, s4)))),
% 12.07/8.04 inference(transitivity,[status(thm)],[1558, 1556])).
% 12.07/8.04 tff(1560,plain,
% 12.07/8.04 ((~![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)))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1561,plain,
% 12.07/8.04 ((~![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)) | node2(c_bit1, s3) | (~m_counter_cell_v_value(c_bit1, s4))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 12.07/8.04 tff(1562,plain,
% 12.07/8.04 (node2(c_bit1, s3) | (~m_counter_cell_v_value(c_bit1, s4))),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1561, 141, 1555])).
% 12.07/8.04 tff(1563,plain,
% 12.07/8.04 (~m_counter_cell_v_value(c_bit1, s4)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1562, 1551])).
% 12.07/8.04 tff(1564,plain,
% 12.07/8.04 (((~![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)))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1565,plain,
% 12.07/8.04 ((~![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)))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1566,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 12.07/8.04 tff(1567,plain,
% 12.07/8.04 (~node4(c_bit0, s4)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1566, 1221, 203])).
% 12.07/8.04 tff(1568,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1569,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1570,plain,
% 12.07/8.04 ((~![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)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 12.07/8.04 tff(1571,plain,
% 12.07/8.04 (~m_counter_cell_v_carry_out(c_bit0, s4)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1570, 1235, 1567])).
% 12.07/8.04 tff(1572,plain,
% 12.07/8.04 (((~![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))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1573,plain,
% 12.07/8.04 ((~![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))),
% 12.07/8.04 inference(quant_inst,[status(thm)],[])).
% 12.07/8.04 tff(1574,plain,
% 12.07/8.04 ((~![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)),
% 12.07/8.04 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 12.07/8.04 tff(1575,plain,
% 12.07/8.04 (~m_counter_cell_v_carry_in(c_bit1, s4)),
% 12.07/8.04 inference(unit_resolution,[status(thm)],[1574, 1249, 1571])).
% 12.07/8.04 tff(1576,plain,
% 12.07/8.04 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit1, s4)) | m_counter_cell_v_value(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) | (~node2(c_bit1, s4)) | m_counter_cell_v_value(c_bit1, s4))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1577,plain,
% 12.07/8.04 ((m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4))) <=> (m_counter_cell_v_carry_in(c_bit1, s4) | (~node2(c_bit1, s4)) | m_counter_cell_v_value(c_bit1, s4))),
% 12.07/8.04 inference(rewrite,[status(thm)],[])).
% 12.07/8.04 tff(1578,plain,
% 12.07/8.04 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit1, s4)) | m_counter_cell_v_value(c_bit1, s4)))),
% 12.07/8.05 inference(monotonicity,[status(thm)],[1577])).
% 12.07/8.05 tff(1579,plain,
% 12.07/8.05 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit1, s4)) | m_counter_cell_v_value(c_bit1, s4))),
% 12.07/8.05 inference(transitivity,[status(thm)],[1578, 1576])).
% 12.07/8.05 tff(1580,plain,
% 12.07/8.05 ((~![I0: $i, X: $i] : (m_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)))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1581,plain,
% 12.07/8.05 ((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit1, s4)) | m_counter_cell_v_value(c_bit1, s4)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 12.07/8.05 tff(1582,plain,
% 12.07/8.05 ((~node2(c_bit1, s4)) | m_counter_cell_v_value(c_bit1, s4)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1581, 1449, 1575])).
% 12.07/8.05 tff(1583,plain,
% 12.07/8.05 (~node2(c_bit1, s4)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1582, 1563])).
% 12.07/8.05 tff(1584,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1585,plain,
% 12.07/8.05 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit1, s4, s5))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1586,plain,
% 12.07/8.05 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit1, s4, s5)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 12.07/8.05 tff(1587,plain,
% 12.07/8.05 (node3(c_bit1, s4, s5)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1586, 21, 220])).
% 12.07/8.05 tff(1588,plain,
% 12.07/8.05 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~node3(c_bit1, s4, s5)) | node2(c_bit1, s4) | (~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)))) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, s5)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1589,plain,
% 12.07/8.05 ((node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5))) <=> ((~node3(c_bit1, s4, s5)) | node2(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, s5)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1590,plain,
% 12.07/8.05 (((~![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)))) | ((~node3(c_bit1, s4, s5)) | node2(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, s5))))),
% 12.07/8.05 inference(monotonicity,[status(thm)],[1589])).
% 12.07/8.05 tff(1591,plain,
% 12.07/8.05 (((~![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)))) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, s5)))),
% 12.07/8.05 inference(transitivity,[status(thm)],[1590, 1588])).
% 12.07/8.05 tff(1592,plain,
% 12.07/8.05 ((~![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)))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1593,plain,
% 12.07/8.05 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit1, s4, s5)) | node2(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, s5))),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 12.07/8.05 tff(1594,plain,
% 12.07/8.05 (node2(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, s5))),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1593, 141, 1587])).
% 12.07/8.05 tff(1595,plain,
% 12.07/8.05 (~m_counter_cell_v_value(c_bit1, s5)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1594, 1583])).
% 12.07/8.05 tff(1596,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1597,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1598,plain,
% 12.07/8.05 ((~![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)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1597, 1596])).
% 12.07/8.05 tff(1599,plain,
% 12.07/8.05 ((~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1598, 1368, 234])).
% 12.07/8.05 tff(1600,plain,
% 12.07/8.05 (m_counter_cell_v_carry_out(c_bit0, s5)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1599, 232])).
% 12.07/8.05 tff(1601,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1602,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1603,plain,
% 12.07/8.05 ((~![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)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 12.07/8.05 tff(1604,plain,
% 12.07/8.05 (m_counter_cell_v_carry_in(c_bit1, s5)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1603, 1383, 1600])).
% 12.07/8.05 tff(1605,plain,
% 12.07/8.05 (((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1606,plain,
% 12.07/8.05 (((~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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1607,plain,
% 12.07/8.05 (((~![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)))),
% 12.07/8.05 inference(monotonicity,[status(thm)],[1606])).
% 12.07/8.05 tff(1608,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(transitivity,[status(thm)],[1607, 1605])).
% 12.07/8.05 tff(1609,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1610,plain,
% 12.07/8.05 ((~![I0: $i, X: $i] : ((~node1(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)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1609, 1608])).
% 12.07/8.05 tff(1611,plain,
% 12.07/8.05 ((~node1(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1610, 77, 1604])).
% 12.07/8.05 tff(1612,plain,
% 12.07/8.05 (~node1(c_bit1, s5)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1611, 1595])).
% 12.07/8.05 tff(1613,plain,
% 12.07/8.05 (((~![Y: $i, 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, s6) | node1(c_bit1, s5) | (~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))) | m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1614,plain,
% 12.07/8.05 ((node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)) | m_counter_cell_v_value(c_bit1, s6)) <=> (m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1615,plain,
% 12.07/8.05 (((~![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))) | (m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6))))),
% 12.07/8.05 inference(monotonicity,[status(thm)],[1614])).
% 12.07/8.05 tff(1616,plain,
% 12.07/8.05 (((~![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))) | m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6)))),
% 12.07/8.05 inference(transitivity,[status(thm)],[1615, 1613])).
% 12.07/8.05 tff(1617,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1618,plain,
% 12.07/8.05 ((~![Y: $i, 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, s6) | node1(c_bit1, s5) | (~node3(c_bit1, s5, s6))),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 12.07/8.05 tff(1619,plain,
% 12.07/8.05 (m_counter_cell_v_value(c_bit1, s6)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1618, 106, 1612, 1423])).
% 12.07/8.05 tff(1620,plain,
% 12.07/8.05 (((~![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)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1621,plain,
% 12.07/8.05 ((~![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)))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1622,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1621, 1620])).
% 12.07/8.05 tff(1623,plain,
% 12.07/8.05 (~node4(c_bit0, s6)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1622, 1221, 258])).
% 12.07/8.05 tff(1624,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1625,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1626,plain,
% 12.07/8.05 ((~![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)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 12.07/8.05 tff(1627,plain,
% 12.07/8.05 (~m_counter_cell_v_carry_out(c_bit0, s6)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1626, 1235, 1623])).
% 12.07/8.05 tff(1628,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1629,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1630,plain,
% 12.07/8.05 ((~![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)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1629, 1628])).
% 12.07/8.05 tff(1631,plain,
% 12.07/8.05 (~m_counter_cell_v_carry_in(c_bit1, s6)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1630, 1249, 1627])).
% 12.07/8.05 tff(1632,plain,
% 12.07/8.05 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1633,plain,
% 12.07/8.05 (((~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)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1634,plain,
% 12.07/8.05 (((~![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))))),
% 12.07/8.05 inference(monotonicity,[status(thm)],[1633])).
% 12.07/8.05 tff(1635,plain,
% 12.07/8.05 (((~![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)))),
% 12.07/8.05 inference(transitivity,[status(thm)],[1634, 1632])).
% 12.07/8.05 tff(1636,plain,
% 12.07/8.05 ((~![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)))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1637,plain,
% 12.07/8.05 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1636, 1635])).
% 12.07/8.05 tff(1638,plain,
% 12.07/8.05 ((~node1(c_bit1, s6)) | (~m_counter_cell_v_value(c_bit1, s6))),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1637, 1517, 1631])).
% 12.07/8.05 tff(1639,plain,
% 12.07/8.05 (~node1(c_bit1, s6)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1638, 1619])).
% 12.07/8.05 tff(1640,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1641,plain,
% 12.07/8.05 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit1, s6, s7))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1642,plain,
% 12.07/8.05 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit1, s6, s7)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1641, 1640])).
% 12.07/8.05 tff(1643,plain,
% 12.07/8.05 (node3(c_bit1, s6, s7)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1642, 21, 272])).
% 12.07/8.05 tff(1644,plain,
% 12.07/8.05 (((~![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) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1645,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1646,plain,
% 12.07/8.05 ((~![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)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 12.07/8.05 tff(1647,plain,
% 12.07/8.05 (node1(c_bit1, s6) | m_counter_cell_v_value(c_bit1, s7)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1646, 106, 1643])).
% 12.07/8.05 tff(1648,plain,
% 12.07/8.05 (m_counter_cell_v_value(c_bit1, s7)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1647, 1639])).
% 12.07/8.05 tff(1649,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1650,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1651,plain,
% 12.07/8.05 ((~![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)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 12.07/8.05 tff(1652,plain,
% 12.07/8.05 ((~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1651, 1368, 286])).
% 12.07/8.05 tff(1653,plain,
% 12.07/8.05 (m_counter_cell_v_carry_out(c_bit0, s7)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1652, 284])).
% 12.07/8.05 tff(1654,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1655,plain,
% 12.07/8.05 ((~![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))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1656,plain,
% 12.07/8.05 ((~![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)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1655, 1654])).
% 12.07/8.05 tff(1657,plain,
% 12.07/8.05 (m_counter_cell_v_carry_in(c_bit1, s7)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1656, 1383, 1653])).
% 12.07/8.05 tff(1658,plain,
% 12.07/8.05 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1659,plain,
% 12.07/8.05 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1660,plain,
% 12.07/8.05 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 12.07/8.05 tff(1661,plain,
% 12.07/8.05 ((~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7))),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1660, 126, 1657])).
% 12.07/8.05 tff(1662,plain,
% 12.07/8.05 (~node2(c_bit1, s7)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1661, 1648])).
% 12.07/8.05 tff(1663,plain,
% 12.07/8.05 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s7) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1664,plain,
% 12.07/8.05 ((node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8))) <=> (node2(c_bit1, s7) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1665,plain,
% 12.07/8.05 (((~![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)))) | (node2(c_bit1, s7) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8))))),
% 12.07/8.05 inference(monotonicity,[status(thm)],[1664])).
% 12.07/8.05 tff(1666,plain,
% 12.07/8.05 (((~![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)))) | node2(c_bit1, s7) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8)))),
% 12.07/8.05 inference(transitivity,[status(thm)],[1665, 1663])).
% 12.07/8.05 tff(1667,plain,
% 12.07/8.05 ((~![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)))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1668,plain,
% 12.07/8.05 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s7) | (~m_counter_cell_v_value(c_bit1, s8)) | (~node3(c_bit1, s7, s8))),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 12.07/8.05 tff(1669,plain,
% 12.07/8.05 (~m_counter_cell_v_value(c_bit1, s8)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1668, 141, 1662, 1419])).
% 12.07/8.05 tff(1670,plain,
% 12.07/8.05 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(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)))) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1671,plain,
% 12.07/8.05 ((m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8))) <=> ((~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.05 tff(1672,plain,
% 12.07/8.05 (((~![I0: $i, X: $i] : (m_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)))) | ((~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8)))),
% 12.07/8.05 inference(monotonicity,[status(thm)],[1671])).
% 12.07/8.05 tff(1673,plain,
% 12.07/8.05 (((~![I0: $i, X: $i] : (m_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)))) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8))),
% 12.07/8.05 inference(transitivity,[status(thm)],[1672, 1670])).
% 12.07/8.05 tff(1674,plain,
% 12.07/8.05 ((~![I0: $i, X: $i] : (m_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)))),
% 12.07/8.05 inference(quant_inst,[status(thm)],[])).
% 12.07/8.05 tff(1675,plain,
% 12.07/8.05 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8)),
% 12.07/8.05 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 12.07/8.05 tff(1676,plain,
% 12.07/8.05 ((~node2(c_bit1, s8)) | m_counter_cell_v_carry_in(c_bit1, s8)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1675, 1449, 1669])).
% 12.07/8.05 tff(1677,plain,
% 12.07/8.05 (~node2(c_bit1, s8)),
% 12.07/8.05 inference(unit_resolution,[status(thm)],[1676, 1415])).
% 12.07/8.05 tff(1678,plain,
% 12.07/8.05 (((~![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))),
% 12.07/8.05 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1679,plain,
% 12.07/8.06 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit1, s8, s9))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1680,plain,
% 12.07/8.06 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit1, s8, s9)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1679, 1678])).
% 12.07/8.06 tff(1681,plain,
% 12.07/8.06 (node3(c_bit1, s8, s9)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1680, 21, 315])).
% 12.07/8.06 tff(1682,plain,
% 12.07/8.06 (((~![Y: $i, 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)) | (~node3(c_bit1, s8, s9)) | node2(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, s9)) | (~node3(c_bit1, s8, s9)) | node2(c_bit1, s8))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1683,plain,
% 12.07/8.06 ((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)) | (~node3(c_bit1, s8, s9)) | node2(c_bit1, s8))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1684,plain,
% 12.07/8.06 (((~![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)) | (~node3(c_bit1, s8, s9)) | node2(c_bit1, s8)))),
% 12.07/8.06 inference(monotonicity,[status(thm)],[1683])).
% 12.07/8.06 tff(1685,plain,
% 12.07/8.06 (((~![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)) | (~node3(c_bit1, s8, s9)) | node2(c_bit1, s8))),
% 12.07/8.06 inference(transitivity,[status(thm)],[1684, 1682])).
% 12.07/8.06 tff(1686,plain,
% 12.07/8.06 ((~![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)))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1687,plain,
% 12.07/8.06 ((~![Y: $i, 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)) | (~node3(c_bit1, s8, s9)) | node2(c_bit1, s8)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 12.07/8.06 tff(1688,plain,
% 12.07/8.06 ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1687, 141, 1681])).
% 12.07/8.06 tff(1689,plain,
% 12.07/8.06 (~m_counter_cell_v_value(c_bit1, s9)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1688, 1677])).
% 12.07/8.06 tff(1690,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1691,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1692,plain,
% 12.07/8.06 ((~![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)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 12.07/8.06 tff(1693,plain,
% 12.07/8.06 ((~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1692, 1368, 329])).
% 12.07/8.06 tff(1694,plain,
% 12.07/8.06 (m_counter_cell_v_carry_out(c_bit0, s9)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1693, 327])).
% 12.07/8.06 tff(1695,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1696,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1697,plain,
% 12.07/8.06 ((~![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)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 12.07/8.06 tff(1698,plain,
% 12.07/8.06 (m_counter_cell_v_carry_in(c_bit1, s9)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1697, 1383, 1694])).
% 12.07/8.06 tff(1699,plain,
% 12.07/8.06 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1700,plain,
% 12.07/8.06 (((~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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1701,plain,
% 12.07/8.06 (((~![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))))),
% 12.07/8.06 inference(monotonicity,[status(thm)],[1700])).
% 12.07/8.06 tff(1702,plain,
% 12.07/8.06 (((~![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)))),
% 12.07/8.06 inference(transitivity,[status(thm)],[1701, 1699])).
% 12.07/8.06 tff(1703,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1704,plain,
% 12.07/8.06 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 12.07/8.06 tff(1705,plain,
% 12.07/8.06 (m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9))),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1704, 77, 1698])).
% 12.07/8.06 tff(1706,plain,
% 12.07/8.06 (~node1(c_bit1, s9)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1705, 1689])).
% 12.07/8.06 tff(1707,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1708,plain,
% 12.07/8.06 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit1, s9, s10))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1709,plain,
% 12.07/8.06 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit1, s9, s10)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 12.07/8.06 tff(1710,plain,
% 12.07/8.06 (node3(c_bit1, s9, s10)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1709, 21, 341])).
% 12.07/8.06 tff(1711,plain,
% 12.07/8.06 (((~![Y: $i, 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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1712,plain,
% 12.07/8.06 ((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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1713,plain,
% 12.07/8.06 (((~![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))))),
% 12.07/8.06 inference(monotonicity,[status(thm)],[1712])).
% 12.07/8.06 tff(1714,plain,
% 12.07/8.06 (((~![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)))),
% 12.07/8.06 inference(transitivity,[status(thm)],[1713, 1711])).
% 12.07/8.06 tff(1715,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1716,plain,
% 12.07/8.06 ((~![Y: $i, 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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 12.07/8.06 tff(1717,plain,
% 12.07/8.06 (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1716, 106, 1710])).
% 12.07/8.06 tff(1718,plain,
% 12.07/8.06 (m_counter_cell_v_value(c_bit1, s10)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1717, 1706])).
% 12.07/8.06 tff(1719,plain,
% 12.07/8.06 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1720,plain,
% 12.07/8.06 (((~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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1721,plain,
% 12.07/8.06 (((~![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))))),
% 12.07/8.06 inference(monotonicity,[status(thm)],[1720])).
% 12.07/8.06 tff(1722,plain,
% 12.07/8.06 (((~![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)))),
% 12.07/8.06 inference(transitivity,[status(thm)],[1721, 1719])).
% 12.07/8.06 tff(1723,plain,
% 12.07/8.06 ((~![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)))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1724,plain,
% 12.07/8.06 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 12.07/8.06 tff(1725,plain,
% 12.07/8.06 (~node1(c_bit1, s10)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1724, 1517, 1718, 1403])).
% 12.07/8.06 tff(1726,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1727,plain,
% 12.07/8.06 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit1, s10, s11))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1728,plain,
% 12.07/8.06 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit1, s10, s11)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 12.07/8.06 tff(1729,plain,
% 12.07/8.06 (node3(c_bit1, s10, s11)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1728, 21, 370])).
% 12.07/8.06 tff(1730,plain,
% 12.07/8.06 (((~![Y: $i, 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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1731,plain,
% 12.07/8.06 ((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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1732,plain,
% 12.07/8.06 (((~![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))))),
% 12.07/8.06 inference(monotonicity,[status(thm)],[1731])).
% 12.07/8.06 tff(1733,plain,
% 12.07/8.06 (((~![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)))),
% 12.07/8.06 inference(transitivity,[status(thm)],[1732, 1730])).
% 12.07/8.06 tff(1734,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1735,plain,
% 12.07/8.06 ((~![Y: $i, 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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1734, 1733])).
% 12.07/8.06 tff(1736,plain,
% 12.07/8.06 (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1735, 106, 1729])).
% 12.07/8.06 tff(1737,plain,
% 12.07/8.06 (m_counter_cell_v_value(c_bit1, s11)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1736, 1725])).
% 12.07/8.06 tff(1738,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1739,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1740,plain,
% 12.07/8.06 ((~![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)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1739, 1738])).
% 12.07/8.06 tff(1741,plain,
% 12.07/8.06 ((~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1740, 1368, 384])).
% 12.07/8.06 tff(1742,plain,
% 12.07/8.06 (m_counter_cell_v_carry_out(c_bit0, s11)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1741, 382])).
% 12.07/8.06 tff(1743,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1744,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1745,plain,
% 12.07/8.06 ((~![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)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1744, 1743])).
% 12.07/8.06 tff(1746,plain,
% 12.07/8.06 (m_counter_cell_v_carry_in(c_bit1, s11)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1745, 1383, 1742])).
% 12.07/8.06 tff(1747,plain,
% 12.07/8.06 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1748,plain,
% 12.07/8.06 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1749,plain,
% 12.07/8.06 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 12.07/8.06 tff(1750,plain,
% 12.07/8.06 ((~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11))),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1749, 126, 1746])).
% 12.07/8.06 tff(1751,plain,
% 12.07/8.06 (~node2(c_bit1, s11)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1750, 1737])).
% 12.07/8.06 tff(1752,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1753,plain,
% 12.07/8.06 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit1, s11, s12))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1754,plain,
% 12.07/8.06 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit1, s11, s12)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 12.07/8.06 tff(1755,plain,
% 12.07/8.06 (node3(c_bit1, s11, s12)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1754, 21, 396])).
% 12.07/8.06 tff(1756,plain,
% 12.07/8.06 (((~![Y: $i, 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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1757,plain,
% 12.07/8.06 ((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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1758,plain,
% 12.07/8.06 (((~![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))))),
% 12.07/8.06 inference(monotonicity,[status(thm)],[1757])).
% 12.07/8.06 tff(1759,plain,
% 12.07/8.06 (((~![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)))),
% 12.07/8.06 inference(transitivity,[status(thm)],[1758, 1756])).
% 12.07/8.06 tff(1760,plain,
% 12.07/8.06 ((~![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)))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1761,plain,
% 12.07/8.06 ((~![Y: $i, 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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 12.07/8.06 tff(1762,plain,
% 12.07/8.06 ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1761, 141, 1755])).
% 12.07/8.06 tff(1763,plain,
% 12.07/8.06 (~m_counter_cell_v_value(c_bit1, s12)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1762, 1751])).
% 12.07/8.06 tff(1764,plain,
% 12.07/8.06 (((~![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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1765,plain,
% 12.07/8.06 ((~![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)))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1766,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 12.07/8.06 tff(1767,plain,
% 12.07/8.06 (~node4(c_bit0, s12)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1766, 1221, 408])).
% 12.07/8.06 tff(1768,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1769,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1770,plain,
% 12.07/8.06 ((~![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)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1769, 1768])).
% 12.07/8.06 tff(1771,plain,
% 12.07/8.06 (~m_counter_cell_v_carry_out(c_bit0, s12)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1770, 1235, 1767])).
% 12.07/8.06 tff(1772,plain,
% 12.07/8.06 (((~![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))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1773,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1774,plain,
% 12.07/8.06 ((~![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)),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 12.07/8.06 tff(1775,plain,
% 12.07/8.06 (~m_counter_cell_v_carry_in(c_bit1, s12)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1774, 1249, 1771])).
% 12.07/8.06 tff(1776,plain,
% 12.07/8.06 (((~![I0: $i, X: $i] : (m_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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1777,plain,
% 12.07/8.06 ((~![I0: $i, X: $i] : (m_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)))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1778,plain,
% 12.07/8.06 ((~![I0: $i, X: $i] : (m_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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 12.07/8.06 tff(1779,plain,
% 12.07/8.06 (m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12))),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1778, 1449, 1775])).
% 12.07/8.06 tff(1780,plain,
% 12.07/8.06 (~node2(c_bit1, s12)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1779, 1763])).
% 12.07/8.06 tff(1781,plain,
% 12.07/8.06 (((~![Y: $i, 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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1782,plain,
% 12.07/8.06 ((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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1783,plain,
% 12.07/8.06 (((~![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))))),
% 12.07/8.06 inference(monotonicity,[status(thm)],[1782])).
% 12.07/8.06 tff(1784,plain,
% 12.07/8.06 (((~![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)))),
% 12.07/8.06 inference(transitivity,[status(thm)],[1783, 1781])).
% 12.07/8.06 tff(1785,plain,
% 12.07/8.06 ((~![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)))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.06 tff(1786,plain,
% 12.07/8.06 ((~![Y: $i, 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))),
% 12.07/8.06 inference(modus_ponens,[status(thm)],[1785, 1784])).
% 12.07/8.06 tff(1787,plain,
% 12.07/8.06 (~m_counter_cell_v_value(c_bit1, s13)),
% 12.07/8.06 inference(unit_resolution,[status(thm)],[1786, 141, 1780, 1391])).
% 12.07/8.06 tff(1788,plain,
% 12.07/8.06 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1789,plain,
% 12.07/8.06 (((~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)))),
% 12.07/8.06 inference(rewrite,[status(thm)],[])).
% 12.07/8.06 tff(1790,plain,
% 12.07/8.06 (((~![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))))),
% 12.07/8.06 inference(monotonicity,[status(thm)],[1789])).
% 12.07/8.06 tff(1791,plain,
% 12.07/8.06 (((~![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)))),
% 12.07/8.06 inference(transitivity,[status(thm)],[1790, 1788])).
% 12.07/8.06 tff(1792,plain,
% 12.07/8.06 ((~![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))),
% 12.07/8.06 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1793,plain,
% 12.07/8.07 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 12.07/8.07 tff(1794,plain,
% 12.07/8.07 ((~m_counter_cell_v_carry_in(c_bit1, s13)) | (~node1(c_bit1, s13))),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1793, 77, 1787])).
% 12.07/8.07 tff(1795,plain,
% 12.07/8.07 (~node1(c_bit1, s13)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1794, 1387])).
% 12.07/8.07 tff(1796,plain,
% 12.07/8.07 (((~![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))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1797,plain,
% 12.07/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit1, s13, s14))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1798,plain,
% 12.07/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit1, s13, s14)),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1797, 1796])).
% 12.07/8.07 tff(1799,plain,
% 12.07/8.07 (node3(c_bit1, s13, s14)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1798, 21, 439])).
% 12.07/8.07 tff(1800,plain,
% 12.07/8.07 (((~![Y: $i, 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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1801,plain,
% 12.07/8.07 ((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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1802,plain,
% 12.07/8.07 (((~![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))))),
% 12.07/8.07 inference(monotonicity,[status(thm)],[1801])).
% 12.07/8.07 tff(1803,plain,
% 12.07/8.07 (((~![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)))),
% 12.07/8.07 inference(transitivity,[status(thm)],[1802, 1800])).
% 12.07/8.07 tff(1804,plain,
% 12.07/8.07 ((~![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))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1805,plain,
% 12.07/8.07 ((~![Y: $i, 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))),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 12.07/8.07 tff(1806,plain,
% 12.07/8.07 (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1805, 106, 1799])).
% 12.07/8.07 tff(1807,plain,
% 12.07/8.07 (m_counter_cell_v_value(c_bit1, s14)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1806, 1795])).
% 12.07/8.07 tff(1808,plain,
% 12.07/8.07 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1809,plain,
% 12.07/8.07 (((~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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1810,plain,
% 12.07/8.07 (((~![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))))),
% 12.07/8.07 inference(monotonicity,[status(thm)],[1809])).
% 12.07/8.07 tff(1811,plain,
% 12.07/8.07 (((~![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)))),
% 12.07/8.07 inference(transitivity,[status(thm)],[1810, 1808])).
% 12.07/8.07 tff(1812,plain,
% 12.07/8.07 ((~![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)))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1813,plain,
% 12.07/8.07 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1812, 1811])).
% 12.07/8.07 tff(1814,plain,
% 12.07/8.07 (m_counter_cell_v_carry_in(c_bit1, s14) | (~node1(c_bit1, s14))),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1813, 1517, 1807])).
% 12.07/8.07 tff(1815,plain,
% 12.07/8.07 (~node1(c_bit1, s14)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1814, 1358])).
% 12.07/8.07 tff(1816,plain,
% 12.07/8.07 (((~![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))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1817,plain,
% 12.07/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit1, s14, s15))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1818,plain,
% 12.07/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit1, s14, s15)),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 12.07/8.07 tff(1819,plain,
% 12.07/8.07 (node3(c_bit1, s14, s15)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1818, 21, 468])).
% 12.07/8.07 tff(1820,plain,
% 12.07/8.07 (((~![Y: $i, 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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1821,plain,
% 12.07/8.07 ((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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1822,plain,
% 12.07/8.07 (((~![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))))),
% 12.07/8.07 inference(monotonicity,[status(thm)],[1821])).
% 12.07/8.07 tff(1823,plain,
% 12.07/8.07 (((~![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)))),
% 12.07/8.07 inference(transitivity,[status(thm)],[1822, 1820])).
% 12.07/8.07 tff(1824,plain,
% 12.07/8.07 ((~![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))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1825,plain,
% 12.07/8.07 ((~![Y: $i, 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))),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 12.07/8.07 tff(1826,plain,
% 12.07/8.07 (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1825, 106, 1819])).
% 12.07/8.07 tff(1827,plain,
% 12.07/8.07 (m_counter_cell_v_value(c_bit1, s15)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1826, 1815])).
% 12.07/8.07 tff(1828,plain,
% 12.07/8.07 (((~![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))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1829,plain,
% 12.07/8.07 ((~![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))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1830,plain,
% 12.07/8.07 ((~![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)),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 12.07/8.07 tff(1831,plain,
% 12.07/8.07 ((~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1830, 1368, 482])).
% 12.07/8.07 tff(1832,plain,
% 12.07/8.07 (m_counter_cell_v_carry_out(c_bit0, s15)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1831, 480])).
% 12.07/8.07 tff(1833,plain,
% 12.07/8.07 (((~![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))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1834,plain,
% 12.07/8.07 ((~![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))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1835,plain,
% 12.07/8.07 ((~![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)),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1834, 1833])).
% 12.07/8.07 tff(1836,plain,
% 12.07/8.07 (m_counter_cell_v_carry_in(c_bit1, s15)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1835, 1383, 1832])).
% 12.07/8.07 tff(1837,plain,
% 12.07/8.07 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1838,plain,
% 12.07/8.07 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1839,plain,
% 12.07/8.07 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1838, 1837])).
% 12.07/8.07 tff(1840,plain,
% 12.07/8.07 ((~m_counter_cell_v_value(c_bit1, s15)) | (~node2(c_bit1, s15))),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1839, 126, 1836])).
% 12.07/8.07 tff(1841,plain,
% 12.07/8.07 (~node2(c_bit1, s15)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1840, 1827])).
% 12.07/8.07 tff(1842,plain,
% 12.07/8.07 (((~![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))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1843,plain,
% 12.07/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit1, s15, s16))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1844,plain,
% 12.07/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit1, s15, s16)),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 12.07/8.07 tff(1845,plain,
% 12.07/8.07 (node3(c_bit1, s15, s16)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1844, 21, 494])).
% 12.07/8.07 tff(1846,plain,
% 12.07/8.07 (((~![Y: $i, 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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1847,plain,
% 12.07/8.07 ((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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1848,plain,
% 12.07/8.07 (((~![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))))),
% 12.07/8.07 inference(monotonicity,[status(thm)],[1847])).
% 12.07/8.07 tff(1849,plain,
% 12.07/8.07 (((~![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)))),
% 12.07/8.07 inference(transitivity,[status(thm)],[1848, 1846])).
% 12.07/8.07 tff(1850,plain,
% 12.07/8.07 ((~![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)))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1851,plain,
% 12.07/8.07 ((~![Y: $i, 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))),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1850, 1849])).
% 12.07/8.07 tff(1852,plain,
% 12.07/8.07 ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1851, 141, 1845])).
% 12.07/8.07 tff(1853,plain,
% 12.07/8.07 (~m_counter_cell_v_value(c_bit1, s16)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1852, 1841])).
% 12.07/8.07 tff(1854,plain,
% 12.07/8.07 (((~![I0: $i, X: $i] : (m_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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1855,plain,
% 12.07/8.07 ((~![I0: $i, X: $i] : (m_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)))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1856,plain,
% 12.07/8.07 ((~![I0: $i, X: $i] : (m_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))),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 12.07/8.07 tff(1857,plain,
% 12.07/8.07 (~node2(c_bit1, s16)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1856, 1449, 1853, 1346])).
% 12.07/8.07 tff(1858,plain,
% 12.07/8.07 (((~![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))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1859,plain,
% 12.07/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit1, s16, s17))),
% 12.07/8.07 inference(quant_inst,[status(thm)],[])).
% 12.07/8.07 tff(1860,plain,
% 12.07/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit1, s16, s17)),
% 12.07/8.07 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 12.07/8.07 tff(1861,plain,
% 12.07/8.07 (node3(c_bit1, s16, s17)),
% 12.07/8.07 inference(unit_resolution,[status(thm)],[1860, 21, 523])).
% 12.07/8.07 tff(1862,plain,
% 12.07/8.07 (((~![Y: $i, 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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1863,plain,
% 12.07/8.07 ((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)))),
% 12.07/8.07 inference(rewrite,[status(thm)],[])).
% 12.07/8.07 tff(1864,plain,
% 12.07/8.07 (((~![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))))),
% 12.07/8.07 inference(monotonicity,[status(thm)],[1863])).
% 12.07/8.07 tff(1865,plain,
% 12.07/8.07 (((~![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)))),
% 12.07/8.07 inference(transitivity,[status(thm)],[1864, 1862])).
% 12.07/8.07 tff(1866,plain,
% 12.07/8.07 ((~![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)))),
% 12.14/8.07 inference(quant_inst,[status(thm)],[])).
% 12.14/8.07 tff(1867,plain,
% 12.14/8.07 ((~![Y: $i, 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))),
% 12.14/8.07 inference(modus_ponens,[status(thm)],[1866, 1865])).
% 12.14/8.07 tff(1868,plain,
% 12.14/8.07 ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16)),
% 12.14/8.07 inference(unit_resolution,[status(thm)],[1867, 141, 1861])).
% 12.14/8.07 tff(1869,plain,
% 12.14/8.07 (~m_counter_cell_v_value(c_bit1, s17)),
% 12.14/8.07 inference(unit_resolution,[status(thm)],[1868, 1857])).
% 12.14/8.07 tff(1870,plain,
% 12.14/8.07 (((~![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))),
% 12.14/8.07 inference(rewrite,[status(thm)],[])).
% 12.14/8.07 tff(1871,plain,
% 12.14/8.07 ((~![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))),
% 12.14/8.07 inference(quant_inst,[status(thm)],[])).
% 12.14/8.07 tff(1872,plain,
% 12.14/8.07 ((~![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)),
% 12.14/8.07 inference(modus_ponens,[status(thm)],[1871, 1870])).
% 12.14/8.07 tff(1873,plain,
% 12.14/8.07 ((~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17)),
% 12.14/8.07 inference(unit_resolution,[status(thm)],[1872, 1368, 539])).
% 12.14/8.07 tff(1874,plain,
% 12.14/8.07 (m_counter_cell_v_carry_out(c_bit0, s17)),
% 12.14/8.07 inference(unit_resolution,[status(thm)],[1873, 535])).
% 12.14/8.07 tff(1875,plain,
% 12.14/8.07 (((~![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))),
% 12.14/8.07 inference(rewrite,[status(thm)],[])).
% 12.14/8.07 tff(1876,plain,
% 12.14/8.07 ((~![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))),
% 12.14/8.07 inference(quant_inst,[status(thm)],[])).
% 12.14/8.07 tff(1877,plain,
% 12.14/8.07 ((~![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)),
% 12.14/8.07 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 12.14/8.07 tff(1878,plain,
% 12.14/8.07 (m_counter_cell_v_carry_in(c_bit1, s17)),
% 12.14/8.07 inference(unit_resolution,[status(thm)],[1877, 1383, 1874])).
% 12.14/8.07 tff(1879,plain,
% 12.14/8.07 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.14/8.07 inference(rewrite,[status(thm)],[])).
% 12.14/8.07 tff(1880,plain,
% 12.14/8.07 (((~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)))),
% 12.15/8.07 inference(rewrite,[status(thm)],[])).
% 12.15/8.07 tff(1881,plain,
% 12.15/8.07 (((~![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))))),
% 12.15/8.07 inference(monotonicity,[status(thm)],[1880])).
% 12.15/8.07 tff(1882,plain,
% 12.15/8.07 (((~![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)))),
% 12.15/8.07 inference(transitivity,[status(thm)],[1881, 1879])).
% 12.15/8.07 tff(1883,plain,
% 12.15/8.07 ((~![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))),
% 12.15/8.07 inference(quant_inst,[status(thm)],[])).
% 12.15/8.07 tff(1884,plain,
% 12.15/8.07 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.15/8.07 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 12.15/8.07 tff(1885,plain,
% 12.15/8.07 (m_counter_cell_v_value(c_bit1, s17) | (~node1(c_bit1, s17))),
% 12.15/8.07 inference(unit_resolution,[status(thm)],[1884, 77, 1878])).
% 12.15/8.07 tff(1886,plain,
% 12.15/8.07 (~node1(c_bit1, s17)),
% 12.15/8.07 inference(unit_resolution,[status(thm)],[1885, 1869])).
% 12.15/8.07 tff(1887,plain,
% 12.15/8.07 (((~![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))),
% 12.15/8.07 inference(rewrite,[status(thm)],[])).
% 12.15/8.07 tff(1888,plain,
% 12.15/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit1, s17, s18))),
% 12.15/8.07 inference(quant_inst,[status(thm)],[])).
% 12.15/8.07 tff(1889,plain,
% 12.15/8.07 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit1, s17, s18)),
% 12.15/8.07 inference(modus_ponens,[status(thm)],[1888, 1887])).
% 12.15/8.07 tff(1890,plain,
% 12.15/8.07 (node3(c_bit1, s17, s18)),
% 12.15/8.07 inference(unit_resolution,[status(thm)],[1889, 21, 551])).
% 12.15/8.07 tff(1891,plain,
% 12.15/8.07 (((~![Y: $i, 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)))),
% 12.15/8.07 inference(rewrite,[status(thm)],[])).
% 12.15/8.07 tff(1892,plain,
% 12.15/8.07 ((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)))),
% 12.15/8.07 inference(rewrite,[status(thm)],[])).
% 12.15/8.07 tff(1893,plain,
% 12.15/8.07 (((~![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))))),
% 12.15/8.07 inference(monotonicity,[status(thm)],[1892])).
% 12.15/8.07 tff(1894,plain,
% 12.15/8.07 (((~![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)))),
% 12.15/8.08 inference(transitivity,[status(thm)],[1893, 1891])).
% 12.15/8.08 tff(1895,plain,
% 12.15/8.08 ((~![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))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1896,plain,
% 12.15/8.08 ((~![Y: $i, 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))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1895, 1894])).
% 12.15/8.08 tff(1897,plain,
% 12.15/8.08 (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1896, 106, 1890])).
% 12.15/8.08 tff(1898,plain,
% 12.15/8.08 (m_counter_cell_v_value(c_bit1, s18)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1897, 1886])).
% 12.15/8.08 tff(1899,plain,
% 12.15/8.08 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1900,plain,
% 12.15/8.08 (((~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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1901,plain,
% 12.15/8.08 (((~![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))))),
% 12.15/8.08 inference(monotonicity,[status(thm)],[1900])).
% 12.15/8.08 tff(1902,plain,
% 12.15/8.08 (((~![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)))),
% 12.15/8.08 inference(transitivity,[status(thm)],[1901, 1899])).
% 12.15/8.08 tff(1903,plain,
% 12.15/8.08 ((~![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)))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1904,plain,
% 12.15/8.08 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 12.15/8.08 tff(1905,plain,
% 12.15/8.08 (m_counter_cell_v_carry_in(c_bit1, s18) | (~node1(c_bit1, s18))),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1904, 1517, 1898])).
% 12.15/8.08 tff(1906,plain,
% 12.15/8.08 (~node1(c_bit1, s18)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1905, 1334])).
% 12.15/8.08 tff(1907,plain,
% 12.15/8.08 (((~![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))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1908,plain,
% 12.15/8.08 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit1, s18, s19))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1909,plain,
% 12.15/8.08 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit1, s18, s19)),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 12.15/8.08 tff(1910,plain,
% 12.15/8.08 (node3(c_bit1, s18, s19)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1909, 21, 582])).
% 12.15/8.08 tff(1911,plain,
% 12.15/8.08 (((~![Y: $i, 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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1912,plain,
% 12.15/8.08 ((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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1913,plain,
% 12.15/8.08 (((~![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))))),
% 12.15/8.08 inference(monotonicity,[status(thm)],[1912])).
% 12.15/8.08 tff(1914,plain,
% 12.15/8.08 (((~![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)))),
% 12.15/8.08 inference(transitivity,[status(thm)],[1913, 1911])).
% 12.15/8.08 tff(1915,plain,
% 12.15/8.08 ((~![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))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1916,plain,
% 12.15/8.08 ((~![Y: $i, 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))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1915, 1914])).
% 12.15/8.08 tff(1917,plain,
% 12.15/8.08 (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1916, 106, 1910])).
% 12.15/8.08 tff(1918,plain,
% 12.15/8.08 (m_counter_cell_v_value(c_bit1, s19)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1917, 1906])).
% 12.15/8.08 tff(1919,plain,
% 12.15/8.08 (((~![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))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1920,plain,
% 12.15/8.08 ((~![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))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1921,plain,
% 12.15/8.08 ((~![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)),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1920, 1919])).
% 12.15/8.08 tff(1922,plain,
% 12.15/8.08 ((~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1921, 1368, 598])).
% 12.15/8.08 tff(1923,plain,
% 12.15/8.08 (m_counter_cell_v_carry_out(c_bit0, s19)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1922, 594])).
% 12.15/8.08 tff(1924,plain,
% 12.15/8.08 (((~![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))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1925,plain,
% 12.15/8.08 ((~![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))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1926,plain,
% 12.15/8.08 ((~![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)),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 12.15/8.08 tff(1927,plain,
% 12.15/8.08 (m_counter_cell_v_carry_in(c_bit1, s19)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1926, 1383, 1923])).
% 12.15/8.08 tff(1928,plain,
% 12.15/8.08 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1929,plain,
% 12.15/8.08 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1930,plain,
% 12.15/8.08 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1929, 1928])).
% 12.15/8.08 tff(1931,plain,
% 12.15/8.08 ((~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19))),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1930, 126, 1927])).
% 12.15/8.08 tff(1932,plain,
% 12.15/8.08 (~node2(c_bit1, s19)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1931, 1918])).
% 12.15/8.08 tff(1933,plain,
% 12.15/8.08 (((~![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))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1934,plain,
% 12.15/8.08 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit1, s19, s20))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1935,plain,
% 12.15/8.08 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit1, s19, s20)),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 12.15/8.08 tff(1936,plain,
% 12.15/8.08 (node3(c_bit1, s19, s20)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1935, 21, 610])).
% 12.15/8.08 tff(1937,plain,
% 12.15/8.08 (((~![Y: $i, 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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1938,plain,
% 12.15/8.08 ((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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1939,plain,
% 12.15/8.08 (((~![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))))),
% 12.15/8.08 inference(monotonicity,[status(thm)],[1938])).
% 12.15/8.08 tff(1940,plain,
% 12.15/8.08 (((~![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)))),
% 12.15/8.08 inference(transitivity,[status(thm)],[1939, 1937])).
% 12.15/8.08 tff(1941,plain,
% 12.15/8.08 ((~![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)))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1942,plain,
% 12.15/8.08 ((~![Y: $i, 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))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1941, 1940])).
% 12.15/8.08 tff(1943,plain,
% 12.15/8.08 ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1942, 141, 1936])).
% 12.15/8.08 tff(1944,plain,
% 12.15/8.08 (~m_counter_cell_v_value(c_bit1, s20)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1943, 1932])).
% 12.15/8.08 tff(1945,plain,
% 12.15/8.08 (((~![I0: $i, X: $i] : (m_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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1946,plain,
% 12.15/8.08 ((~![I0: $i, X: $i] : (m_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)))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1947,plain,
% 12.15/8.08 ((~![I0: $i, X: $i] : (m_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))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 12.15/8.08 tff(1948,plain,
% 12.15/8.08 (m_counter_cell_v_carry_in(c_bit1, s20) | (~node2(c_bit1, s20))),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1947, 1449, 1944])).
% 12.15/8.08 tff(1949,plain,
% 12.15/8.08 (~node2(c_bit1, s20)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1948, 1316])).
% 12.15/8.08 tff(1950,plain,
% 12.15/8.08 (((~![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))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1951,plain,
% 12.15/8.08 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit1, s20, s21))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1952,plain,
% 12.15/8.08 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit1, s20, s21)),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 12.15/8.08 tff(1953,plain,
% 12.15/8.08 (node3(c_bit1, s20, s21)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1952, 21, 641])).
% 12.15/8.08 tff(1954,plain,
% 12.15/8.08 (((~![Y: $i, 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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1955,plain,
% 12.15/8.08 ((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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1956,plain,
% 12.15/8.08 (((~![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))))),
% 12.15/8.08 inference(monotonicity,[status(thm)],[1955])).
% 12.15/8.08 tff(1957,plain,
% 12.15/8.08 (((~![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)))),
% 12.15/8.08 inference(transitivity,[status(thm)],[1956, 1954])).
% 12.15/8.08 tff(1958,plain,
% 12.15/8.08 ((~![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)))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1959,plain,
% 12.15/8.08 ((~![Y: $i, 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))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 12.15/8.08 tff(1960,plain,
% 12.15/8.08 ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1959, 141, 1953])).
% 12.15/8.08 tff(1961,plain,
% 12.15/8.08 (~m_counter_cell_v_value(c_bit1, s21)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1960, 1949])).
% 12.15/8.08 tff(1962,plain,
% 12.15/8.08 (((~![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))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1963,plain,
% 12.15/8.08 ((~![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))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1964,plain,
% 12.15/8.08 ((~![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)),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1963, 1962])).
% 12.15/8.08 tff(1965,plain,
% 12.15/8.08 ((~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1964, 1368, 657])).
% 12.15/8.08 tff(1966,plain,
% 12.15/8.08 (m_counter_cell_v_carry_out(c_bit0, s21)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1965, 653])).
% 12.15/8.08 tff(1967,plain,
% 12.15/8.08 (((~![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))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1968,plain,
% 12.15/8.08 ((~![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))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1969,plain,
% 12.15/8.08 ((~![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)),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1968, 1967])).
% 12.15/8.08 tff(1970,plain,
% 12.15/8.08 (m_counter_cell_v_carry_in(c_bit1, s21)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1969, 1383, 1966])).
% 12.15/8.08 tff(1971,assumption,(node1(c_bit1, s21)), introduced(assumption)).
% 12.15/8.08 tff(1972,assumption,(~m_counter_cell_v_value(c_bit1, s21)), introduced(assumption)).
% 12.15/8.08 tff(1973,plain,
% 12.15/8.08 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1974,plain,
% 12.15/8.08 (((~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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1975,plain,
% 12.15/8.08 (((~![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))))),
% 12.15/8.08 inference(monotonicity,[status(thm)],[1974])).
% 12.15/8.08 tff(1976,plain,
% 12.15/8.08 (((~![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)))),
% 12.15/8.08 inference(transitivity,[status(thm)],[1975, 1973])).
% 12.15/8.08 tff(1977,plain,
% 12.15/8.08 ((~![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))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1978,plain,
% 12.15/8.08 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 12.15/8.08 tff(1979,plain,
% 12.15/8.08 ($false),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1978, 77, 1972, 1971, 1970])).
% 12.15/8.08 tff(1980,plain,((~node1(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21)), inference(lemma,lemma(discharge,[]))).
% 12.15/8.08 tff(1981,plain,
% 12.15/8.08 (~node1(c_bit1, s21)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1980, 1961])).
% 12.15/8.08 tff(1982,plain,
% 12.15/8.08 (((~![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))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1983,plain,
% 12.15/8.08 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit1, s21, s22))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1984,plain,
% 12.15/8.08 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit1, s21, s22)),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 12.15/8.08 tff(1985,plain,
% 12.15/8.08 (node3(c_bit1, s21, s22)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1984, 21, 669])).
% 12.15/8.08 tff(1986,plain,
% 12.15/8.08 (((~![Y: $i, 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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1987,plain,
% 12.15/8.08 ((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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1988,plain,
% 12.15/8.08 (((~![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))))),
% 12.15/8.08 inference(monotonicity,[status(thm)],[1987])).
% 12.15/8.08 tff(1989,plain,
% 12.15/8.08 (((~![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)))),
% 12.15/8.08 inference(transitivity,[status(thm)],[1988, 1986])).
% 12.15/8.08 tff(1990,plain,
% 12.15/8.08 ((~![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))),
% 12.15/8.08 inference(quant_inst,[status(thm)],[])).
% 12.15/8.08 tff(1991,plain,
% 12.15/8.08 ((~![Y: $i, 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))),
% 12.15/8.08 inference(modus_ponens,[status(thm)],[1990, 1989])).
% 12.15/8.08 tff(1992,plain,
% 12.15/8.08 (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1991, 106, 1985])).
% 12.15/8.08 tff(1993,plain,
% 12.15/8.08 (m_counter_cell_v_value(c_bit1, s22)),
% 12.15/8.08 inference(unit_resolution,[status(thm)],[1992, 1981])).
% 12.15/8.08 tff(1994,plain,
% 12.15/8.08 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1995,plain,
% 12.15/8.08 (((~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)))),
% 12.15/8.08 inference(rewrite,[status(thm)],[])).
% 12.15/8.08 tff(1996,plain,
% 12.15/8.08 (((~![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))))),
% 12.15/8.08 inference(monotonicity,[status(thm)],[1995])).
% 12.15/8.08 tff(1997,plain,
% 12.15/8.08 (((~![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)))),
% 12.15/8.09 inference(transitivity,[status(thm)],[1996, 1994])).
% 12.15/8.09 tff(1998,plain,
% 12.15/8.09 ((~![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)))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(1999,plain,
% 12.15/8.09 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 12.15/8.09 tff(2000,plain,
% 12.15/8.09 (m_counter_cell_v_carry_in(c_bit1, s22) | (~node1(c_bit1, s22))),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[1999, 1517, 1993])).
% 12.15/8.09 tff(2001,plain,
% 12.15/8.09 (~node1(c_bit1, s22)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2000, 1294])).
% 12.15/8.09 tff(2002,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2003,plain,
% 12.15/8.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit1, s22, s23))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2004,plain,
% 12.15/8.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit1, s22, s23)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 12.15/8.09 tff(2005,plain,
% 12.15/8.09 (node3(c_bit1, s22, s23)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2004, 21, 700])).
% 12.15/8.09 tff(2006,plain,
% 12.15/8.09 (((~![Y: $i, 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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2007,plain,
% 12.15/8.09 ((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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2008,plain,
% 12.15/8.09 (((~![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))))),
% 12.15/8.09 inference(monotonicity,[status(thm)],[2007])).
% 12.15/8.09 tff(2009,plain,
% 12.15/8.09 (((~![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)))),
% 12.15/8.09 inference(transitivity,[status(thm)],[2008, 2006])).
% 12.15/8.09 tff(2010,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2011,plain,
% 12.15/8.09 ((~![Y: $i, 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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2010, 2009])).
% 12.15/8.09 tff(2012,plain,
% 12.15/8.09 (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2011, 106, 2005])).
% 12.15/8.09 tff(2013,plain,
% 12.15/8.09 (m_counter_cell_v_value(c_bit1, s23)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2012, 2001])).
% 12.15/8.09 tff(2014,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2015,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2016,plain,
% 12.15/8.09 ((~![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)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 12.15/8.09 tff(2017,plain,
% 12.15/8.09 ((~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2016, 1368, 716])).
% 12.15/8.09 tff(2018,plain,
% 12.15/8.09 (m_counter_cell_v_carry_out(c_bit0, s23)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2017, 712])).
% 12.15/8.09 tff(2019,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2020,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2021,plain,
% 12.15/8.09 ((~![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)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 12.15/8.09 tff(2022,plain,
% 12.15/8.09 (m_counter_cell_v_carry_in(c_bit1, s23)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2021, 1383, 2018])).
% 12.15/8.09 tff(2023,plain,
% 12.15/8.09 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2024,plain,
% 12.15/8.09 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2025,plain,
% 12.15/8.09 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 12.15/8.09 tff(2026,plain,
% 12.15/8.09 ((~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23))),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2025, 126, 2022])).
% 12.15/8.09 tff(2027,plain,
% 12.15/8.09 (~node2(c_bit1, s23)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2026, 2013])).
% 12.15/8.09 tff(2028,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2029,plain,
% 12.15/8.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit1, s23, s24))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2030,plain,
% 12.15/8.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit1, s23, s24)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 12.15/8.09 tff(2031,plain,
% 12.15/8.09 (node3(c_bit1, s23, s24)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2030, 21, 728])).
% 12.15/8.09 tff(2032,plain,
% 12.15/8.09 (((~![Y: $i, 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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2033,plain,
% 12.15/8.09 ((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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2034,plain,
% 12.15/8.09 (((~![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))))),
% 12.15/8.09 inference(monotonicity,[status(thm)],[2033])).
% 12.15/8.09 tff(2035,plain,
% 12.15/8.09 (((~![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)))),
% 12.15/8.09 inference(transitivity,[status(thm)],[2034, 2032])).
% 12.15/8.09 tff(2036,plain,
% 12.15/8.09 ((~![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)))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2037,plain,
% 12.15/8.09 ((~![Y: $i, 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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 12.15/8.09 tff(2038,plain,
% 12.15/8.09 ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2037, 141, 2031])).
% 12.15/8.09 tff(2039,plain,
% 12.15/8.09 (~m_counter_cell_v_value(c_bit1, s24)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2038, 2027])).
% 12.15/8.09 tff(2040,plain,
% 12.15/8.09 (((~![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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2041,plain,
% 12.15/8.09 ((~![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)))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2042,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2041, 2040])).
% 12.15/8.09 tff(2043,plain,
% 12.15/8.09 (~node4(c_bit0, s24)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2042, 1221, 740])).
% 12.15/8.09 tff(2044,assumption,(~node4(c_bit0, s24)), introduced(assumption)).
% 12.15/8.09 tff(2045,assumption,(m_counter_cell_v_carry_out(c_bit0, s24)), introduced(assumption)).
% 12.15/8.09 tff(2046,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2047,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2048,plain,
% 12.15/8.09 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 12.15/8.09 tff(2049,plain,
% 12.15/8.09 ($false),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2048, 1235, 2045, 2044])).
% 12.15/8.09 tff(2050,plain,((~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 12.15/8.09 tff(2051,plain,
% 12.15/8.09 (~m_counter_cell_v_carry_out(c_bit0, s24)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2050, 2043])).
% 12.15/8.09 tff(2052,assumption,(m_counter_cell_v_carry_in(c_bit1, s24)), introduced(assumption)).
% 12.15/8.09 tff(2053,assumption,(~m_counter_cell_v_carry_out(c_bit0, s24)), introduced(assumption)).
% 12.15/8.09 tff(2054,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2055,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2056,plain,
% 12.15/8.09 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 12.15/8.09 tff(2057,plain,
% 12.15/8.09 ($false),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2056, 1249, 2053, 2052])).
% 12.15/8.09 tff(2058,plain,(m_counter_cell_v_carry_out(c_bit0, s24) | (~m_counter_cell_v_carry_in(c_bit1, s24))), inference(lemma,lemma(discharge,[]))).
% 12.15/8.09 tff(2059,plain,
% 12.15/8.09 (~m_counter_cell_v_carry_in(c_bit1, s24)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2058, 2051])).
% 12.15/8.09 tff(2060,assumption,(node2(c_bit1, s24)), introduced(assumption)).
% 12.15/8.09 tff(2061,assumption,(~m_counter_cell_v_value(c_bit1, s24)), introduced(assumption)).
% 12.15/8.09 tff(2062,plain,
% 12.15/8.09 (((~![I0: $i, X: $i] : (m_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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2063,plain,
% 12.15/8.09 ((~![I0: $i, X: $i] : (m_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)))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2064,plain,
% 12.15/8.09 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s24) | m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 12.15/8.09 tff(2065,plain,
% 12.15/8.09 ($false),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2064, 1449, 2061, 2060, 2059])).
% 12.15/8.09 tff(2066,plain,((~node2(c_bit1, s24)) | m_counter_cell_v_value(c_bit1, s24)), inference(lemma,lemma(discharge,[]))).
% 12.15/8.09 tff(2067,plain,
% 12.15/8.09 (~node2(c_bit1, s24)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2066, 2039])).
% 12.15/8.09 tff(2068,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2069,plain,
% 12.15/8.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit1, s24, s25))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2070,plain,
% 12.15/8.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit1, s24, s25)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 12.15/8.09 tff(2071,plain,
% 12.15/8.09 (node3(c_bit1, s24, s25)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2070, 21, 759])).
% 12.15/8.09 tff(2072,plain,
% 12.15/8.09 (((~![Y: $i, 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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2073,plain,
% 12.15/8.09 ((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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2074,plain,
% 12.15/8.09 (((~![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))))),
% 12.15/8.09 inference(monotonicity,[status(thm)],[2073])).
% 12.15/8.09 tff(2075,plain,
% 12.15/8.09 (((~![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)))),
% 12.15/8.09 inference(transitivity,[status(thm)],[2074, 2072])).
% 12.15/8.09 tff(2076,plain,
% 12.15/8.09 ((~![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)))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2077,plain,
% 12.15/8.09 ((~![Y: $i, 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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 12.15/8.09 tff(2078,plain,
% 12.15/8.09 ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2077, 141, 2071])).
% 12.15/8.09 tff(2079,plain,
% 12.15/8.09 (~m_counter_cell_v_value(c_bit1, s25)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2078, 2067])).
% 12.15/8.09 tff(2080,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2081,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2082,plain,
% 12.15/8.09 ((~![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)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2081, 2080])).
% 12.15/8.09 tff(2083,plain,
% 12.15/8.09 ((~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2082, 1368, 775])).
% 12.15/8.09 tff(2084,plain,
% 12.15/8.09 (m_counter_cell_v_carry_out(c_bit0, s25)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2083, 771])).
% 12.15/8.09 tff(2085,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2086,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2087,plain,
% 12.15/8.09 ((~![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)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 12.15/8.09 tff(2088,plain,
% 12.15/8.09 (m_counter_cell_v_carry_in(c_bit1, s25)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2087, 1383, 2084])).
% 12.15/8.09 tff(2089,plain,
% 12.15/8.09 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2090,plain,
% 12.15/8.09 (((~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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2091,plain,
% 12.15/8.09 (((~![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))))),
% 12.15/8.09 inference(monotonicity,[status(thm)],[2090])).
% 12.15/8.09 tff(2092,plain,
% 12.15/8.09 (((~![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)))),
% 12.15/8.09 inference(transitivity,[status(thm)],[2091, 2089])).
% 12.15/8.09 tff(2093,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2094,plain,
% 12.15/8.09 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 12.15/8.09 tff(2095,plain,
% 12.15/8.09 (m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25))),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2094, 77, 2088])).
% 12.15/8.09 tff(2096,plain,
% 12.15/8.09 (~node1(c_bit1, s25)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2095, 2079])).
% 12.15/8.09 tff(2097,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2098,plain,
% 12.15/8.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit1, s25, s26))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2099,plain,
% 12.15/8.09 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit1, s25, s26)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 12.15/8.09 tff(2100,plain,
% 12.15/8.09 (node3(c_bit1, s25, s26)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2099, 21, 787])).
% 12.15/8.09 tff(2101,plain,
% 12.15/8.09 (((~![Y: $i, 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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2102,plain,
% 12.15/8.09 ((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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2103,plain,
% 12.15/8.09 (((~![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))))),
% 12.15/8.09 inference(monotonicity,[status(thm)],[2102])).
% 12.15/8.09 tff(2104,plain,
% 12.15/8.09 (((~![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)))),
% 12.15/8.09 inference(transitivity,[status(thm)],[2103, 2101])).
% 12.15/8.09 tff(2105,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2106,plain,
% 12.15/8.09 ((~![Y: $i, 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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2105, 2104])).
% 12.15/8.09 tff(2107,plain,
% 12.15/8.09 (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2106, 106, 2100])).
% 12.15/8.09 tff(2108,plain,
% 12.15/8.09 (m_counter_cell_v_value(c_bit1, s26)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2107, 2096])).
% 12.15/8.09 tff(2109,plain,
% 12.15/8.09 (((~![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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2110,plain,
% 12.15/8.09 ((~![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)))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2111,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2110, 2109])).
% 12.15/8.09 tff(2112,plain,
% 12.15/8.09 (~node4(c_bit0, s26)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2111, 1221, 799])).
% 12.15/8.09 tff(2113,assumption,(m_counter_cell_v_carry_out(c_bit0, s26)), introduced(assumption)).
% 12.15/8.09 tff(2114,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2115,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2116,plain,
% 12.15/8.09 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2115, 2114])).
% 12.15/8.09 tff(2117,plain,
% 12.15/8.09 ($false),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2116, 1235, 2113, 2112])).
% 12.15/8.09 tff(2118,plain,(~m_counter_cell_v_carry_out(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 12.15/8.09 tff(2119,assumption,(m_counter_cell_v_carry_in(c_bit1, s26)), introduced(assumption)).
% 12.15/8.09 tff(2120,assumption,(~m_counter_cell_v_carry_out(c_bit0, s26)), introduced(assumption)).
% 12.15/8.09 tff(2121,plain,
% 12.15/8.09 (((~![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))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2122,plain,
% 12.15/8.09 ((~![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))),
% 12.15/8.09 inference(quant_inst,[status(thm)],[])).
% 12.15/8.09 tff(2123,plain,
% 12.15/8.09 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26)),
% 12.15/8.09 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 12.15/8.09 tff(2124,plain,
% 12.15/8.09 ($false),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2123, 1249, 2120, 2119])).
% 12.15/8.09 tff(2125,plain,(m_counter_cell_v_carry_out(c_bit0, s26) | (~m_counter_cell_v_carry_in(c_bit1, s26))), inference(lemma,lemma(discharge,[]))).
% 12.15/8.09 tff(2126,plain,
% 12.15/8.09 (~m_counter_cell_v_carry_in(c_bit1, s26)),
% 12.15/8.09 inference(unit_resolution,[status(thm)],[2125, 2118])).
% 12.15/8.09 tff(2127,assumption,(node1(c_bit1, s26)), introduced(assumption)).
% 12.15/8.09 tff(2128,assumption,(m_counter_cell_v_value(c_bit1, s26)), introduced(assumption)).
% 12.15/8.09 tff(2129,plain,
% 12.15/8.09 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.15/8.09 inference(rewrite,[status(thm)],[])).
% 12.15/8.09 tff(2130,plain,
% 12.15/8.09 (((~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)))),
% 12.15/8.10 inference(rewrite,[status(thm)],[])).
% 12.15/8.10 tff(2131,plain,
% 12.15/8.10 (((~![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))))),
% 12.15/8.10 inference(monotonicity,[status(thm)],[2130])).
% 12.15/8.10 tff(2132,plain,
% 12.15/8.10 (((~![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)))),
% 12.15/8.10 inference(transitivity,[status(thm)],[2131, 2129])).
% 12.15/8.10 tff(2133,plain,
% 12.15/8.10 ((~![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)))),
% 12.15/8.10 inference(quant_inst,[status(thm)],[])).
% 12.15/8.10 tff(2134,plain,
% 12.15/8.10 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26))),
% 12.15/8.10 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 12.15/8.10 tff(2135,plain,
% 12.15/8.10 ($false),
% 12.15/8.10 inference(unit_resolution,[status(thm)],[2134, 1517, 2128, 2127, 2126])).
% 12.15/8.10 tff(2136,plain,((~m_counter_cell_v_value(c_bit1, s26)) | (~node1(c_bit1, s26))), inference(lemma,lemma(discharge,[]))).
% 12.15/8.10 tff(2137,plain,
% 12.15/8.10 (~node1(c_bit1, s26)),
% 12.15/8.10 inference(unit_resolution,[status(thm)],[2136, 2108])).
% 12.15/8.10 tff(2138,plain,
% 12.15/8.10 (((~![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))),
% 12.15/8.10 inference(rewrite,[status(thm)],[])).
% 12.15/8.10 tff(2139,plain,
% 12.15/8.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit1, s26, s27))),
% 12.15/8.10 inference(quant_inst,[status(thm)],[])).
% 12.15/8.10 tff(2140,plain,
% 12.15/8.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit1, s26, s27)),
% 12.15/8.10 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 12.15/8.10 tff(2141,plain,
% 12.15/8.10 (node3(c_bit1, s26, s27)),
% 12.15/8.10 inference(unit_resolution,[status(thm)],[2140, 21, 818])).
% 12.15/8.10 tff(2142,plain,
% 12.15/8.10 (((~![Y: $i, 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)))),
% 12.15/8.10 inference(rewrite,[status(thm)],[])).
% 12.15/8.10 tff(2143,plain,
% 12.15/8.10 ((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)))),
% 12.15/8.10 inference(rewrite,[status(thm)],[])).
% 12.15/8.10 tff(2144,plain,
% 12.15/8.10 (((~![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))))),
% 12.15/8.10 inference(monotonicity,[status(thm)],[2143])).
% 12.15/8.10 tff(2145,plain,
% 12.15/8.10 (((~![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)))),
% 12.15/8.10 inference(transitivity,[status(thm)],[2144, 2142])).
% 12.15/8.10 tff(2146,plain,
% 12.15/8.10 ((~![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))),
% 12.15/8.10 inference(quant_inst,[status(thm)],[])).
% 12.15/8.10 tff(2147,plain,
% 12.15/8.10 ((~![Y: $i, 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))),
% 12.15/8.10 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 12.15/8.10 tff(2148,plain,
% 12.15/8.10 (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26)),
% 12.15/8.10 inference(unit_resolution,[status(thm)],[2147, 106, 2141])).
% 12.15/8.10 tff(2149,plain,
% 12.15/8.10 (m_counter_cell_v_value(c_bit1, s27)),
% 12.15/8.10 inference(unit_resolution,[status(thm)],[2148, 2137])).
% 12.15/8.10 tff(2150,plain,
% 12.15/8.10 (((~![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))),
% 12.15/8.10 inference(rewrite,[status(thm)],[])).
% 12.15/8.10 tff(2151,plain,
% 12.15/8.10 ((~![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))),
% 12.15/8.10 inference(quant_inst,[status(thm)],[])).
% 12.15/8.10 tff(2152,plain,
% 12.15/8.10 ((~![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)),
% 12.15/8.10 inference(modus_ponens,[status(thm)],[2151, 2150])).
% 12.15/8.10 tff(2153,plain,
% 12.15/8.10 ((~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27)),
% 12.15/8.10 inference(unit_resolution,[status(thm)],[2152, 1368, 834])).
% 12.15/8.10 tff(2154,plain,
% 12.15/8.10 (m_counter_cell_v_carry_out(c_bit0, s27)),
% 12.15/8.10 inference(unit_resolution,[status(thm)],[2153, 830])).
% 12.15/8.10 tff(2155,plain,
% 12.15/8.10 (((~![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))),
% 12.15/8.10 inference(rewrite,[status(thm)],[])).
% 12.15/8.10 tff(2156,plain,
% 12.15/8.10 ((~![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))),
% 12.15/8.10 inference(quant_inst,[status(thm)],[])).
% 12.15/8.10 tff(2157,plain,
% 12.15/8.10 ((~![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)),
% 12.15/8.10 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 12.15/8.10 tff(2158,plain,
% 12.15/8.10 (m_counter_cell_v_carry_in(c_bit1, s27)),
% 12.15/8.10 inference(unit_resolution,[status(thm)],[2157, 1383, 2154])).
% 12.15/8.10 tff(2159,plain,
% 12.15/8.10 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2160,plain,
% 12.17/8.10 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2161,plain,
% 12.17/8.10 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2160, 2159])).
% 12.17/8.10 tff(2162,plain,
% 12.17/8.10 ((~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27))),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2161, 126, 2158])).
% 12.17/8.10 tff(2163,plain,
% 12.17/8.10 (~node2(c_bit1, s27)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2162, 2149])).
% 12.17/8.10 tff(2164,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2165,plain,
% 12.17/8.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit1, s27, s28))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2166,plain,
% 12.17/8.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit1, s27, s28)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2165, 2164])).
% 12.17/8.10 tff(2167,plain,
% 12.17/8.10 (node3(c_bit1, s27, s28)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2166, 21, 846])).
% 12.17/8.10 tff(2168,plain,
% 12.17/8.10 (((~![Y: $i, 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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2169,plain,
% 12.17/8.10 ((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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2170,plain,
% 12.17/8.10 (((~![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))))),
% 12.17/8.10 inference(monotonicity,[status(thm)],[2169])).
% 12.17/8.10 tff(2171,plain,
% 12.17/8.10 (((~![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)))),
% 12.17/8.10 inference(transitivity,[status(thm)],[2170, 2168])).
% 12.17/8.10 tff(2172,plain,
% 12.17/8.10 ((~![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)))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2173,plain,
% 12.17/8.10 ((~![Y: $i, 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))),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 12.17/8.10 tff(2174,plain,
% 12.17/8.10 ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2173, 141, 2167])).
% 12.17/8.10 tff(2175,plain,
% 12.17/8.10 (~m_counter_cell_v_value(c_bit1, s28)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2174, 2163])).
% 12.17/8.10 tff(2176,assumption,(node2(c_bit1, s28)), introduced(assumption)).
% 12.17/8.10 tff(2177,plain,
% 12.17/8.10 (((~![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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2178,plain,
% 12.17/8.10 ((~![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)))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2179,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 12.17/8.10 tff(2180,plain,
% 12.17/8.10 (~node4(c_bit0, s28)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2179, 1221, 858])).
% 12.17/8.10 tff(2181,assumption,(m_counter_cell_v_carry_out(c_bit0, s28)), introduced(assumption)).
% 12.17/8.10 tff(2182,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2183,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2184,plain,
% 12.17/8.10 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s28)) | node4(c_bit0, s28)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 12.17/8.10 tff(2185,plain,
% 12.17/8.10 ($false),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2184, 1235, 2181, 2180])).
% 12.17/8.10 tff(2186,plain,(~m_counter_cell_v_carry_out(c_bit0, s28)), inference(lemma,lemma(discharge,[]))).
% 12.17/8.10 tff(2187,assumption,(m_counter_cell_v_carry_in(c_bit1, s28)), introduced(assumption)).
% 12.17/8.10 tff(2188,assumption,(~m_counter_cell_v_carry_out(c_bit0, s28)), introduced(assumption)).
% 12.17/8.10 tff(2189,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2190,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2191,plain,
% 12.17/8.10 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s28)) | m_counter_cell_v_carry_out(c_bit0, s28)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2190, 2189])).
% 12.17/8.10 tff(2192,plain,
% 12.17/8.10 ($false),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2191, 1249, 2188, 2187])).
% 12.17/8.10 tff(2193,plain,(m_counter_cell_v_carry_out(c_bit0, s28) | (~m_counter_cell_v_carry_in(c_bit1, s28))), inference(lemma,lemma(discharge,[]))).
% 12.17/8.10 tff(2194,plain,
% 12.17/8.10 (~m_counter_cell_v_carry_in(c_bit1, s28)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2193, 2186])).
% 12.17/8.10 tff(2195,assumption,(~m_counter_cell_v_value(c_bit1, s28)), introduced(assumption)).
% 12.17/8.10 tff(2196,plain,
% 12.17/8.10 (((~![I0: $i, X: $i] : (m_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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2197,plain,
% 12.17/8.10 ((~![I0: $i, X: $i] : (m_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)))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2198,plain,
% 12.17/8.10 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s28) | m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28))),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 12.17/8.10 tff(2199,plain,
% 12.17/8.10 ($false),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2198, 1449, 2195, 2194, 2176])).
% 12.17/8.10 tff(2200,plain,((~node2(c_bit1, s28)) | m_counter_cell_v_value(c_bit1, s28)), inference(lemma,lemma(discharge,[]))).
% 12.17/8.10 tff(2201,plain,
% 12.17/8.10 (~node2(c_bit1, s28)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2200, 2175])).
% 12.17/8.10 tff(2202,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2203,plain,
% 12.17/8.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit1, s28, s29))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2204,plain,
% 12.17/8.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit1, s28, s29)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 12.17/8.10 tff(2205,plain,
% 12.17/8.10 (node3(c_bit1, s28, s29)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2204, 21, 877])).
% 12.17/8.10 tff(2206,plain,
% 12.17/8.10 (((~![Y: $i, 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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2207,plain,
% 12.17/8.10 ((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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2208,plain,
% 12.17/8.10 (((~![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))))),
% 12.17/8.10 inference(monotonicity,[status(thm)],[2207])).
% 12.17/8.10 tff(2209,plain,
% 12.17/8.10 (((~![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)))),
% 12.17/8.10 inference(transitivity,[status(thm)],[2208, 2206])).
% 12.17/8.10 tff(2210,plain,
% 12.17/8.10 ((~![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)))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2211,plain,
% 12.17/8.10 ((~![Y: $i, 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))),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2210, 2209])).
% 12.17/8.10 tff(2212,plain,
% 12.17/8.10 ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2211, 141, 2205])).
% 12.17/8.10 tff(2213,plain,
% 12.17/8.10 (~m_counter_cell_v_value(c_bit1, s29)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2212, 2201])).
% 12.17/8.10 tff(2214,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2215,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2216,plain,
% 12.17/8.10 ((~![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)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 12.17/8.10 tff(2217,plain,
% 12.17/8.10 ((~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2216, 1368, 893])).
% 12.17/8.10 tff(2218,plain,
% 12.17/8.10 (m_counter_cell_v_carry_out(c_bit0, s29)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2217, 889])).
% 12.17/8.10 tff(2219,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2220,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2221,plain,
% 12.17/8.10 ((~![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)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 12.17/8.10 tff(2222,plain,
% 12.17/8.10 (m_counter_cell_v_carry_in(c_bit1, s29)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2221, 1383, 2218])).
% 12.17/8.10 tff(2223,plain,
% 12.17/8.10 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2224,plain,
% 12.17/8.10 (((~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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2225,plain,
% 12.17/8.10 (((~![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))))),
% 12.17/8.10 inference(monotonicity,[status(thm)],[2224])).
% 12.17/8.10 tff(2226,plain,
% 12.17/8.10 (((~![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)))),
% 12.17/8.10 inference(transitivity,[status(thm)],[2225, 2223])).
% 12.17/8.10 tff(2227,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2228,plain,
% 12.17/8.10 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2227, 2226])).
% 12.17/8.10 tff(2229,plain,
% 12.17/8.10 (m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29))),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2228, 77, 2222])).
% 12.17/8.10 tff(2230,plain,
% 12.17/8.10 (~node1(c_bit1, s29)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2229, 2213])).
% 12.17/8.10 tff(2231,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2232,plain,
% 12.17/8.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit1, s29, s30))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2233,plain,
% 12.17/8.10 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit1, s29, s30)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 12.17/8.10 tff(2234,plain,
% 12.17/8.10 (node3(c_bit1, s29, s30)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2233, 21, 905])).
% 12.17/8.10 tff(2235,plain,
% 12.17/8.10 (((~![Y: $i, 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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2236,plain,
% 12.17/8.10 ((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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2237,plain,
% 12.17/8.10 (((~![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))))),
% 12.17/8.10 inference(monotonicity,[status(thm)],[2236])).
% 12.17/8.10 tff(2238,plain,
% 12.17/8.10 (((~![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)))),
% 12.17/8.10 inference(transitivity,[status(thm)],[2237, 2235])).
% 12.17/8.10 tff(2239,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2240,plain,
% 12.17/8.10 ((~![Y: $i, 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))),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2239, 2238])).
% 12.17/8.10 tff(2241,plain,
% 12.17/8.10 (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2240, 106, 2234])).
% 12.17/8.10 tff(2242,plain,
% 12.17/8.10 (m_counter_cell_v_value(c_bit1, s30)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2241, 2230])).
% 12.17/8.10 tff(2243,assumption,(node1(c_bit1, s30)), introduced(assumption)).
% 12.17/8.10 tff(2244,plain,
% 12.17/8.10 (((~![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)))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2245,plain,
% 12.17/8.10 ((~![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)))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2246,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 12.17/8.10 tff(2247,plain,
% 12.17/8.10 (~node4(c_bit0, s30)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2246, 1221, 917])).
% 12.17/8.10 tff(2248,assumption,(m_counter_cell_v_carry_out(c_bit0, s30)), introduced(assumption)).
% 12.17/8.10 tff(2249,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2250,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2251,plain,
% 12.17/8.10 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 12.17/8.10 tff(2252,plain,
% 12.17/8.10 ($false),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2251, 1235, 2248, 2247])).
% 12.17/8.10 tff(2253,plain,(~m_counter_cell_v_carry_out(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 12.17/8.10 tff(2254,assumption,(m_counter_cell_v_carry_in(c_bit1, s30)), introduced(assumption)).
% 12.17/8.10 tff(2255,assumption,(~m_counter_cell_v_carry_out(c_bit0, s30)), introduced(assumption)).
% 12.17/8.10 tff(2256,plain,
% 12.17/8.10 (((~![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))),
% 12.17/8.10 inference(rewrite,[status(thm)],[])).
% 12.17/8.10 tff(2257,plain,
% 12.17/8.10 ((~![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))),
% 12.17/8.10 inference(quant_inst,[status(thm)],[])).
% 12.17/8.10 tff(2258,plain,
% 12.17/8.10 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30)),
% 12.17/8.10 inference(modus_ponens,[status(thm)],[2257, 2256])).
% 12.17/8.10 tff(2259,plain,
% 12.17/8.10 ($false),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2258, 1249, 2255, 2254])).
% 12.17/8.10 tff(2260,plain,(m_counter_cell_v_carry_out(c_bit0, s30) | (~m_counter_cell_v_carry_in(c_bit1, s30))), inference(lemma,lemma(discharge,[]))).
% 12.17/8.10 tff(2261,plain,
% 12.17/8.10 (~m_counter_cell_v_carry_in(c_bit1, s30)),
% 12.17/8.10 inference(unit_resolution,[status(thm)],[2260, 2253])).
% 12.17/8.10 tff(2262,assumption,(m_counter_cell_v_value(c_bit1, s30)), introduced(assumption)).
% 12.17/8.11 tff(2263,plain,
% 12.17/8.11 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2264,plain,
% 12.17/8.11 (((~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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2265,plain,
% 12.17/8.11 (((~![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))))),
% 12.17/8.11 inference(monotonicity,[status(thm)],[2264])).
% 12.17/8.11 tff(2266,plain,
% 12.17/8.11 (((~![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)))),
% 12.17/8.11 inference(transitivity,[status(thm)],[2265, 2263])).
% 12.17/8.11 tff(2267,plain,
% 12.17/8.11 ((~![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)))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2268,plain,
% 12.17/8.11 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 12.17/8.11 tff(2269,plain,
% 12.17/8.11 ($false),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2268, 1517, 2262, 2261, 2243])).
% 12.17/8.11 tff(2270,plain,((~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30))), inference(lemma,lemma(discharge,[]))).
% 12.17/8.11 tff(2271,plain,
% 12.17/8.11 (~node1(c_bit1, s30)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2270, 2242])).
% 12.17/8.11 tff(2272,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2273,plain,
% 12.17/8.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit1, s30, s31))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2274,plain,
% 12.17/8.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit1, s30, s31)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2273, 2272])).
% 12.17/8.11 tff(2275,plain,
% 12.17/8.11 (node3(c_bit1, s30, s31)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2274, 21, 936])).
% 12.17/8.11 tff(2276,plain,
% 12.17/8.11 (((~![Y: $i, 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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2277,plain,
% 12.17/8.11 ((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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2278,plain,
% 12.17/8.11 (((~![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))))),
% 12.17/8.11 inference(monotonicity,[status(thm)],[2277])).
% 12.17/8.11 tff(2279,plain,
% 12.17/8.11 (((~![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)))),
% 12.17/8.11 inference(transitivity,[status(thm)],[2278, 2276])).
% 12.17/8.11 tff(2280,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2281,plain,
% 12.17/8.11 ((~![Y: $i, 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))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2280, 2279])).
% 12.17/8.11 tff(2282,plain,
% 12.17/8.11 (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2281, 106, 2275])).
% 12.17/8.11 tff(2283,plain,
% 12.17/8.11 (m_counter_cell_v_value(c_bit1, s31)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2282, 2271])).
% 12.17/8.11 tff(2284,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2285,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2286,plain,
% 12.17/8.11 ((~![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)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2285, 2284])).
% 12.17/8.11 tff(2287,plain,
% 12.17/8.11 ((~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2286, 1368, 952])).
% 12.17/8.11 tff(2288,plain,
% 12.17/8.11 (m_counter_cell_v_carry_out(c_bit0, s31)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2287, 948])).
% 12.17/8.11 tff(2289,assumption,(~m_counter_cell_v_carry_in(c_bit1, s31)), introduced(assumption)).
% 12.17/8.11 tff(2290,assumption,(m_counter_cell_v_carry_out(c_bit0, s31)), introduced(assumption)).
% 12.17/8.11 tff(2291,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2292,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2293,plain,
% 12.17/8.11 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 12.17/8.11 tff(2294,plain,
% 12.17/8.11 ($false),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2293, 1383, 2290, 2289])).
% 12.17/8.11 tff(2295,plain,((~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31)), inference(lemma,lemma(discharge,[]))).
% 12.17/8.11 tff(2296,plain,
% 12.17/8.11 (m_counter_cell_v_carry_in(c_bit1, s31)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2295, 2288])).
% 12.17/8.11 tff(2297,assumption,(node2(c_bit1, s31)), introduced(assumption)).
% 12.17/8.11 tff(2298,assumption,(m_counter_cell_v_value(c_bit1, s31)), introduced(assumption)).
% 12.17/8.11 tff(2299,plain,
% 12.17/8.11 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2300,plain,
% 12.17/8.11 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2301,plain,
% 12.17/8.11 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 12.17/8.11 tff(2302,plain,
% 12.17/8.11 ($false),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2301, 126, 2298, 2297, 2296])).
% 12.17/8.11 tff(2303,plain,((~node2(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31))), inference(lemma,lemma(discharge,[]))).
% 12.17/8.11 tff(2304,plain,
% 12.17/8.11 (~node2(c_bit1, s31)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2303, 2283])).
% 12.17/8.11 tff(2305,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2306,plain,
% 12.17/8.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit1, s31, s32))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2307,plain,
% 12.17/8.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit1, s31, s32)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2306, 2305])).
% 12.17/8.11 tff(2308,plain,
% 12.17/8.11 (node3(c_bit1, s31, s32)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2307, 21, 964])).
% 12.17/8.11 tff(2309,plain,
% 12.17/8.11 (((~![Y: $i, 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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2310,plain,
% 12.17/8.11 ((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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2311,plain,
% 12.17/8.11 (((~![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))))),
% 12.17/8.11 inference(monotonicity,[status(thm)],[2310])).
% 12.17/8.11 tff(2312,plain,
% 12.17/8.11 (((~![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)))),
% 12.17/8.11 inference(transitivity,[status(thm)],[2311, 2309])).
% 12.17/8.11 tff(2313,plain,
% 12.17/8.11 ((~![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)))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2314,plain,
% 12.17/8.11 ((~![Y: $i, 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))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 12.17/8.11 tff(2315,plain,
% 12.17/8.11 ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2314, 141, 2308])).
% 12.17/8.11 tff(2316,plain,
% 12.17/8.11 (~m_counter_cell_v_value(c_bit1, s32)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2315, 2304])).
% 12.17/8.11 tff(2317,plain,
% 12.17/8.11 (((~![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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2318,plain,
% 12.17/8.11 ((~![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)))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2319,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2318, 2317])).
% 12.17/8.11 tff(2320,plain,
% 12.17/8.11 (~node4(c_bit0, s32)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2319, 1221, 976])).
% 12.17/8.11 tff(2321,assumption,(m_counter_cell_v_carry_out(c_bit0, s32)), introduced(assumption)).
% 12.17/8.11 tff(2322,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2323,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2324,plain,
% 12.17/8.11 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 12.17/8.11 tff(2325,plain,
% 12.17/8.11 ($false),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2324, 1235, 2321, 2320])).
% 12.17/8.11 tff(2326,plain,(~m_counter_cell_v_carry_out(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 12.17/8.11 tff(2327,assumption,(m_counter_cell_v_carry_in(c_bit1, s32)), introduced(assumption)).
% 12.17/8.11 tff(2328,assumption,(~m_counter_cell_v_carry_out(c_bit0, s32)), introduced(assumption)).
% 12.17/8.11 tff(2329,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2330,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2331,plain,
% 12.17/8.11 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2330, 2329])).
% 12.17/8.11 tff(2332,plain,
% 12.17/8.11 ($false),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2331, 1249, 2328, 2327])).
% 12.17/8.11 tff(2333,plain,((~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 12.17/8.11 tff(2334,plain,
% 12.17/8.11 (~m_counter_cell_v_carry_in(c_bit1, s32)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2333, 2326])).
% 12.17/8.11 tff(2335,assumption,(~m_counter_cell_v_value(c_bit1, s32)), introduced(assumption)).
% 12.17/8.11 tff(2336,assumption,(node2(c_bit1, s32)), introduced(assumption)).
% 12.17/8.11 tff(2337,plain,
% 12.17/8.11 (((~![I0: $i, X: $i] : (m_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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2338,plain,
% 12.17/8.11 ((~![I0: $i, X: $i] : (m_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)))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2339,plain,
% 12.17/8.11 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 12.17/8.11 tff(2340,plain,
% 12.17/8.11 ($false),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2339, 1449, 2336, 2335, 2334])).
% 12.17/8.11 tff(2341,plain,(m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32))), inference(lemma,lemma(discharge,[]))).
% 12.17/8.11 tff(2342,plain,
% 12.17/8.11 (~node2(c_bit1, s32)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2341, 2316])).
% 12.17/8.11 tff(2343,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2344,plain,
% 12.17/8.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit1, s32, s33))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2345,plain,
% 12.17/8.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit1, s32, s33)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 12.17/8.11 tff(2346,plain,
% 12.17/8.11 (node3(c_bit1, s32, s33)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2345, 21, 995])).
% 12.17/8.11 tff(2347,plain,
% 12.17/8.11 (((~![Y: $i, 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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2348,plain,
% 12.17/8.11 ((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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2349,plain,
% 12.17/8.11 (((~![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))))),
% 12.17/8.11 inference(monotonicity,[status(thm)],[2348])).
% 12.17/8.11 tff(2350,plain,
% 12.17/8.11 (((~![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)))),
% 12.17/8.11 inference(transitivity,[status(thm)],[2349, 2347])).
% 12.17/8.11 tff(2351,plain,
% 12.17/8.11 ((~![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)))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2352,plain,
% 12.17/8.11 ((~![Y: $i, 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))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 12.17/8.11 tff(2353,plain,
% 12.17/8.11 ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2352, 141, 2346])).
% 12.17/8.11 tff(2354,plain,
% 12.17/8.11 (~m_counter_cell_v_value(c_bit1, s33)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2353, 2342])).
% 12.17/8.11 tff(2355,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2356,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2357,plain,
% 12.17/8.11 ((~![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)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 12.17/8.11 tff(2358,plain,
% 12.17/8.11 ((~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2357, 1368, 1011])).
% 12.17/8.11 tff(2359,plain,
% 12.17/8.11 (m_counter_cell_v_carry_out(c_bit0, s33)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2358, 1007])).
% 12.17/8.11 tff(2360,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2361,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2362,plain,
% 12.17/8.11 ((~![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)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2361, 2360])).
% 12.17/8.11 tff(2363,plain,
% 12.17/8.11 (m_counter_cell_v_carry_in(c_bit1, s33)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2362, 1383, 2359])).
% 12.17/8.11 tff(2364,plain,
% 12.17/8.11 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2365,plain,
% 12.17/8.11 (((~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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2366,plain,
% 12.17/8.11 (((~![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))))),
% 12.17/8.11 inference(monotonicity,[status(thm)],[2365])).
% 12.17/8.11 tff(2367,plain,
% 12.17/8.11 (((~![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)))),
% 12.17/8.11 inference(transitivity,[status(thm)],[2366, 2364])).
% 12.17/8.11 tff(2368,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2369,plain,
% 12.17/8.11 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2368, 2367])).
% 12.17/8.11 tff(2370,plain,
% 12.17/8.11 (m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33))),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2369, 77, 2363])).
% 12.17/8.11 tff(2371,plain,
% 12.17/8.11 (~node1(c_bit1, s33)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2370, 2354])).
% 12.17/8.11 tff(2372,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2373,plain,
% 12.17/8.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit1, s33, s34))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2374,plain,
% 12.17/8.11 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit1, s33, s34)),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2373, 2372])).
% 12.17/8.11 tff(2375,plain,
% 12.17/8.11 (node3(c_bit1, s33, s34)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2374, 21, 1023])).
% 12.17/8.11 tff(2376,plain,
% 12.17/8.11 (((~![Y: $i, 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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2377,plain,
% 12.17/8.11 ((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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2378,plain,
% 12.17/8.11 (((~![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))))),
% 12.17/8.11 inference(monotonicity,[status(thm)],[2377])).
% 12.17/8.11 tff(2379,plain,
% 12.17/8.11 (((~![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)))),
% 12.17/8.11 inference(transitivity,[status(thm)],[2378, 2376])).
% 12.17/8.11 tff(2380,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2381,plain,
% 12.17/8.11 ((~![Y: $i, 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))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 12.17/8.11 tff(2382,plain,
% 12.17/8.11 (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2381, 106, 2375])).
% 12.17/8.11 tff(2383,plain,
% 12.17/8.11 (m_counter_cell_v_value(c_bit1, s34)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2382, 2371])).
% 12.17/8.11 tff(2384,assumption,(node1(c_bit1, s34)), introduced(assumption)).
% 12.17/8.11 tff(2385,plain,
% 12.17/8.11 (((~![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)))),
% 12.17/8.11 inference(rewrite,[status(thm)],[])).
% 12.17/8.11 tff(2386,plain,
% 12.17/8.11 ((~![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)))),
% 12.17/8.11 inference(quant_inst,[status(thm)],[])).
% 12.17/8.11 tff(2387,plain,
% 12.17/8.11 ((~![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))),
% 12.17/8.11 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 12.17/8.11 tff(2388,plain,
% 12.17/8.11 (~node4(c_bit0, s34)),
% 12.17/8.11 inference(unit_resolution,[status(thm)],[2387, 1221, 1035])).
% 12.17/8.11 tff(2389,assumption,(~node4(c_bit0, s34)), introduced(assumption)).
% 12.17/8.11 tff(2390,assumption,(m_counter_cell_v_carry_out(c_bit0, s34)), introduced(assumption)).
% 12.17/8.11 tff(2391,plain,
% 12.17/8.11 (((~![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))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2392,plain,
% 12.17/8.12 ((~![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))),
% 12.17/8.12 inference(quant_inst,[status(thm)],[])).
% 12.17/8.12 tff(2393,plain,
% 12.17/8.12 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34)),
% 12.17/8.12 inference(modus_ponens,[status(thm)],[2392, 2391])).
% 12.17/8.12 tff(2394,plain,
% 12.17/8.12 ($false),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2393, 1235, 2390, 2389])).
% 12.17/8.12 tff(2395,plain,((~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 12.17/8.12 tff(2396,plain,
% 12.17/8.12 (~m_counter_cell_v_carry_out(c_bit0, s34)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2395, 2388])).
% 12.17/8.12 tff(2397,assumption,(m_counter_cell_v_carry_in(c_bit1, s34)), introduced(assumption)).
% 12.17/8.12 tff(2398,assumption,(~m_counter_cell_v_carry_out(c_bit0, s34)), introduced(assumption)).
% 12.17/8.12 tff(2399,plain,
% 12.17/8.12 (((~![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))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2400,plain,
% 12.17/8.12 ((~![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))),
% 12.17/8.12 inference(quant_inst,[status(thm)],[])).
% 12.17/8.12 tff(2401,plain,
% 12.17/8.12 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)),
% 12.17/8.12 inference(modus_ponens,[status(thm)],[2400, 2399])).
% 12.17/8.12 tff(2402,plain,
% 12.17/8.12 ($false),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2401, 1249, 2398, 2397])).
% 12.17/8.12 tff(2403,plain,(m_counter_cell_v_carry_out(c_bit0, s34) | (~m_counter_cell_v_carry_in(c_bit1, s34))), inference(lemma,lemma(discharge,[]))).
% 12.17/8.12 tff(2404,plain,
% 12.17/8.12 (~m_counter_cell_v_carry_in(c_bit1, s34)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2403, 2396])).
% 12.17/8.12 tff(2405,assumption,(m_counter_cell_v_value(c_bit1, s34)), introduced(assumption)).
% 12.17/8.12 tff(2406,plain,
% 12.17/8.12 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2407,plain,
% 12.17/8.12 (((~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)))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2408,plain,
% 12.17/8.12 (((~![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))))),
% 12.17/8.12 inference(monotonicity,[status(thm)],[2407])).
% 12.17/8.12 tff(2409,plain,
% 12.17/8.12 (((~![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)))),
% 12.17/8.12 inference(transitivity,[status(thm)],[2408, 2406])).
% 12.17/8.12 tff(2410,plain,
% 12.17/8.12 ((~![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)))),
% 12.17/8.12 inference(quant_inst,[status(thm)],[])).
% 12.17/8.12 tff(2411,plain,
% 12.17/8.12 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34))),
% 12.17/8.12 inference(modus_ponens,[status(thm)],[2410, 2409])).
% 12.17/8.12 tff(2412,plain,
% 12.17/8.12 ($false),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2411, 1517, 2405, 2404, 2384])).
% 12.17/8.12 tff(2413,plain,((~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34))), inference(lemma,lemma(discharge,[]))).
% 12.17/8.12 tff(2414,plain,
% 12.17/8.12 (~node1(c_bit1, s34)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2413, 2383])).
% 12.17/8.12 tff(2415,plain,
% 12.17/8.12 (((~![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))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2416,plain,
% 12.17/8.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit1, s34, s35))),
% 12.17/8.12 inference(quant_inst,[status(thm)],[])).
% 12.17/8.12 tff(2417,plain,
% 12.17/8.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit1, s34, s35)),
% 12.17/8.12 inference(modus_ponens,[status(thm)],[2416, 2415])).
% 12.17/8.12 tff(2418,plain,
% 12.17/8.12 (node3(c_bit1, s34, s35)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2417, 21, 1054])).
% 12.17/8.12 tff(2419,plain,
% 12.17/8.12 (((~![Y: $i, 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)))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2420,plain,
% 12.17/8.12 ((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)))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2421,plain,
% 12.17/8.12 (((~![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))))),
% 12.17/8.12 inference(monotonicity,[status(thm)],[2420])).
% 12.17/8.12 tff(2422,plain,
% 12.17/8.12 (((~![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)))),
% 12.17/8.12 inference(transitivity,[status(thm)],[2421, 2419])).
% 12.17/8.12 tff(2423,plain,
% 12.17/8.12 ((~![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))),
% 12.17/8.12 inference(quant_inst,[status(thm)],[])).
% 12.17/8.12 tff(2424,plain,
% 12.17/8.12 ((~![Y: $i, 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))),
% 12.17/8.12 inference(modus_ponens,[status(thm)],[2423, 2422])).
% 12.17/8.12 tff(2425,plain,
% 12.17/8.12 (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2424, 106, 2418])).
% 12.17/8.12 tff(2426,plain,
% 12.17/8.12 (m_counter_cell_v_value(c_bit1, s35)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2425, 2414])).
% 12.17/8.12 tff(2427,assumption,(node2(c_bit1, s35)), introduced(assumption)).
% 12.17/8.12 tff(2428,plain,
% 12.17/8.12 (((~![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))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2429,plain,
% 12.17/8.12 ((~![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))),
% 12.17/8.12 inference(quant_inst,[status(thm)],[])).
% 12.17/8.12 tff(2430,plain,
% 12.17/8.12 ((~![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)),
% 12.17/8.12 inference(modus_ponens,[status(thm)],[2429, 2428])).
% 12.17/8.12 tff(2431,plain,
% 12.17/8.12 ((~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2430, 1368, 1070])).
% 12.17/8.12 tff(2432,plain,
% 12.17/8.12 (m_counter_cell_v_carry_out(c_bit0, s35)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2431, 1066])).
% 12.17/8.12 tff(2433,plain,
% 12.17/8.12 (((~![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))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2434,plain,
% 12.17/8.12 ((~![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))),
% 12.17/8.12 inference(quant_inst,[status(thm)],[])).
% 12.17/8.12 tff(2435,plain,
% 12.17/8.12 ((~![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)),
% 12.17/8.12 inference(modus_ponens,[status(thm)],[2434, 2433])).
% 12.17/8.12 tff(2436,plain,
% 12.17/8.12 (m_counter_cell_v_carry_in(c_bit1, s35)),
% 12.17/8.12 inference(unit_resolution,[status(thm)],[2435, 1383, 2432])).
% 12.17/8.12 tff(2437,assumption,(m_counter_cell_v_value(c_bit1, s35)), introduced(assumption)).
% 12.17/8.12 tff(2438,plain,
% 12.17/8.12 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.17/8.12 inference(rewrite,[status(thm)],[])).
% 12.17/8.12 tff(2439,plain,
% 12.17/8.12 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.17/8.12 inference(quant_inst,[status(thm)],[])).
% 12.17/8.12 tff(2440,plain,
% 12.17/8.12 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35))),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2439, 2438])).
% 12.19/8.12 tff(2441,plain,
% 12.19/8.12 ($false),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2440, 126, 2437, 2436, 2427])).
% 12.19/8.12 tff(2442,plain,((~node2(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.12 tff(2443,plain,
% 12.19/8.12 (~node2(c_bit1, s35)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2442, 2426])).
% 12.19/8.12 tff(2444,plain,
% 12.19/8.12 (((~![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))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2445,plain,
% 12.19/8.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit1, s35, s36))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2446,plain,
% 12.19/8.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit1, s35, s36)),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 12.19/8.12 tff(2447,plain,
% 12.19/8.12 (node3(c_bit1, s35, s36)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2446, 21, 1082])).
% 12.19/8.12 tff(2448,plain,
% 12.19/8.12 (((~![Y: $i, 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)))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2449,plain,
% 12.19/8.12 ((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)))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2450,plain,
% 12.19/8.12 (((~![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))))),
% 12.19/8.12 inference(monotonicity,[status(thm)],[2449])).
% 12.19/8.12 tff(2451,plain,
% 12.19/8.12 (((~![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)))),
% 12.19/8.12 inference(transitivity,[status(thm)],[2450, 2448])).
% 12.19/8.12 tff(2452,plain,
% 12.19/8.12 ((~![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)))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2453,plain,
% 12.19/8.12 ((~![Y: $i, 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))),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2452, 2451])).
% 12.19/8.12 tff(2454,plain,
% 12.19/8.12 ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2453, 141, 2447])).
% 12.19/8.12 tff(2455,plain,
% 12.19/8.12 (~m_counter_cell_v_value(c_bit1, s36)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2454, 2443])).
% 12.19/8.12 tff(2456,plain,
% 12.19/8.12 (((~![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)))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2457,plain,
% 12.19/8.12 ((~![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)))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2458,plain,
% 12.19/8.12 ((~![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))),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2457, 2456])).
% 12.19/8.12 tff(2459,plain,
% 12.19/8.12 (~node4(c_bit0, s36)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2458, 1221, 1094])).
% 12.19/8.12 tff(2460,assumption,(m_counter_cell_v_carry_out(c_bit0, s36)), introduced(assumption)).
% 12.19/8.12 tff(2461,plain,
% 12.19/8.12 (((~![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))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2462,plain,
% 12.19/8.12 ((~![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))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2463,plain,
% 12.19/8.12 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36)),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2462, 2461])).
% 12.19/8.12 tff(2464,plain,
% 12.19/8.12 ($false),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2463, 1235, 2460, 2459])).
% 12.19/8.12 tff(2465,plain,(~m_counter_cell_v_carry_out(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.12 tff(2466,assumption,(m_counter_cell_v_carry_in(c_bit1, s36)), introduced(assumption)).
% 12.19/8.12 tff(2467,assumption,(~m_counter_cell_v_carry_out(c_bit0, s36)), introduced(assumption)).
% 12.19/8.12 tff(2468,plain,
% 12.19/8.12 (((~![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))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2469,plain,
% 12.19/8.12 ((~![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))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2470,plain,
% 12.19/8.12 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36)),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2469, 2468])).
% 12.19/8.12 tff(2471,plain,
% 12.19/8.12 ($false),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2470, 1249, 2467, 2466])).
% 12.19/8.12 tff(2472,plain,(m_counter_cell_v_carry_out(c_bit0, s36) | (~m_counter_cell_v_carry_in(c_bit1, s36))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.12 tff(2473,plain,
% 12.19/8.12 (~m_counter_cell_v_carry_in(c_bit1, s36)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2472, 2465])).
% 12.19/8.12 tff(2474,assumption,(node2(c_bit1, s36)), introduced(assumption)).
% 12.19/8.12 tff(2475,assumption,(~m_counter_cell_v_value(c_bit1, s36)), introduced(assumption)).
% 12.19/8.12 tff(2476,plain,
% 12.19/8.12 (((~![I0: $i, X: $i] : (m_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)))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2477,plain,
% 12.19/8.12 ((~![I0: $i, X: $i] : (m_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)))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2478,plain,
% 12.19/8.12 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36))),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2477, 2476])).
% 12.19/8.12 tff(2479,plain,
% 12.19/8.12 ($false),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2478, 1449, 2475, 2474, 2473])).
% 12.19/8.12 tff(2480,plain,(m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.12 tff(2481,plain,
% 12.19/8.12 (~node2(c_bit1, s36)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2480, 2455])).
% 12.19/8.12 tff(2482,plain,
% 12.19/8.12 (((~![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))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2483,plain,
% 12.19/8.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit1, s36, s37))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2484,plain,
% 12.19/8.12 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit1, s36, s37)),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 12.19/8.12 tff(2485,plain,
% 12.19/8.12 (node3(c_bit1, s36, s37)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2484, 21, 1113])).
% 12.19/8.12 tff(2486,plain,
% 12.19/8.12 (((~![Y: $i, 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)))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2487,plain,
% 12.19/8.12 ((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)))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2488,plain,
% 12.19/8.12 (((~![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))))),
% 12.19/8.12 inference(monotonicity,[status(thm)],[2487])).
% 12.19/8.12 tff(2489,plain,
% 12.19/8.12 (((~![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)))),
% 12.19/8.12 inference(transitivity,[status(thm)],[2488, 2486])).
% 12.19/8.12 tff(2490,plain,
% 12.19/8.12 ((~![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)))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2491,plain,
% 12.19/8.12 ((~![Y: $i, 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))),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2490, 2489])).
% 12.19/8.12 tff(2492,plain,
% 12.19/8.12 ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2491, 141, 2485])).
% 12.19/8.12 tff(2493,plain,
% 12.19/8.12 (~m_counter_cell_v_value(c_bit1, s37)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2492, 2481])).
% 12.19/8.12 tff(2494,plain,
% 12.19/8.12 (((~![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))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2495,plain,
% 12.19/8.12 ((~![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))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2496,plain,
% 12.19/8.12 ((~![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)),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 12.19/8.12 tff(2497,plain,
% 12.19/8.12 ((~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2496, 1368, 1129])).
% 12.19/8.12 tff(2498,plain,
% 12.19/8.12 (m_counter_cell_v_carry_out(c_bit0, s37)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2497, 1125])).
% 12.19/8.12 tff(2499,plain,
% 12.19/8.12 (((~![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))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2500,plain,
% 12.19/8.12 ((~![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))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2501,plain,
% 12.19/8.12 ((~![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)),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 12.19/8.12 tff(2502,plain,
% 12.19/8.12 (m_counter_cell_v_carry_in(c_bit1, s37)),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2501, 1383, 2498])).
% 12.19/8.12 tff(2503,assumption,(~m_counter_cell_v_value(c_bit1, s37)), introduced(assumption)).
% 12.19/8.12 tff(2504,assumption,(m_counter_cell_v_carry_in(c_bit1, s37)), introduced(assumption)).
% 12.19/8.12 tff(2505,assumption,(node1(c_bit1, s37)), introduced(assumption)).
% 12.19/8.12 tff(2506,plain,
% 12.19/8.12 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2507,plain,
% 12.19/8.12 (((~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)))),
% 12.19/8.12 inference(rewrite,[status(thm)],[])).
% 12.19/8.12 tff(2508,plain,
% 12.19/8.12 (((~![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))))),
% 12.19/8.12 inference(monotonicity,[status(thm)],[2507])).
% 12.19/8.12 tff(2509,plain,
% 12.19/8.12 (((~![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)))),
% 12.19/8.12 inference(transitivity,[status(thm)],[2508, 2506])).
% 12.19/8.12 tff(2510,plain,
% 12.19/8.12 ((~![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))),
% 12.19/8.12 inference(quant_inst,[status(thm)],[])).
% 12.19/8.12 tff(2511,plain,
% 12.19/8.12 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s37)) | m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37))),
% 12.19/8.12 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 12.19/8.12 tff(2512,plain,
% 12.19/8.12 ($false),
% 12.19/8.12 inference(unit_resolution,[status(thm)],[2511, 77, 2505, 2504, 2503])).
% 12.19/8.12 tff(2513,plain,(m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37)) | (~m_counter_cell_v_carry_in(c_bit1, s37))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.12 tff(2514,plain,
% 12.19/8.13 (m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37))),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2513, 2502])).
% 12.19/8.13 tff(2515,plain,
% 12.19/8.13 (~node1(c_bit1, s37)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2514, 2493])).
% 12.19/8.13 tff(2516,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2517,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit1, s37, s38))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2518,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit1, s37, s38)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2517, 2516])).
% 12.19/8.13 tff(2519,plain,
% 12.19/8.13 (node3(c_bit1, s37, s38)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2518, 21, 1141])).
% 12.19/8.13 tff(2520,plain,
% 12.19/8.13 (((~![Y: $i, 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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2521,plain,
% 12.19/8.13 ((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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2522,plain,
% 12.19/8.13 (((~![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))))),
% 12.19/8.13 inference(monotonicity,[status(thm)],[2521])).
% 12.19/8.13 tff(2523,plain,
% 12.19/8.13 (((~![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)))),
% 12.19/8.13 inference(transitivity,[status(thm)],[2522, 2520])).
% 12.19/8.13 tff(2524,plain,
% 12.19/8.13 ((~![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))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2525,plain,
% 12.19/8.13 ((~![Y: $i, 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))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 12.19/8.13 tff(2526,plain,
% 12.19/8.13 (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2525, 106, 2519])).
% 12.19/8.13 tff(2527,plain,
% 12.19/8.13 (m_counter_cell_v_value(c_bit1, s38)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2526, 2515])).
% 12.19/8.13 tff(2528,plain,
% 12.19/8.13 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2529,plain,
% 12.19/8.13 (((~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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2530,plain,
% 12.19/8.13 (((~![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))))),
% 12.19/8.13 inference(monotonicity,[status(thm)],[2529])).
% 12.19/8.13 tff(2531,plain,
% 12.19/8.13 (((~![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)))),
% 12.19/8.13 inference(transitivity,[status(thm)],[2530, 2528])).
% 12.19/8.13 tff(2532,plain,
% 12.19/8.13 ((~![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)))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2533,plain,
% 12.19/8.13 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2532, 2531])).
% 12.19/8.13 tff(2534,plain,
% 12.19/8.13 (~node1(c_bit1, s38)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2533, 1517, 2527, 1276])).
% 12.19/8.13 tff(2535,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2536,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit1, s38, s39))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2537,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit1, s38, s39)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2536, 2535])).
% 12.19/8.13 tff(2538,plain,
% 12.19/8.13 (node3(c_bit1, s38, s39)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2537, 21, 1172])).
% 12.19/8.13 tff(2539,plain,
% 12.19/8.13 (((~![Y: $i, 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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2540,plain,
% 12.19/8.13 ((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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2541,plain,
% 12.19/8.13 (((~![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))))),
% 12.19/8.13 inference(monotonicity,[status(thm)],[2540])).
% 12.19/8.13 tff(2542,plain,
% 12.19/8.13 (((~![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)))),
% 12.19/8.13 inference(transitivity,[status(thm)],[2541, 2539])).
% 12.19/8.13 tff(2543,plain,
% 12.19/8.13 ((~![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))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2544,plain,
% 12.19/8.13 ((~![Y: $i, 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))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 12.19/8.13 tff(2545,plain,
% 12.19/8.13 (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2544, 106, 2538])).
% 12.19/8.13 tff(2546,plain,
% 12.19/8.13 (m_counter_cell_v_value(c_bit1, s39)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2545, 2534])).
% 12.19/8.13 tff(2547,assumption,(node2(c_bit1, s39)), introduced(assumption)).
% 12.19/8.13 tff(2548,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2549,plain,
% 12.19/8.13 ((~![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))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2550,plain,
% 12.19/8.13 ((~![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)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 12.19/8.13 tff(2551,plain,
% 12.19/8.13 ((~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2550, 1368, 1188])).
% 12.19/8.13 tff(2552,plain,
% 12.19/8.13 (m_counter_cell_v_carry_out(c_bit0, s39)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2551, 1184])).
% 12.19/8.13 tff(2553,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2554,plain,
% 12.19/8.13 ((~![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))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2555,plain,
% 12.19/8.13 ((~![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)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2554, 2553])).
% 12.19/8.13 tff(2556,plain,
% 12.19/8.13 (m_counter_cell_v_carry_in(c_bit1, s39)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2555, 1383, 2552])).
% 12.19/8.13 tff(2557,assumption,(m_counter_cell_v_value(c_bit1, s39)), introduced(assumption)).
% 12.19/8.13 tff(2558,plain,
% 12.19/8.13 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2559,plain,
% 12.19/8.13 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2560,plain,
% 12.19/8.13 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 12.19/8.13 tff(2561,plain,
% 12.19/8.13 ($false),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2560, 126, 2557, 2556, 2547])).
% 12.19/8.13 tff(2562,plain,((~node2(c_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.13 tff(2563,plain,
% 12.19/8.13 (~node2(c_bit1, s39)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2562, 2546])).
% 12.19/8.13 tff(2564,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2565,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit1, s39, s40))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2566,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit1, s39, s40)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 12.19/8.13 tff(2567,plain,
% 12.19/8.13 (node3(c_bit1, s39, s40)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2566, 21, 1200])).
% 12.19/8.13 tff(2568,plain,
% 12.19/8.13 (((~![Y: $i, 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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2569,plain,
% 12.19/8.13 ((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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2570,plain,
% 12.19/8.13 (((~![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))))),
% 12.19/8.13 inference(monotonicity,[status(thm)],[2569])).
% 12.19/8.13 tff(2571,plain,
% 12.19/8.13 (((~![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)))),
% 12.19/8.13 inference(transitivity,[status(thm)],[2570, 2568])).
% 12.19/8.13 tff(2572,plain,
% 12.19/8.13 ((~![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)))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2573,plain,
% 12.19/8.13 ((~![Y: $i, 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))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2572, 2571])).
% 12.19/8.13 tff(2574,plain,
% 12.19/8.13 ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2573, 141, 2567])).
% 12.19/8.13 tff(2575,plain,
% 12.19/8.13 (~m_counter_cell_v_value(c_bit1, s40)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2574, 2563])).
% 12.19/8.13 tff(2576,plain,
% 12.19/8.13 (((~![I0: $i, X: $i] : (m_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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2577,plain,
% 12.19/8.13 ((~![I0: $i, X: $i] : (m_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)))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2578,plain,
% 12.19/8.13 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 12.19/8.13 tff(2579,plain,
% 12.19/8.13 ($false),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2578, 1449, 2575, 1256, 1255])).
% 12.19/8.13 tff(2580,plain,(~node2(c_bit1, s40)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.13 tff(2581,plain,
% 12.19/8.13 (succ(s40, s41) <=> succ(s40, s41)),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2582,axiom,(succ(s40, s41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound41')).
% 12.19/8.13 tff(2583,plain,
% 12.19/8.13 (succ(s40, s41)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2582, 2581])).
% 12.19/8.13 tff(2584,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2585,plain,
% 12.19/8.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2586,plain,
% 12.19/8.13 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 12.19/8.13 tff(2587,plain,
% 12.19/8.13 (trans(s40, s41)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2586, 2583, 7])).
% 12.19/8.13 tff(2588,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2589,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit1, s40, s41))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2590,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit1, s40, s41)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2589, 2588])).
% 12.19/8.13 tff(2591,plain,
% 12.19/8.13 (node3(c_bit1, s40, s41)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2590, 21, 2587])).
% 12.19/8.13 tff(2592,plain,
% 12.19/8.13 (((~![Y: $i, 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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2593,plain,
% 12.19/8.13 ((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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2594,plain,
% 12.19/8.13 (((~![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))))),
% 12.19/8.13 inference(monotonicity,[status(thm)],[2593])).
% 12.19/8.13 tff(2595,plain,
% 12.19/8.13 (((~![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)))),
% 12.19/8.13 inference(transitivity,[status(thm)],[2594, 2592])).
% 12.19/8.13 tff(2596,plain,
% 12.19/8.13 ((~![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)))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2597,plain,
% 12.19/8.13 ((~![Y: $i, 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))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2596, 2595])).
% 12.19/8.13 tff(2598,plain,
% 12.19/8.13 ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2597, 141, 2591])).
% 12.19/8.13 tff(2599,plain,
% 12.19/8.13 (~m_counter_cell_v_value(c_bit1, s41)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2598, 2580])).
% 12.19/8.13 tff(2600,assumption,(~m_counter_cell_v_carry_in(c_bit0, s40)), introduced(assumption)).
% 12.19/8.13 tff(2601,plain,
% 12.19/8.13 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s40)),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2602,plain,
% 12.19/8.13 ($false),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2601, 65, 2600])).
% 12.19/8.13 tff(2603,plain,(m_counter_cell_v_carry_in(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.13 tff(2604,plain,
% 12.19/8.13 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2605,plain,
% 12.19/8.13 (((~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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2606,plain,
% 12.19/8.13 (((~![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))))),
% 12.19/8.13 inference(monotonicity,[status(thm)],[2605])).
% 12.19/8.13 tff(2607,plain,
% 12.19/8.13 (((~![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)))),
% 12.19/8.13 inference(transitivity,[status(thm)],[2606, 2604])).
% 12.19/8.13 tff(2608,plain,
% 12.19/8.13 ((~![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))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2609,plain,
% 12.19/8.13 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2608, 2607])).
% 12.19/8.13 tff(2610,plain,
% 12.19/8.13 (m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2609, 77, 2603])).
% 12.19/8.13 tff(2611,plain,
% 12.19/8.13 (~node1(c_bit0, s40)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2610, 1212])).
% 12.19/8.13 tff(2612,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2613,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit0, s40, s41))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2614,plain,
% 12.19/8.13 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit0, s40, s41)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2613, 2612])).
% 12.19/8.13 tff(2615,plain,
% 12.19/8.13 (node3(c_bit0, s40, s41)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2614, 21, 2587])).
% 12.19/8.13 tff(2616,plain,
% 12.19/8.13 (((~![Y: $i, 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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2617,plain,
% 12.19/8.13 ((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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2618,plain,
% 12.19/8.13 (((~![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))))),
% 12.19/8.13 inference(monotonicity,[status(thm)],[2617])).
% 12.19/8.13 tff(2619,plain,
% 12.19/8.13 (((~![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)))),
% 12.19/8.13 inference(transitivity,[status(thm)],[2618, 2616])).
% 12.19/8.13 tff(2620,plain,
% 12.19/8.13 ((~![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))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2621,plain,
% 12.19/8.13 ((~![Y: $i, 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))),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2620, 2619])).
% 12.19/8.13 tff(2622,plain,
% 12.19/8.13 (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2621, 106, 2615])).
% 12.19/8.13 tff(2623,plain,
% 12.19/8.13 (m_counter_cell_v_value(c_bit0, s41)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2622, 2611])).
% 12.19/8.13 tff(2624,assumption,(~m_counter_cell_v_carry_in(c_bit0, s41)), introduced(assumption)).
% 12.19/8.13 tff(2625,plain,
% 12.19/8.13 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s41)),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2626,plain,
% 12.19/8.13 ($false),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2625, 65, 2624])).
% 12.19/8.13 tff(2627,plain,(m_counter_cell_v_carry_in(c_bit0, s41)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.13 tff(2628,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2629,plain,
% 12.19/8.13 ((~![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))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2630,plain,
% 12.19/8.13 ((~![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)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 12.19/8.13 tff(2631,plain,
% 12.19/8.13 ((~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2630, 1368, 2627])).
% 12.19/8.13 tff(2632,plain,
% 12.19/8.13 (m_counter_cell_v_carry_out(c_bit0, s41)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2631, 2623])).
% 12.19/8.13 tff(2633,plain,
% 12.19/8.13 (((~![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))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2634,plain,
% 12.19/8.13 ((~![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))),
% 12.19/8.13 inference(quant_inst,[status(thm)],[])).
% 12.19/8.13 tff(2635,plain,
% 12.19/8.13 ((~![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)),
% 12.19/8.13 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 12.19/8.13 tff(2636,plain,
% 12.19/8.13 (m_counter_cell_v_carry_in(c_bit1, s41)),
% 12.19/8.13 inference(unit_resolution,[status(thm)],[2635, 1383, 2632])).
% 12.19/8.13 tff(2637,plain,
% 12.19/8.13 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2638,plain,
% 12.19/8.13 (((~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)))),
% 12.19/8.13 inference(rewrite,[status(thm)],[])).
% 12.19/8.13 tff(2639,plain,
% 12.19/8.13 (((~![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))))),
% 12.19/8.13 inference(monotonicity,[status(thm)],[2638])).
% 12.19/8.13 tff(2640,plain,
% 12.19/8.13 (((~![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)))),
% 12.19/8.14 inference(transitivity,[status(thm)],[2639, 2637])).
% 12.19/8.14 tff(2641,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2642,plain,
% 12.19/8.14 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2641, 2640])).
% 12.19/8.14 tff(2643,plain,
% 12.19/8.14 (m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41))),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2642, 77, 2636])).
% 12.19/8.14 tff(2644,plain,
% 12.19/8.14 (~node1(c_bit1, s41)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2643, 2599])).
% 12.19/8.14 tff(2645,plain,
% 12.19/8.14 (succ(s41, s42) <=> succ(s41, s42)),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2646,axiom,(succ(s41, s42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound42')).
% 12.19/8.14 tff(2647,plain,
% 12.19/8.14 (succ(s41, s42)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2646, 2645])).
% 12.19/8.14 tff(2648,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2649,plain,
% 12.19/8.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2650,plain,
% 12.19/8.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2649, 2648])).
% 12.19/8.14 tff(2651,plain,
% 12.19/8.14 (trans(s41, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2650, 2647, 7])).
% 12.19/8.14 tff(2652,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2653,plain,
% 12.19/8.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit1, s41, s42))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2654,plain,
% 12.19/8.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit1, s41, s42)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 12.19/8.14 tff(2655,plain,
% 12.19/8.14 (node3(c_bit1, s41, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2654, 21, 2651])).
% 12.19/8.14 tff(2656,plain,
% 12.19/8.14 (((~![Y: $i, 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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2657,plain,
% 12.19/8.14 ((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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2658,plain,
% 12.19/8.14 (((~![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))))),
% 12.19/8.14 inference(monotonicity,[status(thm)],[2657])).
% 12.19/8.14 tff(2659,plain,
% 12.19/8.14 (((~![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)))),
% 12.19/8.14 inference(transitivity,[status(thm)],[2658, 2656])).
% 12.19/8.14 tff(2660,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2661,plain,
% 12.19/8.14 ((~![Y: $i, 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))),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2660, 2659])).
% 12.19/8.14 tff(2662,plain,
% 12.19/8.14 (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2661, 106, 2655])).
% 12.19/8.14 tff(2663,plain,
% 12.19/8.14 (m_counter_cell_v_value(c_bit1, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2662, 2644])).
% 12.19/8.14 tff(2664,plain,
% 12.19/8.14 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2665,plain,
% 12.19/8.14 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2666,plain,
% 12.19/8.14 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2665, 2664])).
% 12.19/8.14 tff(2667,plain,
% 12.19/8.14 ((~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41))),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2666, 126, 2627])).
% 12.19/8.14 tff(2668,plain,
% 12.19/8.14 (~node2(c_bit0, s41)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2667, 2623])).
% 12.19/8.14 tff(2669,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2670,plain,
% 12.19/8.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit0, s41, s42))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2671,plain,
% 12.19/8.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit0, s41, s42)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2670, 2669])).
% 12.19/8.14 tff(2672,plain,
% 12.19/8.14 (node3(c_bit0, s41, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2671, 21, 2651])).
% 12.19/8.14 tff(2673,plain,
% 12.19/8.14 (((~![Y: $i, 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)) | (~node3(c_bit0, s41, s42)) | node2(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, s42)) | (~node3(c_bit0, s41, s42)) | node2(c_bit0, s41))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2674,plain,
% 12.19/8.14 ((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)) | (~node3(c_bit0, s41, s42)) | node2(c_bit0, s41))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2675,plain,
% 12.19/8.14 (((~![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)) | (~node3(c_bit0, s41, s42)) | node2(c_bit0, s41)))),
% 12.19/8.14 inference(monotonicity,[status(thm)],[2674])).
% 12.19/8.14 tff(2676,plain,
% 12.19/8.14 (((~![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)) | (~node3(c_bit0, s41, s42)) | node2(c_bit0, s41))),
% 12.19/8.14 inference(transitivity,[status(thm)],[2675, 2673])).
% 12.19/8.14 tff(2677,plain,
% 12.19/8.14 ((~![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)))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2678,plain,
% 12.19/8.14 ((~![Y: $i, 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)) | (~node3(c_bit0, s41, s42)) | node2(c_bit0, s41)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 12.19/8.14 tff(2679,plain,
% 12.19/8.14 ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2678, 141, 2672])).
% 12.19/8.14 tff(2680,plain,
% 12.19/8.14 (~m_counter_cell_v_value(c_bit0, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2679, 2668])).
% 12.19/8.14 tff(2681,plain,
% 12.19/8.14 (((~![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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2682,plain,
% 12.19/8.14 ((~![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)))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2683,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 12.19/8.14 tff(2684,plain,
% 12.19/8.14 (~node4(c_bit0, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2683, 1221, 2680])).
% 12.19/8.14 tff(2685,assumption,(~node4(c_bit0, s42)), introduced(assumption)).
% 12.19/8.14 tff(2686,assumption,(m_counter_cell_v_carry_out(c_bit0, s42)), introduced(assumption)).
% 12.19/8.14 tff(2687,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2688,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2689,plain,
% 12.19/8.14 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2688, 2687])).
% 12.19/8.14 tff(2690,plain,
% 12.19/8.14 ($false),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2689, 1235, 2686, 2685])).
% 12.19/8.14 tff(2691,plain,((~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.14 tff(2692,plain,
% 12.19/8.14 (~m_counter_cell_v_carry_out(c_bit0, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2691, 2684])).
% 12.19/8.14 tff(2693,assumption,(m_counter_cell_v_carry_in(c_bit1, s42)), introduced(assumption)).
% 12.19/8.14 tff(2694,assumption,(~m_counter_cell_v_carry_out(c_bit0, s42)), introduced(assumption)).
% 12.19/8.14 tff(2695,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2696,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2697,plain,
% 12.19/8.14 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2696, 2695])).
% 12.19/8.14 tff(2698,plain,
% 12.19/8.14 ($false),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2697, 1249, 2694, 2693])).
% 12.19/8.14 tff(2699,plain,(m_counter_cell_v_carry_out(c_bit0, s42) | (~m_counter_cell_v_carry_in(c_bit1, s42))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.14 tff(2700,plain,
% 12.19/8.14 (~m_counter_cell_v_carry_in(c_bit1, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2699, 2692])).
% 12.19/8.14 tff(2701,assumption,(m_counter_cell_v_value(c_bit1, s42)), introduced(assumption)).
% 12.19/8.14 tff(2702,assumption,(node1(c_bit1, s42)), introduced(assumption)).
% 12.19/8.14 tff(2703,plain,
% 12.19/8.14 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2704,plain,
% 12.19/8.14 (((~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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2705,plain,
% 12.19/8.14 (((~![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))))),
% 12.19/8.14 inference(monotonicity,[status(thm)],[2704])).
% 12.19/8.14 tff(2706,plain,
% 12.19/8.14 (((~![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)))),
% 12.19/8.14 inference(transitivity,[status(thm)],[2705, 2703])).
% 12.19/8.14 tff(2707,plain,
% 12.19/8.14 ((~![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)))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2708,plain,
% 12.19/8.14 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42))),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2707, 2706])).
% 12.19/8.14 tff(2709,plain,
% 12.19/8.14 ($false),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2708, 1517, 2702, 2701, 2700])).
% 12.19/8.14 tff(2710,plain,((~m_counter_cell_v_value(c_bit1, s42)) | (~node1(c_bit1, s42))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.14 tff(2711,plain,
% 12.19/8.14 (~node1(c_bit1, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2710, 2663])).
% 12.19/8.14 tff(2712,plain,
% 12.19/8.14 (succ(s42, s43) <=> succ(s42, s43)),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2713,axiom,(succ(s42, s43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound43')).
% 12.19/8.14 tff(2714,plain,
% 12.19/8.14 (succ(s42, s43)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2713, 2712])).
% 12.19/8.14 tff(2715,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2716,plain,
% 12.19/8.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2717,plain,
% 12.19/8.14 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 12.19/8.14 tff(2718,plain,
% 12.19/8.14 (trans(s42, s43)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2717, 2714, 7])).
% 12.19/8.14 tff(2719,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2720,plain,
% 12.19/8.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit1, s42, s43))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2721,plain,
% 12.19/8.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit1, s42, s43)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2720, 2719])).
% 12.19/8.14 tff(2722,plain,
% 12.19/8.14 (node3(c_bit1, s42, s43)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2721, 21, 2718])).
% 12.19/8.14 tff(2723,plain,
% 12.19/8.14 (((~![Y: $i, 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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2724,plain,
% 12.19/8.14 ((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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2725,plain,
% 12.19/8.14 (((~![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))))),
% 12.19/8.14 inference(monotonicity,[status(thm)],[2724])).
% 12.19/8.14 tff(2726,plain,
% 12.19/8.14 (((~![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)))),
% 12.19/8.14 inference(transitivity,[status(thm)],[2725, 2723])).
% 12.19/8.14 tff(2727,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2728,plain,
% 12.19/8.14 ((~![Y: $i, 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))),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2727, 2726])).
% 12.19/8.14 tff(2729,plain,
% 12.19/8.14 (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2728, 106, 2722])).
% 12.19/8.14 tff(2730,plain,
% 12.19/8.14 (m_counter_cell_v_value(c_bit1, s43)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2729, 2711])).
% 12.19/8.14 tff(2731,assumption,(~m_counter_cell_v_carry_in(c_bit0, s42)), introduced(assumption)).
% 12.19/8.14 tff(2732,plain,
% 12.19/8.14 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s42)),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2733,plain,
% 12.19/8.14 ($false),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2732, 65, 2731])).
% 12.19/8.14 tff(2734,plain,(m_counter_cell_v_carry_in(c_bit0, s42)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.14 tff(2735,plain,
% 12.19/8.14 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2736,plain,
% 12.19/8.14 (((~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)))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2737,plain,
% 12.19/8.14 (((~![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))))),
% 12.19/8.14 inference(monotonicity,[status(thm)],[2736])).
% 12.19/8.14 tff(2738,plain,
% 12.19/8.14 (((~![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)))),
% 12.19/8.14 inference(transitivity,[status(thm)],[2737, 2735])).
% 12.19/8.14 tff(2739,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2740,plain,
% 12.19/8.14 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 12.19/8.14 tff(2741,plain,
% 12.19/8.14 (m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2740, 77, 2734])).
% 12.19/8.14 tff(2742,plain,
% 12.19/8.14 (~node1(c_bit0, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2741, 2680])).
% 12.19/8.14 tff(2743,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2744,plain,
% 12.19/8.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit0, s42, s43))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2745,plain,
% 12.19/8.14 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit0, s42, s43)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2744, 2743])).
% 12.19/8.14 tff(2746,plain,
% 12.19/8.14 (node3(c_bit0, s42, s43)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2745, 21, 2718])).
% 12.19/8.14 tff(2747,plain,
% 12.19/8.14 (((~![Y: $i, 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) | (~node3(c_bit0, s42, s43)) | node1(c_bit0, 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_bit0, s43) | (~node3(c_bit0, s42, s43)) | node1(c_bit0, s42))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2748,plain,
% 12.19/8.14 ((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) | (~node3(c_bit0, s42, s43)) | node1(c_bit0, s42))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2749,plain,
% 12.19/8.14 (((~![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) | (~node3(c_bit0, s42, s43)) | node1(c_bit0, s42)))),
% 12.19/8.14 inference(monotonicity,[status(thm)],[2748])).
% 12.19/8.14 tff(2750,plain,
% 12.19/8.14 (((~![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) | (~node3(c_bit0, s42, s43)) | node1(c_bit0, s42))),
% 12.19/8.14 inference(transitivity,[status(thm)],[2749, 2747])).
% 12.19/8.14 tff(2751,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2752,plain,
% 12.19/8.14 ((~![Y: $i, 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) | (~node3(c_bit0, s42, s43)) | node1(c_bit0, s42)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2751, 2750])).
% 12.19/8.14 tff(2753,plain,
% 12.19/8.14 (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2752, 106, 2746])).
% 12.19/8.14 tff(2754,plain,
% 12.19/8.14 (m_counter_cell_v_value(c_bit0, s43)),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2753, 2742])).
% 12.19/8.14 tff(2755,assumption,(~m_counter_cell_v_carry_in(c_bit0, s43)), introduced(assumption)).
% 12.19/8.14 tff(2756,plain,
% 12.19/8.14 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s43)),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2757,plain,
% 12.19/8.14 ($false),
% 12.19/8.14 inference(unit_resolution,[status(thm)],[2756, 65, 2755])).
% 12.19/8.14 tff(2758,plain,(m_counter_cell_v_carry_in(c_bit0, s43)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.14 tff(2759,plain,
% 12.19/8.14 (((~![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))),
% 12.19/8.14 inference(rewrite,[status(thm)],[])).
% 12.19/8.14 tff(2760,plain,
% 12.19/8.14 ((~![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))),
% 12.19/8.14 inference(quant_inst,[status(thm)],[])).
% 12.19/8.14 tff(2761,plain,
% 12.19/8.14 ((~![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)),
% 12.19/8.14 inference(modus_ponens,[status(thm)],[2760, 2759])).
% 12.19/8.14 tff(2762,plain,
% 12.19/8.15 ((~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2761, 1368, 2758])).
% 12.19/8.15 tff(2763,plain,
% 12.19/8.15 (m_counter_cell_v_carry_out(c_bit0, s43)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2762, 2754])).
% 12.19/8.15 tff(2764,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2765,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2766,plain,
% 12.19/8.15 ((~![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)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2765, 2764])).
% 12.19/8.15 tff(2767,plain,
% 12.19/8.15 (m_counter_cell_v_carry_in(c_bit1, s43)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2766, 1383, 2763])).
% 12.19/8.15 tff(2768,plain,
% 12.19/8.15 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2769,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2770,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 12.19/8.15 tff(2771,plain,
% 12.19/8.15 ((~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43))),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2770, 126, 2767])).
% 12.19/8.15 tff(2772,plain,
% 12.19/8.15 (~node2(c_bit1, s43)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2771, 2730])).
% 12.19/8.15 tff(2773,plain,
% 12.19/8.15 (succ(s43, s44) <=> succ(s43, s44)),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2774,axiom,(succ(s43, s44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound44')).
% 12.19/8.15 tff(2775,plain,
% 12.19/8.15 (succ(s43, s44)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 12.19/8.15 tff(2776,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2777,plain,
% 12.19/8.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2778,plain,
% 12.19/8.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2777, 2776])).
% 12.19/8.15 tff(2779,plain,
% 12.19/8.15 (trans(s43, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2778, 2775, 7])).
% 12.19/8.15 tff(2780,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2781,plain,
% 12.19/8.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit1, s43, s44))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2782,plain,
% 12.19/8.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit1, s43, s44)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2781, 2780])).
% 12.19/8.15 tff(2783,plain,
% 12.19/8.15 (node3(c_bit1, s43, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2782, 21, 2779])).
% 12.19/8.15 tff(2784,plain,
% 12.19/8.15 (((~![Y: $i, 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)) | (~node3(c_bit1, s43, s44)) | node2(c_bit1, s43))) <=> ((~![Y: $i, 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)) | (~node3(c_bit1, s43, s44)) | node2(c_bit1, s43))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2785,plain,
% 12.19/8.15 ((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)) | (~node3(c_bit1, s43, s44)) | node2(c_bit1, s43))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2786,plain,
% 12.19/8.15 (((~![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)) | (~node3(c_bit1, s43, s44)) | node2(c_bit1, s43)))),
% 12.19/8.15 inference(monotonicity,[status(thm)],[2785])).
% 12.19/8.15 tff(2787,plain,
% 12.19/8.15 (((~![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)) | (~node3(c_bit1, s43, s44)) | node2(c_bit1, s43))),
% 12.19/8.15 inference(transitivity,[status(thm)],[2786, 2784])).
% 12.19/8.15 tff(2788,plain,
% 12.19/8.15 ((~![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)))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2789,plain,
% 12.19/8.15 ((~![Y: $i, 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)) | (~node3(c_bit1, s43, s44)) | node2(c_bit1, s43)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2788, 2787])).
% 12.19/8.15 tff(2790,plain,
% 12.19/8.15 ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2789, 141, 2783])).
% 12.19/8.15 tff(2791,plain,
% 12.19/8.15 (~m_counter_cell_v_value(c_bit1, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2790, 2772])).
% 12.19/8.15 tff(2792,plain,
% 12.19/8.15 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2793,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2794,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2793, 2792])).
% 12.19/8.15 tff(2795,plain,
% 12.19/8.15 ((~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43))),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2794, 126, 2758])).
% 12.19/8.15 tff(2796,plain,
% 12.19/8.15 (~node2(c_bit0, s43)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2795, 2754])).
% 12.19/8.15 tff(2797,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2798,plain,
% 12.19/8.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit0, s43, s44))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2799,plain,
% 12.19/8.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit0, s43, s44)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2798, 2797])).
% 12.19/8.15 tff(2800,plain,
% 12.19/8.15 (node3(c_bit0, s43, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2799, 21, 2779])).
% 12.19/8.15 tff(2801,plain,
% 12.19/8.15 (((~![Y: $i, 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)) | (~node3(c_bit0, s43, s44)) | node2(c_bit0, s43))) <=> ((~![Y: $i, 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)) | (~node3(c_bit0, s43, s44)) | node2(c_bit0, s43))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2802,plain,
% 12.19/8.15 ((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)) | (~node3(c_bit0, s43, s44)) | node2(c_bit0, s43))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2803,plain,
% 12.19/8.15 (((~![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)) | (~node3(c_bit0, s43, s44)) | node2(c_bit0, s43)))),
% 12.19/8.15 inference(monotonicity,[status(thm)],[2802])).
% 12.19/8.15 tff(2804,plain,
% 12.19/8.15 (((~![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)) | (~node3(c_bit0, s43, s44)) | node2(c_bit0, s43))),
% 12.19/8.15 inference(transitivity,[status(thm)],[2803, 2801])).
% 12.19/8.15 tff(2805,plain,
% 12.19/8.15 ((~![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)))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2806,plain,
% 12.19/8.15 ((~![Y: $i, 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)) | (~node3(c_bit0, s43, s44)) | node2(c_bit0, s43)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2805, 2804])).
% 12.19/8.15 tff(2807,plain,
% 12.19/8.15 ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2806, 141, 2800])).
% 12.19/8.15 tff(2808,plain,
% 12.19/8.15 (~m_counter_cell_v_value(c_bit0, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2807, 2796])).
% 12.19/8.15 tff(2809,plain,
% 12.19/8.15 (((~![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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2810,plain,
% 12.19/8.15 ((~![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)))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2811,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2810, 2809])).
% 12.19/8.15 tff(2812,plain,
% 12.19/8.15 (~node4(c_bit0, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2811, 1221, 2808])).
% 12.19/8.15 tff(2813,assumption,(~node4(c_bit0, s44)), introduced(assumption)).
% 12.19/8.15 tff(2814,assumption,(m_counter_cell_v_carry_out(c_bit0, s44)), introduced(assumption)).
% 12.19/8.15 tff(2815,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2816,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2817,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2816, 2815])).
% 12.19/8.15 tff(2818,plain,
% 12.19/8.15 ($false),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2817, 1235, 2814, 2813])).
% 12.19/8.15 tff(2819,plain,((~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.15 tff(2820,plain,
% 12.19/8.15 (~m_counter_cell_v_carry_out(c_bit0, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2819, 2812])).
% 12.19/8.15 tff(2821,assumption,(m_counter_cell_v_carry_in(c_bit1, s44)), introduced(assumption)).
% 12.19/8.15 tff(2822,assumption,(~m_counter_cell_v_carry_out(c_bit0, s44)), introduced(assumption)).
% 12.19/8.15 tff(2823,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2824,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2825,plain,
% 12.19/8.15 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2824, 2823])).
% 12.19/8.15 tff(2826,plain,
% 12.19/8.15 ($false),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2825, 1249, 2822, 2821])).
% 12.19/8.15 tff(2827,plain,(m_counter_cell_v_carry_out(c_bit0, s44) | (~m_counter_cell_v_carry_in(c_bit1, s44))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.15 tff(2828,plain,
% 12.19/8.15 (~m_counter_cell_v_carry_in(c_bit1, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2827, 2820])).
% 12.19/8.15 tff(2829,assumption,(node2(c_bit1, s44)), introduced(assumption)).
% 12.19/8.15 tff(2830,assumption,(~m_counter_cell_v_carry_in(c_bit1, s44)), introduced(assumption)).
% 12.19/8.15 tff(2831,assumption,(~m_counter_cell_v_value(c_bit1, s44)), introduced(assumption)).
% 12.19/8.15 tff(2832,plain,
% 12.19/8.15 (((~![I0: $i, X: $i] : (m_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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2833,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : (m_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)))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2834,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44))),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2833, 2832])).
% 12.19/8.15 tff(2835,plain,
% 12.19/8.15 ($false),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2834, 1449, 2831, 2830, 2829])).
% 12.19/8.15 tff(2836,plain,(m_counter_cell_v_value(c_bit1, s44) | m_counter_cell_v_carry_in(c_bit1, s44) | (~node2(c_bit1, s44))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.15 tff(2837,plain,
% 12.19/8.15 (m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44))),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2836, 2828])).
% 12.19/8.15 tff(2838,plain,
% 12.19/8.15 (~node2(c_bit1, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2837, 2791])).
% 12.19/8.15 tff(2839,plain,
% 12.19/8.15 (succ(s44, s45) <=> succ(s44, s45)),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2840,axiom,(succ(s44, s45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound45')).
% 12.19/8.15 tff(2841,plain,
% 12.19/8.15 (succ(s44, s45)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2840, 2839])).
% 12.19/8.15 tff(2842,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2843,plain,
% 12.19/8.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2844,plain,
% 12.19/8.15 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 12.19/8.15 tff(2845,plain,
% 12.19/8.15 (trans(s44, s45)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2844, 2841, 7])).
% 12.19/8.15 tff(2846,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2847,plain,
% 12.19/8.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit1, s44, s45))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2848,plain,
% 12.19/8.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit1, s44, s45)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2847, 2846])).
% 12.19/8.15 tff(2849,plain,
% 12.19/8.15 (node3(c_bit1, s44, s45)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2848, 21, 2845])).
% 12.19/8.15 tff(2850,plain,
% 12.19/8.15 (((~![Y: $i, 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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2851,plain,
% 12.19/8.15 ((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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2852,plain,
% 12.19/8.15 (((~![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))))),
% 12.19/8.15 inference(monotonicity,[status(thm)],[2851])).
% 12.19/8.15 tff(2853,plain,
% 12.19/8.15 (((~![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)))),
% 12.19/8.15 inference(transitivity,[status(thm)],[2852, 2850])).
% 12.19/8.15 tff(2854,plain,
% 12.19/8.15 ((~![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)))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2855,plain,
% 12.19/8.15 ((~![Y: $i, 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))),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 12.19/8.15 tff(2856,plain,
% 12.19/8.15 ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2855, 141, 2849])).
% 12.19/8.15 tff(2857,plain,
% 12.19/8.15 (~m_counter_cell_v_value(c_bit1, s45)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2856, 2838])).
% 12.19/8.15 tff(2858,assumption,(~m_counter_cell_v_carry_in(c_bit0, s44)), introduced(assumption)).
% 12.19/8.15 tff(2859,plain,
% 12.19/8.15 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s44)),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2860,plain,
% 12.19/8.15 ($false),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2859, 65, 2858])).
% 12.19/8.15 tff(2861,plain,(m_counter_cell_v_carry_in(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.15 tff(2862,plain,
% 12.19/8.15 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2863,plain,
% 12.19/8.15 (((~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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2864,plain,
% 12.19/8.15 (((~![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))))),
% 12.19/8.15 inference(monotonicity,[status(thm)],[2863])).
% 12.19/8.15 tff(2865,plain,
% 12.19/8.15 (((~![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)))),
% 12.19/8.15 inference(transitivity,[status(thm)],[2864, 2862])).
% 12.19/8.15 tff(2866,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2867,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2866, 2865])).
% 12.19/8.15 tff(2868,plain,
% 12.19/8.15 (m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2867, 77, 2861])).
% 12.19/8.15 tff(2869,plain,
% 12.19/8.15 (~node1(c_bit0, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2868, 2808])).
% 12.19/8.15 tff(2870,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2871,plain,
% 12.19/8.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit0, s44, s45))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2872,plain,
% 12.19/8.15 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit0, s44, s45)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2871, 2870])).
% 12.19/8.15 tff(2873,plain,
% 12.19/8.15 (node3(c_bit0, s44, s45)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2872, 21, 2845])).
% 12.19/8.15 tff(2874,plain,
% 12.19/8.15 (((~![Y: $i, 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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2875,plain,
% 12.19/8.15 ((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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2876,plain,
% 12.19/8.15 (((~![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))))),
% 12.19/8.15 inference(monotonicity,[status(thm)],[2875])).
% 12.19/8.15 tff(2877,plain,
% 12.19/8.15 (((~![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)))),
% 12.19/8.15 inference(transitivity,[status(thm)],[2876, 2874])).
% 12.19/8.15 tff(2878,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2879,plain,
% 12.19/8.15 ((~![Y: $i, 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))),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2878, 2877])).
% 12.19/8.15 tff(2880,plain,
% 12.19/8.15 (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2879, 106, 2873])).
% 12.19/8.15 tff(2881,plain,
% 12.19/8.15 (m_counter_cell_v_value(c_bit0, s45)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2880, 2869])).
% 12.19/8.15 tff(2882,assumption,(~m_counter_cell_v_carry_in(c_bit0, s45)), introduced(assumption)).
% 12.19/8.15 tff(2883,plain,
% 12.19/8.15 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s45)),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2884,plain,
% 12.19/8.15 ($false),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2883, 65, 2882])).
% 12.19/8.15 tff(2885,plain,(m_counter_cell_v_carry_in(c_bit0, s45)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.15 tff(2886,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2887,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2888,plain,
% 12.19/8.15 ((~![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)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2887, 2886])).
% 12.19/8.15 tff(2889,plain,
% 12.19/8.15 ((~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2888, 1368, 2885])).
% 12.19/8.15 tff(2890,plain,
% 12.19/8.15 (m_counter_cell_v_carry_out(c_bit0, s45)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2889, 2881])).
% 12.19/8.15 tff(2891,plain,
% 12.19/8.15 (((~![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))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2892,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2893,plain,
% 12.19/8.15 ((~![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)),
% 12.19/8.15 inference(modus_ponens,[status(thm)],[2892, 2891])).
% 12.19/8.15 tff(2894,plain,
% 12.19/8.15 (m_counter_cell_v_carry_in(c_bit1, s45)),
% 12.19/8.15 inference(unit_resolution,[status(thm)],[2893, 1383, 2890])).
% 12.19/8.15 tff(2895,plain,
% 12.19/8.15 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2896,plain,
% 12.19/8.15 (((~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)))),
% 12.19/8.15 inference(rewrite,[status(thm)],[])).
% 12.19/8.15 tff(2897,plain,
% 12.19/8.15 (((~![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))))),
% 12.19/8.15 inference(monotonicity,[status(thm)],[2896])).
% 12.19/8.15 tff(2898,plain,
% 12.19/8.15 (((~![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)))),
% 12.19/8.15 inference(transitivity,[status(thm)],[2897, 2895])).
% 12.19/8.15 tff(2899,plain,
% 12.19/8.15 ((~![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))),
% 12.19/8.15 inference(quant_inst,[status(thm)],[])).
% 12.19/8.15 tff(2900,plain,
% 12.19/8.15 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2899, 2898])).
% 12.19/8.16 tff(2901,plain,
% 12.19/8.16 (m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45))),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2900, 77, 2894])).
% 12.19/8.16 tff(2902,plain,
% 12.19/8.16 (~node1(c_bit1, s45)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2901, 2857])).
% 12.19/8.16 tff(2903,plain,
% 12.19/8.16 (succ(s45, s46) <=> succ(s45, s46)),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2904,axiom,(succ(s45, s46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound46')).
% 12.19/8.16 tff(2905,plain,
% 12.19/8.16 (succ(s45, s46)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2904, 2903])).
% 12.19/8.16 tff(2906,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2907,plain,
% 12.19/8.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2908,plain,
% 12.19/8.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2907, 2906])).
% 12.19/8.16 tff(2909,plain,
% 12.19/8.16 (trans(s45, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2908, 2905, 7])).
% 12.19/8.16 tff(2910,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2911,plain,
% 12.19/8.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit1, s45, s46))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2912,plain,
% 12.19/8.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit1, s45, s46)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2911, 2910])).
% 12.19/8.16 tff(2913,plain,
% 12.19/8.16 (node3(c_bit1, s45, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2912, 21, 2909])).
% 12.19/8.16 tff(2914,plain,
% 12.19/8.16 (((~![Y: $i, 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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2915,plain,
% 12.19/8.16 ((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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2916,plain,
% 12.19/8.16 (((~![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))))),
% 12.19/8.16 inference(monotonicity,[status(thm)],[2915])).
% 12.19/8.16 tff(2917,plain,
% 12.19/8.16 (((~![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)))),
% 12.19/8.16 inference(transitivity,[status(thm)],[2916, 2914])).
% 12.19/8.16 tff(2918,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2919,plain,
% 12.19/8.16 ((~![Y: $i, 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))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2918, 2917])).
% 12.19/8.16 tff(2920,plain,
% 12.19/8.16 (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2919, 106, 2913])).
% 12.19/8.16 tff(2921,plain,
% 12.19/8.16 (m_counter_cell_v_value(c_bit1, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2920, 2902])).
% 12.19/8.16 tff(2922,assumption,(m_counter_cell_v_carry_in(c_bit1, s46)), introduced(assumption)).
% 12.19/8.16 tff(2923,plain,
% 12.19/8.16 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2924,plain,
% 12.19/8.16 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2925,plain,
% 12.19/8.16 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2924, 2923])).
% 12.19/8.16 tff(2926,plain,
% 12.19/8.16 ((~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45))),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2925, 126, 2885])).
% 12.19/8.16 tff(2927,plain,
% 12.19/8.16 (~node2(c_bit0, s45)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2926, 2881])).
% 12.19/8.16 tff(2928,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2929,plain,
% 12.19/8.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit0, s45, s46))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2930,plain,
% 12.19/8.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit0, s45, s46)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 12.19/8.16 tff(2931,plain,
% 12.19/8.16 (node3(c_bit0, s45, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2930, 21, 2909])).
% 12.19/8.16 tff(2932,plain,
% 12.19/8.16 (((~![Y: $i, 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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2933,plain,
% 12.19/8.16 ((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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2934,plain,
% 12.19/8.16 (((~![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))))),
% 12.19/8.16 inference(monotonicity,[status(thm)],[2933])).
% 12.19/8.16 tff(2935,plain,
% 12.19/8.16 (((~![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)))),
% 12.19/8.16 inference(transitivity,[status(thm)],[2934, 2932])).
% 12.19/8.16 tff(2936,plain,
% 12.19/8.16 ((~![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)))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2937,plain,
% 12.19/8.16 ((~![Y: $i, 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))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 12.19/8.16 tff(2938,plain,
% 12.19/8.16 ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2937, 141, 2931])).
% 12.19/8.16 tff(2939,plain,
% 12.19/8.16 (~m_counter_cell_v_value(c_bit0, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2938, 2927])).
% 12.19/8.16 tff(2940,plain,
% 12.19/8.16 (((~![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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2941,plain,
% 12.19/8.16 ((~![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)))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2942,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2941, 2940])).
% 12.19/8.16 tff(2943,plain,
% 12.19/8.16 (~node4(c_bit0, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2942, 1221, 2939])).
% 12.19/8.16 tff(2944,assumption,(~node4(c_bit0, s46)), introduced(assumption)).
% 12.19/8.16 tff(2945,assumption,(m_counter_cell_v_carry_out(c_bit0, s46)), introduced(assumption)).
% 12.19/8.16 tff(2946,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2947,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2948,plain,
% 12.19/8.16 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2947, 2946])).
% 12.19/8.16 tff(2949,plain,
% 12.19/8.16 ($false),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2948, 1235, 2945, 2944])).
% 12.19/8.16 tff(2950,plain,((~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.16 tff(2951,plain,
% 12.19/8.16 (~m_counter_cell_v_carry_out(c_bit0, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2950, 2943])).
% 12.19/8.16 tff(2952,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2953,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2954,plain,
% 12.19/8.16 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2953, 2952])).
% 12.19/8.16 tff(2955,plain,
% 12.19/8.16 ($false),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2954, 1249, 2951, 2922])).
% 12.19/8.16 tff(2956,plain,(~m_counter_cell_v_carry_in(c_bit1, s46)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.16 tff(2957,assumption,(~m_counter_cell_v_carry_in(c_bit1, s46)), introduced(assumption)).
% 12.19/8.16 tff(2958,assumption,(node1(c_bit1, s46)), introduced(assumption)).
% 12.19/8.16 tff(2959,assumption,(m_counter_cell_v_value(c_bit1, s46)), introduced(assumption)).
% 12.19/8.16 tff(2960,plain,
% 12.19/8.16 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2961,plain,
% 12.19/8.16 (((~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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2962,plain,
% 12.19/8.16 (((~![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))))),
% 12.19/8.16 inference(monotonicity,[status(thm)],[2961])).
% 12.19/8.16 tff(2963,plain,
% 12.19/8.16 (((~![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)))),
% 12.19/8.16 inference(transitivity,[status(thm)],[2962, 2960])).
% 12.19/8.16 tff(2964,plain,
% 12.19/8.16 ((~![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)))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2965,plain,
% 12.19/8.16 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2964, 2963])).
% 12.19/8.16 tff(2966,plain,
% 12.19/8.16 ($false),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2965, 1517, 2959, 2958, 2957])).
% 12.19/8.16 tff(2967,plain,((~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit1, s46)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.16 tff(2968,plain,
% 12.19/8.16 ((~m_counter_cell_v_value(c_bit1, s46)) | (~node1(c_bit1, s46))),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2967, 2956])).
% 12.19/8.16 tff(2969,plain,
% 12.19/8.16 (~node1(c_bit1, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2968, 2921])).
% 12.19/8.16 tff(2970,plain,
% 12.19/8.16 (succ(s46, s47) <=> succ(s46, s47)),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2971,axiom,(succ(s46, s47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound47')).
% 12.19/8.16 tff(2972,plain,
% 12.19/8.16 (succ(s46, s47)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2971, 2970])).
% 12.19/8.16 tff(2973,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2974,plain,
% 12.19/8.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2975,plain,
% 12.19/8.16 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2974, 2973])).
% 12.19/8.16 tff(2976,plain,
% 12.19/8.16 (trans(s46, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2975, 2972, 7])).
% 12.19/8.16 tff(2977,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2978,plain,
% 12.19/8.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit1, s46, s47))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2979,plain,
% 12.19/8.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit1, s46, s47)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2978, 2977])).
% 12.19/8.16 tff(2980,plain,
% 12.19/8.16 (node3(c_bit1, s46, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2979, 21, 2976])).
% 12.19/8.16 tff(2981,plain,
% 12.19/8.16 (((~![Y: $i, 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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2982,plain,
% 12.19/8.16 ((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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2983,plain,
% 12.19/8.16 (((~![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))))),
% 12.19/8.16 inference(monotonicity,[status(thm)],[2982])).
% 12.19/8.16 tff(2984,plain,
% 12.19/8.16 (((~![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)))),
% 12.19/8.16 inference(transitivity,[status(thm)],[2983, 2981])).
% 12.19/8.16 tff(2985,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2986,plain,
% 12.19/8.16 ((~![Y: $i, 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))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 12.19/8.16 tff(2987,plain,
% 12.19/8.16 (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2986, 106, 2980])).
% 12.19/8.16 tff(2988,plain,
% 12.19/8.16 (m_counter_cell_v_value(c_bit1, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2987, 2969])).
% 12.19/8.16 tff(2989,assumption,(~m_counter_cell_v_carry_in(c_bit0, s46)), introduced(assumption)).
% 12.19/8.16 tff(2990,plain,
% 12.19/8.16 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s46)),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2991,plain,
% 12.19/8.16 ($false),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2990, 65, 2989])).
% 12.19/8.16 tff(2992,plain,(m_counter_cell_v_carry_in(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.16 tff(2993,plain,
% 12.19/8.16 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2994,plain,
% 12.19/8.16 (((~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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(2995,plain,
% 12.19/8.16 (((~![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))))),
% 12.19/8.16 inference(monotonicity,[status(thm)],[2994])).
% 12.19/8.16 tff(2996,plain,
% 12.19/8.16 (((~![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)))),
% 12.19/8.16 inference(transitivity,[status(thm)],[2995, 2993])).
% 12.19/8.16 tff(2997,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(2998,plain,
% 12.19/8.16 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[2997, 2996])).
% 12.19/8.16 tff(2999,plain,
% 12.19/8.16 (m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2998, 77, 2992])).
% 12.19/8.16 tff(3000,plain,
% 12.19/8.16 (~node1(c_bit0, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[2999, 2939])).
% 12.19/8.16 tff(3001,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(3002,plain,
% 12.19/8.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit0, s46, s47))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(3003,plain,
% 12.19/8.16 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit0, s46, s47)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 12.19/8.16 tff(3004,plain,
% 12.19/8.16 (node3(c_bit0, s46, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3003, 21, 2976])).
% 12.19/8.16 tff(3005,plain,
% 12.19/8.16 (((~![Y: $i, 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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(3006,plain,
% 12.19/8.16 ((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)))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(3007,plain,
% 12.19/8.16 (((~![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))))),
% 12.19/8.16 inference(monotonicity,[status(thm)],[3006])).
% 12.19/8.16 tff(3008,plain,
% 12.19/8.16 (((~![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)))),
% 12.19/8.16 inference(transitivity,[status(thm)],[3007, 3005])).
% 12.19/8.16 tff(3009,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(3010,plain,
% 12.19/8.16 ((~![Y: $i, 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))),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 12.19/8.16 tff(3011,plain,
% 12.19/8.16 (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3010, 106, 3004])).
% 12.19/8.16 tff(3012,plain,
% 12.19/8.16 (m_counter_cell_v_value(c_bit0, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3011, 3000])).
% 12.19/8.16 tff(3013,assumption,(~m_counter_cell_v_carry_in(c_bit0, s47)), introduced(assumption)).
% 12.19/8.16 tff(3014,plain,
% 12.19/8.16 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s47)),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(3015,plain,
% 12.19/8.16 ($false),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3014, 65, 3013])).
% 12.19/8.16 tff(3016,plain,(m_counter_cell_v_carry_in(c_bit0, s47)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.16 tff(3017,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(3018,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(3019,plain,
% 12.19/8.16 ((~![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)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 12.19/8.16 tff(3020,plain,
% 12.19/8.16 ((~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3019, 1368, 3016])).
% 12.19/8.16 tff(3021,plain,
% 12.19/8.16 (m_counter_cell_v_carry_out(c_bit0, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3020, 3012])).
% 12.19/8.16 tff(3022,plain,
% 12.19/8.16 (((~![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))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(3023,plain,
% 12.19/8.16 ((~![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))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(3024,plain,
% 12.19/8.16 ((~![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)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[3023, 3022])).
% 12.19/8.16 tff(3025,plain,
% 12.19/8.16 (m_counter_cell_v_carry_in(c_bit1, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3024, 1383, 3021])).
% 12.19/8.16 tff(3026,assumption,(~m_counter_cell_v_carry_out(c_bit1, s47)), introduced(assumption)).
% 12.19/8.16 tff(3027,assumption,(m_counter_cell_v_carry_in(c_bit1, s47)), introduced(assumption)).
% 12.19/8.16 tff(3028,assumption,(m_counter_cell_v_value(c_bit1, s47)), introduced(assumption)).
% 12.19/8.16 tff(3029,plain,
% 12.19/8.16 (((~![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, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | m_counter_cell_v_carry_out(c_bit1, 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_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | m_counter_cell_v_carry_out(c_bit1, s47))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(3030,plain,
% 12.19/8.16 ((~![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, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | m_counter_cell_v_carry_out(c_bit1, s47))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(3031,plain,
% 12.19/8.16 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | m_counter_cell_v_carry_out(c_bit1, s47)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[3030, 3029])).
% 12.19/8.16 tff(3032,plain,
% 12.19/8.16 ($false),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3031, 1368, 3028, 3027, 3026])).
% 12.19/8.16 tff(3033,plain,(m_counter_cell_v_carry_out(c_bit1, s47) | (~m_counter_cell_v_value(c_bit1, s47)) | (~m_counter_cell_v_carry_in(c_bit1, s47))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.16 tff(3034,plain,
% 12.19/8.16 (m_counter_cell_v_carry_out(c_bit1, s47) | (~m_counter_cell_v_value(c_bit1, s47))),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3033, 3025])).
% 12.19/8.16 tff(3035,plain,
% 12.19/8.16 (m_counter_cell_v_carry_out(c_bit1, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3034, 2988])).
% 12.19/8.16 tff(3036,assumption,(m_counter_cell_v_carry_out(c_bit1, s47)), introduced(assumption)).
% 12.19/8.16 tff(3037,assumption,(~node4(c_bit1, s47)), introduced(assumption)).
% 12.19/8.16 tff(3038,plain,
% 12.19/8.16 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s47)) | node4(c_bit1, s47))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s47)) | node4(c_bit1, s47))),
% 12.19/8.16 inference(rewrite,[status(thm)],[])).
% 12.19/8.16 tff(3039,plain,
% 12.19/8.16 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s47)) | node4(c_bit1, s47))),
% 12.19/8.16 inference(quant_inst,[status(thm)],[])).
% 12.19/8.16 tff(3040,plain,
% 12.19/8.16 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s47)) | node4(c_bit1, s47)),
% 12.19/8.16 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 12.19/8.16 tff(3041,plain,
% 12.19/8.16 ($false),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3040, 1235, 3037, 3036])).
% 12.19/8.16 tff(3042,plain,((~m_counter_cell_v_carry_out(c_bit1, s47)) | node4(c_bit1, s47)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.16 tff(3043,plain,
% 12.19/8.16 (node4(c_bit1, s47)),
% 12.19/8.16 inference(unit_resolution,[status(thm)],[3042, 3035])).
% 12.19/8.16 tff(3044,assumption,(node4(c_bit1, s47)), introduced(assumption)).
% 12.19/8.16 tff(3045,plain,
% 12.19/8.16 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s47) | (~node4(c_bit1, s47)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s47) | (~node4(c_bit1, s47)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3046,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s47) | (~node4(c_bit1, s47)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3047,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s47) | (~node4(c_bit1, s47))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3046, 3045])).
% 12.19/8.17 tff(3048,plain,
% 12.19/8.17 (m_counter_cell_v_value(c_bit1, s47)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3047, 1221, 3044])).
% 12.19/8.17 tff(3049,plain,
% 12.19/8.17 (^[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))))),
% 12.19/8.17 inference(bind,[status(th)],[])).
% 12.19/8.17 tff(3050,plain,
% 12.19/8.17 (![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)))),
% 12.19/8.17 inference(quant_intro,[status(thm)],[3049])).
% 12.19/8.17 tff(3051,plain,
% 12.19/8.17 (![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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3052,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')).
% 12.19/8.17 tff(3053,plain,
% 12.19/8.17 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3052, 3051])).
% 12.19/8.17 tff(3054,plain,(
% 12.19/8.17 ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 12.19/8.17 inference(skolemize,[status(sab)],[3053])).
% 12.19/8.17 tff(3055,plain,
% 12.19/8.17 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3054, 3050])).
% 12.19/8.17 tff(3056,plain,
% 12.19/8.17 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s47) | (~node4(c_bit1, s47)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s47) | (~node4(c_bit1, s47)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3057,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s47) | (~node4(c_bit1, s47)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3058,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s47) | (~node4(c_bit1, s47))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3057, 3056])).
% 12.19/8.17 tff(3059,plain,
% 12.19/8.17 (m_counter_cell_v_carry_in(c_bit1, s47)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3058, 3055, 3044])).
% 12.19/8.17 tff(3060,assumption,(node2(c_bit1, s47)), introduced(assumption)).
% 12.19/8.17 tff(3061,plain,
% 12.19/8.17 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3062,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3063,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 12.19/8.17 tff(3064,plain,
% 12.19/8.17 ((~m_counter_cell_v_carry_in(c_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47))),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3063, 126, 3060])).
% 12.19/8.17 tff(3065,plain,
% 12.19/8.17 ($false),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3064, 3059, 3048])).
% 12.19/8.17 tff(3066,plain,((~node4(c_bit1, s47)) | (~node2(c_bit1, s47))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.17 tff(3067,plain,
% 12.19/8.17 (~node2(c_bit1, s47)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3066, 3043])).
% 12.19/8.17 tff(3068,plain,
% 12.19/8.17 (succ(s47, s48) <=> succ(s47, s48)),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3069,axiom,(succ(s47, s48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound48')).
% 12.19/8.17 tff(3070,plain,
% 12.19/8.17 (succ(s47, s48)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3069, 3068])).
% 12.19/8.17 tff(3071,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3072,plain,
% 12.19/8.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3073,plain,
% 12.19/8.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3072, 3071])).
% 12.19/8.17 tff(3074,plain,
% 12.19/8.17 (trans(s47, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3073, 3070, 7])).
% 12.19/8.17 tff(3075,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3076,plain,
% 12.19/8.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit1, s47, s48))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3077,plain,
% 12.19/8.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit1, s47, s48)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3076, 3075])).
% 12.19/8.17 tff(3078,plain,
% 12.19/8.17 (node3(c_bit1, s47, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3077, 21, 3074])).
% 12.19/8.17 tff(3079,plain,
% 12.19/8.17 (((~![Y: $i, 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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3080,plain,
% 12.19/8.17 ((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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3081,plain,
% 12.19/8.17 (((~![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))))),
% 12.19/8.17 inference(monotonicity,[status(thm)],[3080])).
% 12.19/8.17 tff(3082,plain,
% 12.19/8.17 (((~![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)))),
% 12.19/8.17 inference(transitivity,[status(thm)],[3081, 3079])).
% 12.19/8.17 tff(3083,plain,
% 12.19/8.17 ((~![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)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3084,plain,
% 12.19/8.17 ((~![Y: $i, 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))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3083, 3082])).
% 12.19/8.17 tff(3085,plain,
% 12.19/8.17 ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3084, 141, 3078])).
% 12.19/8.17 tff(3086,plain,
% 12.19/8.17 (~m_counter_cell_v_value(c_bit1, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3085, 3067])).
% 12.19/8.17 tff(3087,plain,
% 12.19/8.17 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3088,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3089,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3088, 3087])).
% 12.19/8.17 tff(3090,plain,
% 12.19/8.17 ((~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47))),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3089, 126, 3016])).
% 12.19/8.17 tff(3091,plain,
% 12.19/8.17 (~node2(c_bit0, s47)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3090, 3012])).
% 12.19/8.17 tff(3092,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3093,plain,
% 12.19/8.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit0, s47, s48))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3094,plain,
% 12.19/8.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit0, s47, s48)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3093, 3092])).
% 12.19/8.17 tff(3095,plain,
% 12.19/8.17 (node3(c_bit0, s47, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3094, 21, 3074])).
% 12.19/8.17 tff(3096,plain,
% 12.19/8.17 (((~![Y: $i, 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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3097,plain,
% 12.19/8.17 ((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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3098,plain,
% 12.19/8.17 (((~![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))))),
% 12.19/8.17 inference(monotonicity,[status(thm)],[3097])).
% 12.19/8.17 tff(3099,plain,
% 12.19/8.17 (((~![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)))),
% 12.19/8.17 inference(transitivity,[status(thm)],[3098, 3096])).
% 12.19/8.17 tff(3100,plain,
% 12.19/8.17 ((~![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)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3101,plain,
% 12.19/8.17 ((~![Y: $i, 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))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3100, 3099])).
% 12.19/8.17 tff(3102,plain,
% 12.19/8.17 ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3101, 141, 3095])).
% 12.19/8.17 tff(3103,plain,
% 12.19/8.17 (~m_counter_cell_v_value(c_bit0, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3102, 3091])).
% 12.19/8.17 tff(3104,plain,
% 12.19/8.17 (((~![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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3105,plain,
% 12.19/8.17 ((~![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)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3106,plain,
% 12.19/8.17 ((~![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))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3105, 3104])).
% 12.19/8.17 tff(3107,plain,
% 12.19/8.17 (~node4(c_bit0, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3106, 1221, 3103])).
% 12.19/8.17 tff(3108,assumption,(~node4(c_bit0, s48)), introduced(assumption)).
% 12.19/8.17 tff(3109,assumption,(m_counter_cell_v_carry_out(c_bit0, s48)), introduced(assumption)).
% 12.19/8.17 tff(3110,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3111,plain,
% 12.19/8.17 ((~![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))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3112,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3111, 3110])).
% 12.19/8.17 tff(3113,plain,
% 12.19/8.17 ($false),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3112, 1235, 3109, 3108])).
% 12.19/8.17 tff(3114,plain,((~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.17 tff(3115,plain,
% 12.19/8.17 (~m_counter_cell_v_carry_out(c_bit0, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3114, 3107])).
% 12.19/8.17 tff(3116,assumption,(m_counter_cell_v_carry_in(c_bit1, s48)), introduced(assumption)).
% 12.19/8.17 tff(3117,assumption,(~m_counter_cell_v_carry_out(c_bit0, s48)), introduced(assumption)).
% 12.19/8.17 tff(3118,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3119,plain,
% 12.19/8.17 ((~![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))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3120,plain,
% 12.19/8.17 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3119, 3118])).
% 12.19/8.17 tff(3121,plain,
% 12.19/8.17 ($false),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3120, 1249, 3117, 3116])).
% 12.19/8.17 tff(3122,plain,((~m_counter_cell_v_carry_in(c_bit1, s48)) | m_counter_cell_v_carry_out(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.17 tff(3123,plain,
% 12.19/8.17 (~m_counter_cell_v_carry_in(c_bit1, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3122, 3115])).
% 12.19/8.17 tff(3124,plain,
% 12.19/8.17 (((~![I0: $i, X: $i] : (m_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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3125,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : (m_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)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3126,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : (m_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))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3125, 3124])).
% 12.19/8.17 tff(3127,plain,
% 12.19/8.17 (~node2(c_bit1, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3126, 1449, 3123, 3086])).
% 12.19/8.17 tff(3128,plain,
% 12.19/8.17 (succ(s48, s49) <=> succ(s48, s49)),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3129,axiom,(succ(s48, s49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound49')).
% 12.19/8.17 tff(3130,plain,
% 12.19/8.17 (succ(s48, s49)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3129, 3128])).
% 12.19/8.17 tff(3131,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3132,plain,
% 12.19/8.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3133,plain,
% 12.19/8.17 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3132, 3131])).
% 12.19/8.17 tff(3134,plain,
% 12.19/8.17 (trans(s48, s49)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3133, 3130, 7])).
% 12.19/8.17 tff(3135,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3136,plain,
% 12.19/8.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit1, s48, s49))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3137,plain,
% 12.19/8.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit1, s48, s49)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3136, 3135])).
% 12.19/8.17 tff(3138,plain,
% 12.19/8.17 (node3(c_bit1, s48, s49)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3137, 21, 3134])).
% 12.19/8.17 tff(3139,plain,
% 12.19/8.17 (((~![Y: $i, 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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3140,plain,
% 12.19/8.17 ((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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3141,plain,
% 12.19/8.17 (((~![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))))),
% 12.19/8.17 inference(monotonicity,[status(thm)],[3140])).
% 12.19/8.17 tff(3142,plain,
% 12.19/8.17 (((~![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)))),
% 12.19/8.17 inference(transitivity,[status(thm)],[3141, 3139])).
% 12.19/8.17 tff(3143,plain,
% 12.19/8.17 ((~![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)))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3144,plain,
% 12.19/8.17 ((~![Y: $i, 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))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3143, 3142])).
% 12.19/8.17 tff(3145,plain,
% 12.19/8.17 ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3144, 141, 3138])).
% 12.19/8.17 tff(3146,plain,
% 12.19/8.17 (~m_counter_cell_v_value(c_bit1, s49)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3145, 3127])).
% 12.19/8.17 tff(3147,assumption,(~m_counter_cell_v_carry_in(c_bit0, s48)), introduced(assumption)).
% 12.19/8.17 tff(3148,plain,
% 12.19/8.17 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s48)),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3149,plain,
% 12.19/8.17 ($false),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3148, 65, 3147])).
% 12.19/8.17 tff(3150,plain,(m_counter_cell_v_carry_in(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.17 tff(3151,plain,
% 12.19/8.17 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3152,plain,
% 12.19/8.17 (((~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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3153,plain,
% 12.19/8.17 (((~![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))))),
% 12.19/8.17 inference(monotonicity,[status(thm)],[3152])).
% 12.19/8.17 tff(3154,plain,
% 12.19/8.17 (((~![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)))),
% 12.19/8.17 inference(transitivity,[status(thm)],[3153, 3151])).
% 12.19/8.17 tff(3155,plain,
% 12.19/8.17 ((~![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))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3156,plain,
% 12.19/8.17 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3155, 3154])).
% 12.19/8.17 tff(3157,plain,
% 12.19/8.17 (m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3156, 77, 3150])).
% 12.19/8.17 tff(3158,plain,
% 12.19/8.17 (~node1(c_bit0, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3157, 3103])).
% 12.19/8.17 tff(3159,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3160,plain,
% 12.19/8.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit0, s48, s49))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3161,plain,
% 12.19/8.17 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit0, s48, s49)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3160, 3159])).
% 12.19/8.17 tff(3162,plain,
% 12.19/8.17 (node3(c_bit0, s48, s49)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3161, 21, 3134])).
% 12.19/8.17 tff(3163,plain,
% 12.19/8.17 (((~![Y: $i, 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) | (~node3(c_bit0, s48, s49)) | node1(c_bit0, s48))) <=> ((~![Y: $i, 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) | (~node3(c_bit0, s48, s49)) | node1(c_bit0, s48))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3164,plain,
% 12.19/8.17 ((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) | (~node3(c_bit0, s48, s49)) | node1(c_bit0, s48))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3165,plain,
% 12.19/8.17 (((~![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) | (~node3(c_bit0, s48, s49)) | node1(c_bit0, s48)))),
% 12.19/8.17 inference(monotonicity,[status(thm)],[3164])).
% 12.19/8.17 tff(3166,plain,
% 12.19/8.17 (((~![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) | (~node3(c_bit0, s48, s49)) | node1(c_bit0, s48))),
% 12.19/8.17 inference(transitivity,[status(thm)],[3165, 3163])).
% 12.19/8.17 tff(3167,plain,
% 12.19/8.17 ((~![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))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3168,plain,
% 12.19/8.17 ((~![Y: $i, 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) | (~node3(c_bit0, s48, s49)) | node1(c_bit0, s48)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3167, 3166])).
% 12.19/8.17 tff(3169,plain,
% 12.19/8.17 (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3168, 106, 3162])).
% 12.19/8.17 tff(3170,plain,
% 12.19/8.17 (m_counter_cell_v_value(c_bit0, s49)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3169, 3158])).
% 12.19/8.17 tff(3171,assumption,(~m_counter_cell_v_carry_in(c_bit0, s49)), introduced(assumption)).
% 12.19/8.17 tff(3172,plain,
% 12.19/8.17 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s49)),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3173,plain,
% 12.19/8.17 ($false),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3172, 65, 3171])).
% 12.19/8.17 tff(3174,plain,(m_counter_cell_v_carry_in(c_bit0, s49)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.17 tff(3175,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3176,plain,
% 12.19/8.17 ((~![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))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3177,plain,
% 12.19/8.17 ((~![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)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3176, 3175])).
% 12.19/8.17 tff(3178,plain,
% 12.19/8.17 ((~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3177, 1368, 3174])).
% 12.19/8.17 tff(3179,plain,
% 12.19/8.17 (m_counter_cell_v_carry_out(c_bit0, s49)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3178, 3170])).
% 12.19/8.17 tff(3180,plain,
% 12.19/8.17 (((~![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))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3181,plain,
% 12.19/8.17 ((~![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))),
% 12.19/8.17 inference(quant_inst,[status(thm)],[])).
% 12.19/8.17 tff(3182,plain,
% 12.19/8.17 ((~![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)),
% 12.19/8.17 inference(modus_ponens,[status(thm)],[3181, 3180])).
% 12.19/8.17 tff(3183,plain,
% 12.19/8.17 (m_counter_cell_v_carry_in(c_bit1, s49)),
% 12.19/8.17 inference(unit_resolution,[status(thm)],[3182, 1383, 3179])).
% 12.19/8.17 tff(3184,assumption,(m_counter_cell_v_carry_in(c_bit1, s49)), introduced(assumption)).
% 12.19/8.17 tff(3185,assumption,(node1(c_bit1, s49)), introduced(assumption)).
% 12.19/8.17 tff(3186,assumption,(~m_counter_cell_v_value(c_bit1, s49)), introduced(assumption)).
% 12.19/8.17 tff(3187,plain,
% 12.19/8.17 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.19/8.17 inference(rewrite,[status(thm)],[])).
% 12.19/8.17 tff(3188,plain,
% 12.19/8.17 (((~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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3189,plain,
% 12.19/8.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 12.19/8.18 inference(monotonicity,[status(thm)],[3188])).
% 12.19/8.18 tff(3190,plain,
% 12.19/8.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 12.19/8.18 inference(transitivity,[status(thm)],[3189, 3187])).
% 12.19/8.18 tff(3191,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3192,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49))),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3191, 3190])).
% 12.19/8.18 tff(3193,plain,
% 12.19/8.18 ($false),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3192, 77, 3186, 3185, 3184])).
% 12.19/8.18 tff(3194,plain,((~node1(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~m_counter_cell_v_carry_in(c_bit1, s49))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.18 tff(3195,plain,
% 12.19/8.18 ((~node1(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3194, 3183])).
% 12.19/8.18 tff(3196,plain,
% 12.19/8.18 (~node1(c_bit1, s49)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3195, 3146])).
% 12.19/8.18 tff(3197,plain,
% 12.19/8.18 (succ(s49, s50) <=> succ(s49, s50)),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3198,axiom,(succ(s49, s50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound50')).
% 12.19/8.18 tff(3199,plain,
% 12.19/8.18 (succ(s49, s50)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3198, 3197])).
% 12.19/8.18 tff(3200,plain,
% 12.19/8.18 (((~![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))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3201,plain,
% 12.19/8.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3202,plain,
% 12.19/8.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3201, 3200])).
% 12.19/8.18 tff(3203,plain,
% 12.19/8.18 (trans(s49, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3202, 3199, 7])).
% 12.19/8.18 tff(3204,plain,
% 12.19/8.18 (((~![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))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3205,plain,
% 12.19/8.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit1, s49, s50))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3206,plain,
% 12.19/8.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit1, s49, s50)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3205, 3204])).
% 12.19/8.18 tff(3207,plain,
% 12.19/8.18 (node3(c_bit1, s49, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3206, 21, 3203])).
% 12.19/8.18 tff(3208,plain,
% 12.19/8.18 (((~![Y: $i, 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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3209,plain,
% 12.19/8.18 ((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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3210,plain,
% 12.19/8.18 (((~![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))))),
% 12.19/8.18 inference(monotonicity,[status(thm)],[3209])).
% 12.19/8.18 tff(3211,plain,
% 12.19/8.18 (((~![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)))),
% 12.19/8.18 inference(transitivity,[status(thm)],[3210, 3208])).
% 12.19/8.18 tff(3212,plain,
% 12.19/8.18 ((~![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))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3213,plain,
% 12.19/8.18 ((~![Y: $i, 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))),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3212, 3211])).
% 12.19/8.18 tff(3214,plain,
% 12.19/8.18 (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3213, 106, 3207])).
% 12.19/8.18 tff(3215,plain,
% 12.19/8.18 (m_counter_cell_v_value(c_bit1, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3214, 3196])).
% 12.19/8.18 tff(3216,assumption,(node4(c_bit1, s50)), introduced(assumption)).
% 12.19/8.18 tff(3217,plain,
% 12.19/8.18 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3218,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3219,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3218, 3217])).
% 12.19/8.18 tff(3220,plain,
% 12.19/8.18 ((~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49))),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3219, 126, 3174])).
% 12.19/8.18 tff(3221,plain,
% 12.19/8.18 (~node2(c_bit0, s49)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3220, 3170])).
% 12.19/8.18 tff(3222,plain,
% 12.19/8.18 (((~![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))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3223,plain,
% 12.19/8.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit0, s49, s50))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3224,plain,
% 12.19/8.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit0, s49, s50)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3223, 3222])).
% 12.19/8.18 tff(3225,plain,
% 12.19/8.18 (node3(c_bit0, s49, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3224, 21, 3203])).
% 12.19/8.18 tff(3226,plain,
% 12.19/8.18 (((~![Y: $i, 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)) | (~node3(c_bit0, s49, s50)) | node2(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, s50)) | (~node3(c_bit0, s49, s50)) | node2(c_bit0, s49))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3227,plain,
% 12.19/8.18 ((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)) | (~node3(c_bit0, s49, s50)) | node2(c_bit0, s49))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3228,plain,
% 12.19/8.18 (((~![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)) | (~node3(c_bit0, s49, s50)) | node2(c_bit0, s49)))),
% 12.19/8.18 inference(monotonicity,[status(thm)],[3227])).
% 12.19/8.18 tff(3229,plain,
% 12.19/8.18 (((~![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)) | (~node3(c_bit0, s49, s50)) | node2(c_bit0, s49))),
% 12.19/8.18 inference(transitivity,[status(thm)],[3228, 3226])).
% 12.19/8.18 tff(3230,plain,
% 12.19/8.18 ((~![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)))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3231,plain,
% 12.19/8.18 ((~![Y: $i, 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)) | (~node3(c_bit0, s49, s50)) | node2(c_bit0, s49)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3230, 3229])).
% 12.19/8.18 tff(3232,plain,
% 12.19/8.18 ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3231, 141, 3225])).
% 12.19/8.18 tff(3233,plain,
% 12.19/8.18 (~m_counter_cell_v_value(c_bit0, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3232, 3221])).
% 12.19/8.18 tff(3234,plain,
% 12.19/8.18 (((~![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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3235,plain,
% 12.19/8.18 ((~![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)))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3236,plain,
% 12.19/8.18 ((~![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))),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 12.19/8.18 tff(3237,plain,
% 12.19/8.18 (~node4(c_bit0, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3236, 1221, 3233])).
% 12.19/8.18 tff(3238,assumption,(~node4(c_bit0, s50)), introduced(assumption)).
% 12.19/8.18 tff(3239,assumption,(m_counter_cell_v_carry_out(c_bit0, s50)), introduced(assumption)).
% 12.19/8.18 tff(3240,plain,
% 12.19/8.18 (((~![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))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3241,plain,
% 12.19/8.18 ((~![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))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3242,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3241, 3240])).
% 12.19/8.18 tff(3243,plain,
% 12.19/8.18 ($false),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3242, 1235, 3239, 3238])).
% 12.19/8.18 tff(3244,plain,((~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.18 tff(3245,plain,
% 12.19/8.18 (~m_counter_cell_v_carry_out(c_bit0, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3244, 3237])).
% 12.19/8.18 tff(3246,assumption,(m_counter_cell_v_carry_in(c_bit1, s50)), introduced(assumption)).
% 12.19/8.18 tff(3247,assumption,(~m_counter_cell_v_carry_out(c_bit0, s50)), introduced(assumption)).
% 12.19/8.18 tff(3248,plain,
% 12.19/8.18 (((~![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))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3249,plain,
% 12.19/8.18 ((~![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))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3250,plain,
% 12.19/8.18 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3249, 3248])).
% 12.19/8.18 tff(3251,plain,
% 12.19/8.18 ($false),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3250, 1249, 3247, 3246])).
% 12.19/8.18 tff(3252,plain,(m_counter_cell_v_carry_out(c_bit0, s50) | (~m_counter_cell_v_carry_in(c_bit1, s50))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.18 tff(3253,plain,
% 12.19/8.18 (~m_counter_cell_v_carry_in(c_bit1, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3252, 3245])).
% 12.19/8.18 tff(3254,plain,
% 12.19/8.18 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s50) | (~node4(c_bit1, s50)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~node4(c_bit1, s50)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3255,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s50) | (~node4(c_bit1, s50)))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3256,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~node4(c_bit1, s50))),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3255, 3254])).
% 12.19/8.18 tff(3257,plain,
% 12.19/8.18 ($false),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3256, 3055, 3253, 3216])).
% 12.19/8.18 tff(3258,plain,(~node4(c_bit1, s50)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.18 tff(3259,plain,
% 12.19/8.18 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s50)) | node4(c_bit1, s50))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s50)) | node4(c_bit1, s50))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3260,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s50)) | node4(c_bit1, s50))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3261,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s50)) | node4(c_bit1, s50)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3260, 3259])).
% 12.19/8.18 tff(3262,plain,
% 12.19/8.18 (~m_counter_cell_v_carry_out(c_bit1, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3261, 1235, 3258])).
% 12.19/8.18 tff(3263,assumption,(m_counter_cell_v_value(c_bit1, s50)), introduced(assumption)).
% 12.19/8.18 tff(3264,assumption,(~m_counter_cell_v_carry_out(c_bit1, s50)), introduced(assumption)).
% 12.19/8.18 tff(3265,plain,
% 12.19/8.18 (((~![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, s50)) | (~m_counter_cell_v_value(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit1, 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_bit1, s50)) | (~m_counter_cell_v_value(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit1, s50))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3266,plain,
% 12.19/8.18 ((~![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, s50)) | (~m_counter_cell_v_value(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit1, s50))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3267,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s50)) | (~m_counter_cell_v_value(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit1, s50)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3266, 3265])).
% 12.19/8.18 tff(3268,plain,
% 12.19/8.18 ($false),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3267, 1368, 3263, 3246, 3264])).
% 12.19/8.18 tff(3269,plain,(m_counter_cell_v_carry_out(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~m_counter_cell_v_carry_in(c_bit1, s50))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.18 tff(3270,plain,
% 12.19/8.18 (~m_counter_cell_v_carry_in(c_bit1, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3269, 3263, 3264])).
% 12.19/8.18 tff(3271,assumption,(node1(c_bit1, s50)), introduced(assumption)).
% 12.19/8.18 tff(3272,plain,
% 12.19/8.18 (((~![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_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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3273,plain,
% 12.19/8.18 (((~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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3274,plain,
% 12.19/8.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_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))))),
% 12.19/8.18 inference(monotonicity,[status(thm)],[3273])).
% 12.19/8.18 tff(3275,plain,
% 12.19/8.18 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_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)))),
% 12.19/8.18 inference(transitivity,[status(thm)],[3274, 3272])).
% 12.19/8.18 tff(3276,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s50)) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3277,plain,
% 12.19/8.18 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50))),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3276, 3275])).
% 12.19/8.18 tff(3278,plain,
% 12.19/8.18 (m_counter_cell_v_carry_in(c_bit1, s50) | (~m_counter_cell_v_value(c_bit1, s50))),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3277, 1517, 3271])).
% 12.19/8.18 tff(3279,plain,
% 12.19/8.18 ($false),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3278, 3270, 3263])).
% 12.19/8.18 tff(3280,plain,((~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit1, s50)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.18 tff(3281,plain,
% 12.19/8.18 ((~m_counter_cell_v_value(c_bit1, s50)) | (~node1(c_bit1, s50))),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3280, 3262])).
% 12.19/8.18 tff(3282,plain,
% 12.19/8.18 (~node1(c_bit1, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3281, 3215])).
% 12.19/8.18 tff(3283,plain,
% 12.19/8.18 (succ(s50, s51) <=> succ(s50, s51)),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3284,axiom,(succ(s50, s51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound51')).
% 12.19/8.18 tff(3285,plain,
% 12.19/8.18 (succ(s50, s51)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3284, 3283])).
% 12.19/8.18 tff(3286,plain,
% 12.19/8.18 (((~![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))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3287,plain,
% 12.19/8.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3288,plain,
% 12.19/8.18 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 12.19/8.18 tff(3289,plain,
% 12.19/8.18 (trans(s50, s51)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3288, 3285, 7])).
% 12.19/8.18 tff(3290,plain,
% 12.19/8.18 (((~![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))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3291,plain,
% 12.19/8.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit1, s50, s51))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3292,plain,
% 12.19/8.18 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit1, s50, s51)),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3291, 3290])).
% 12.19/8.18 tff(3293,plain,
% 12.19/8.18 (node3(c_bit1, s50, s51)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3292, 21, 3289])).
% 12.19/8.18 tff(3294,plain,
% 12.19/8.18 (((~![Y: $i, 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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3295,plain,
% 12.19/8.18 ((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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3296,plain,
% 12.19/8.18 (((~![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))))),
% 12.19/8.18 inference(monotonicity,[status(thm)],[3295])).
% 12.19/8.18 tff(3297,plain,
% 12.19/8.18 (((~![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)))),
% 12.19/8.18 inference(transitivity,[status(thm)],[3296, 3294])).
% 12.19/8.18 tff(3298,plain,
% 12.19/8.18 ((~![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))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3299,plain,
% 12.19/8.18 ((~![Y: $i, 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))),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3298, 3297])).
% 12.19/8.18 tff(3300,plain,
% 12.19/8.18 (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3299, 106, 3293])).
% 12.19/8.18 tff(3301,plain,
% 12.19/8.18 (m_counter_cell_v_value(c_bit1, s51)),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3300, 3282])).
% 12.19/8.18 tff(3302,assumption,(~m_counter_cell_v_carry_in(c_bit0, s50)), introduced(assumption)).
% 12.19/8.18 tff(3303,plain,
% 12.19/8.18 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s50)),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3304,plain,
% 12.19/8.18 ($false),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3303, 65, 3302])).
% 12.19/8.18 tff(3305,plain,(m_counter_cell_v_carry_in(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.18 tff(3306,plain,
% 12.19/8.18 (((~![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, 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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3307,plain,
% 12.19/8.18 (((~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)))),
% 12.19/8.18 inference(rewrite,[status(thm)],[])).
% 12.19/8.18 tff(3308,plain,
% 12.19/8.18 (((~![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, 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))))),
% 12.19/8.18 inference(monotonicity,[status(thm)],[3307])).
% 12.19/8.18 tff(3309,plain,
% 12.19/8.18 (((~![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, 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)))),
% 12.19/8.18 inference(transitivity,[status(thm)],[3308, 3306])).
% 12.19/8.18 tff(3310,plain,
% 12.19/8.18 ((~![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, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50))),
% 12.19/8.18 inference(quant_inst,[status(thm)],[])).
% 12.19/8.18 tff(3311,plain,
% 12.19/8.18 ((~![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, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))),
% 12.19/8.18 inference(modus_ponens,[status(thm)],[3310, 3309])).
% 12.19/8.18 tff(3312,plain,
% 12.19/8.18 (m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))),
% 12.19/8.18 inference(unit_resolution,[status(thm)],[3311, 77, 3305])).
% 12.19/8.19 tff(3313,plain,
% 12.19/8.19 (~node1(c_bit0, s50)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3312, 3233])).
% 12.19/8.19 tff(3314,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3315,plain,
% 12.19/8.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit0, s50, s51))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3316,plain,
% 12.19/8.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit0, s50, s51)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 12.19/8.19 tff(3317,plain,
% 12.19/8.19 (node3(c_bit0, s50, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3316, 21, 3289])).
% 12.19/8.19 tff(3318,plain,
% 12.19/8.19 (((~![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, s51) | (~node3(c_bit0, s50, s51)) | node1(c_bit0, 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_bit0, s51) | (~node3(c_bit0, s50, s51)) | node1(c_bit0, s50))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3319,plain,
% 12.19/8.19 ((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) | (~node3(c_bit0, s50, s51)) | node1(c_bit0, s50))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3320,plain,
% 12.19/8.19 (((~![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) | (~node3(c_bit0, s50, s51)) | node1(c_bit0, s50)))),
% 12.19/8.19 inference(monotonicity,[status(thm)],[3319])).
% 12.19/8.19 tff(3321,plain,
% 12.19/8.19 (((~![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) | (~node3(c_bit0, s50, s51)) | node1(c_bit0, s50))),
% 12.19/8.19 inference(transitivity,[status(thm)],[3320, 3318])).
% 12.19/8.19 tff(3322,plain,
% 12.19/8.19 ((~![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))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3323,plain,
% 12.19/8.19 ((~![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, s51) | (~node3(c_bit0, s50, s51)) | node1(c_bit0, s50)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3322, 3321])).
% 12.19/8.19 tff(3324,plain,
% 12.19/8.19 (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3323, 106, 3317])).
% 12.19/8.19 tff(3325,plain,
% 12.19/8.19 (m_counter_cell_v_value(c_bit0, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3324, 3313])).
% 12.19/8.19 tff(3326,assumption,(~m_counter_cell_v_carry_in(c_bit0, s51)), introduced(assumption)).
% 12.19/8.19 tff(3327,plain,
% 12.19/8.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s51)),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3328,plain,
% 12.19/8.19 ($false),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3327, 65, 3326])).
% 12.19/8.19 tff(3329,plain,(m_counter_cell_v_carry_in(c_bit0, s51)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.19 tff(3330,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3331,plain,
% 12.19/8.19 ((~![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))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3332,plain,
% 12.19/8.19 ((~![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)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3331, 3330])).
% 12.19/8.19 tff(3333,plain,
% 12.19/8.19 ((~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3332, 1368, 3329])).
% 12.19/8.19 tff(3334,plain,
% 12.19/8.19 (m_counter_cell_v_carry_out(c_bit0, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3333, 3325])).
% 12.19/8.19 tff(3335,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3336,plain,
% 12.19/8.19 ((~![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))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3337,plain,
% 12.19/8.19 ((~![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)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3336, 3335])).
% 12.19/8.19 tff(3338,plain,
% 12.19/8.19 (m_counter_cell_v_carry_in(c_bit1, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3337, 1383, 3334])).
% 12.19/8.19 tff(3339,assumption,(m_counter_cell_v_carry_in(c_bit1, s51)), introduced(assumption)).
% 12.19/8.19 tff(3340,assumption,(node2(c_bit1, s51)), introduced(assumption)).
% 12.19/8.19 tff(3341,assumption,(m_counter_cell_v_value(c_bit1, s51)), introduced(assumption)).
% 12.19/8.19 tff(3342,plain,
% 12.19/8.19 (((~![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_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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3343,plain,
% 12.19/8.19 ((~![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_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51)))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3344,plain,
% 12.19/8.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51))),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3343, 3342])).
% 12.19/8.19 tff(3345,plain,
% 12.19/8.19 ($false),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3344, 126, 3341, 3340, 3339])).
% 12.19/8.19 tff(3346,plain,((~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51)) | (~m_counter_cell_v_carry_in(c_bit1, s51))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.19 tff(3347,plain,
% 12.19/8.19 ((~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51))),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3346, 3338])).
% 12.19/8.19 tff(3348,plain,
% 12.19/8.19 (~node2(c_bit1, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3347, 3301])).
% 12.19/8.19 tff(3349,plain,
% 12.19/8.19 (succ(s51, s52) <=> succ(s51, s52)),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3350,axiom,(succ(s51, s52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound52')).
% 12.19/8.19 tff(3351,plain,
% 12.19/8.19 (succ(s51, s52)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3350, 3349])).
% 12.19/8.19 tff(3352,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3353,plain,
% 12.19/8.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3354,plain,
% 12.19/8.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3353, 3352])).
% 12.19/8.19 tff(3355,plain,
% 12.19/8.19 (trans(s51, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3354, 3351, 7])).
% 12.19/8.19 tff(3356,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3357,plain,
% 12.19/8.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit1, s51, s52))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3358,plain,
% 12.19/8.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit1, s51, s52)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3357, 3356])).
% 12.19/8.19 tff(3359,plain,
% 12.19/8.19 (node3(c_bit1, s51, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3358, 21, 3355])).
% 12.19/8.19 tff(3360,plain,
% 12.19/8.19 (((~![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_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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3361,plain,
% 12.19/8.19 ((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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3362,plain,
% 12.19/8.19 (((~![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))))),
% 12.19/8.19 inference(monotonicity,[status(thm)],[3361])).
% 12.19/8.19 tff(3363,plain,
% 12.19/8.19 (((~![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)))),
% 12.19/8.19 inference(transitivity,[status(thm)],[3362, 3360])).
% 12.19/8.19 tff(3364,plain,
% 12.19/8.19 ((~![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)))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3365,plain,
% 12.19/8.19 ((~![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_bit1, s52)) | node2(c_bit1, s51) | (~node3(c_bit1, s51, s52))),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3364, 3363])).
% 12.19/8.19 tff(3366,plain,
% 12.19/8.19 ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3365, 141, 3359])).
% 12.19/8.19 tff(3367,plain,
% 12.19/8.19 (~m_counter_cell_v_value(c_bit1, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3366, 3348])).
% 12.19/8.19 tff(3368,plain,
% 12.19/8.19 (((~![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, 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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3369,plain,
% 12.19/8.19 ((~![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, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51)))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3370,plain,
% 12.19/8.19 ((~![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, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51))),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3369, 3368])).
% 12.19/8.19 tff(3371,plain,
% 12.19/8.19 ((~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51))),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3370, 126, 3329])).
% 12.19/8.19 tff(3372,plain,
% 12.19/8.19 (~node2(c_bit0, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3371, 3325])).
% 12.19/8.19 tff(3373,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3374,plain,
% 12.19/8.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit0, s51, s52))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3375,plain,
% 12.19/8.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit0, s51, s52)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3374, 3373])).
% 12.19/8.19 tff(3376,plain,
% 12.19/8.19 (node3(c_bit0, s51, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3375, 21, 3355])).
% 12.19/8.19 tff(3377,plain,
% 12.19/8.19 (((~![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, 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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3378,plain,
% 12.19/8.19 ((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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3379,plain,
% 12.19/8.19 (((~![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))))),
% 12.19/8.19 inference(monotonicity,[status(thm)],[3378])).
% 12.19/8.19 tff(3380,plain,
% 12.19/8.19 (((~![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)))),
% 12.19/8.19 inference(transitivity,[status(thm)],[3379, 3377])).
% 12.19/8.19 tff(3381,plain,
% 12.19/8.19 ((~![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)))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3382,plain,
% 12.19/8.19 ((~![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, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52))),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 12.19/8.19 tff(3383,plain,
% 12.19/8.19 ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3382, 141, 3376])).
% 12.19/8.19 tff(3384,plain,
% 12.19/8.19 (~m_counter_cell_v_value(c_bit0, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3383, 3372])).
% 12.19/8.19 tff(3385,plain,
% 12.19/8.19 (((~![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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3386,plain,
% 12.19/8.19 ((~![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)))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3387,plain,
% 12.19/8.19 ((~![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))),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3386, 3385])).
% 12.19/8.19 tff(3388,plain,
% 12.19/8.19 (~node4(c_bit0, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3387, 1221, 3384])).
% 12.19/8.19 tff(3389,assumption,(m_counter_cell_v_carry_out(c_bit0, s52)), introduced(assumption)).
% 12.19/8.19 tff(3390,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3391,plain,
% 12.19/8.19 ((~![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))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3392,plain,
% 12.19/8.19 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3391, 3390])).
% 12.19/8.19 tff(3393,plain,
% 12.19/8.19 ($false),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3392, 1235, 3389, 3388])).
% 12.19/8.19 tff(3394,plain,(~m_counter_cell_v_carry_out(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.19 tff(3395,assumption,(m_counter_cell_v_carry_in(c_bit1, s52)), introduced(assumption)).
% 12.19/8.19 tff(3396,assumption,(~m_counter_cell_v_carry_out(c_bit0, s52)), introduced(assumption)).
% 12.19/8.19 tff(3397,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3398,plain,
% 12.19/8.19 ((~![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))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3399,plain,
% 12.19/8.19 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3398, 3397])).
% 12.19/8.19 tff(3400,plain,
% 12.19/8.19 ($false),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3399, 1249, 3396, 3395])).
% 12.19/8.19 tff(3401,plain,(m_counter_cell_v_carry_out(c_bit0, s52) | (~m_counter_cell_v_carry_in(c_bit1, s52))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.19 tff(3402,plain,
% 12.19/8.19 (~m_counter_cell_v_carry_in(c_bit1, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3401, 3394])).
% 12.19/8.19 tff(3403,assumption,(~m_counter_cell_v_carry_in(c_bit1, s52)), introduced(assumption)).
% 12.19/8.19 tff(3404,assumption,(~m_counter_cell_v_value(c_bit1, s52)), introduced(assumption)).
% 12.19/8.19 tff(3405,assumption,(node2(c_bit1, s52)), introduced(assumption)).
% 12.19/8.19 tff(3406,plain,
% 12.19/8.19 (((~![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_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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3407,plain,
% 12.19/8.19 ((~![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_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52)))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3408,plain,
% 12.19/8.19 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s52) | m_counter_cell_v_value(c_bit1, s52) | (~node2(c_bit1, s52))),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 12.19/8.19 tff(3409,plain,
% 12.19/8.19 ($false),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3408, 1449, 3405, 3404, 3403])).
% 12.19/8.19 tff(3410,plain,((~node2(c_bit1, s52)) | m_counter_cell_v_value(c_bit1, s52) | m_counter_cell_v_carry_in(c_bit1, s52)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.19 tff(3411,plain,
% 12.19/8.19 ((~node2(c_bit1, s52)) | m_counter_cell_v_value(c_bit1, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3410, 3402])).
% 12.19/8.19 tff(3412,plain,
% 12.19/8.19 (~node2(c_bit1, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3411, 3367])).
% 12.19/8.19 tff(3413,plain,
% 12.19/8.19 (succ(s52, s53) <=> succ(s52, s53)),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3414,axiom,(succ(s52, s53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound53')).
% 12.19/8.19 tff(3415,plain,
% 12.19/8.19 (succ(s52, s53)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3414, 3413])).
% 12.19/8.19 tff(3416,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3417,plain,
% 12.19/8.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3418,plain,
% 12.19/8.19 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3417, 3416])).
% 12.19/8.19 tff(3419,plain,
% 12.19/8.19 (trans(s52, s53)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3418, 3415, 7])).
% 12.19/8.19 tff(3420,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3421,plain,
% 12.19/8.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit1, s52, s53))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3422,plain,
% 12.19/8.19 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit1, s52, s53)),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 12.19/8.19 tff(3423,plain,
% 12.19/8.19 (node3(c_bit1, s52, s53)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3422, 21, 3419])).
% 12.19/8.19 tff(3424,plain,
% 12.19/8.19 (((~![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_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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3425,plain,
% 12.19/8.19 ((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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3426,plain,
% 12.19/8.19 (((~![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))))),
% 12.19/8.19 inference(monotonicity,[status(thm)],[3425])).
% 12.19/8.19 tff(3427,plain,
% 12.19/8.19 (((~![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)))),
% 12.19/8.19 inference(transitivity,[status(thm)],[3426, 3424])).
% 12.19/8.19 tff(3428,plain,
% 12.19/8.19 ((~![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)))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3429,plain,
% 12.19/8.19 ((~![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_bit1, s53)) | node2(c_bit1, s52) | (~node3(c_bit1, s52, s53))),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3428, 3427])).
% 12.19/8.19 tff(3430,plain,
% 12.19/8.19 ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3429, 141, 3423])).
% 12.19/8.19 tff(3431,plain,
% 12.19/8.19 (~m_counter_cell_v_value(c_bit1, s53)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3430, 3412])).
% 12.19/8.19 tff(3432,assumption,(~m_counter_cell_v_carry_in(c_bit0, s52)), introduced(assumption)).
% 12.19/8.19 tff(3433,plain,
% 12.19/8.19 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s52)),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3434,plain,
% 12.19/8.19 ($false),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3433, 65, 3432])).
% 12.19/8.19 tff(3435,plain,(m_counter_cell_v_carry_in(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.19 tff(3436,plain,
% 12.19/8.19 (((~![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_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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3437,plain,
% 12.19/8.19 (((~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)))),
% 12.19/8.19 inference(rewrite,[status(thm)],[])).
% 12.19/8.19 tff(3438,plain,
% 12.19/8.19 (((~![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, 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))))),
% 12.19/8.19 inference(monotonicity,[status(thm)],[3437])).
% 12.19/8.19 tff(3439,plain,
% 12.19/8.19 (((~![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, 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)))),
% 12.19/8.19 inference(transitivity,[status(thm)],[3438, 3436])).
% 12.19/8.19 tff(3440,plain,
% 12.19/8.19 ((~![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, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52))),
% 12.19/8.19 inference(quant_inst,[status(thm)],[])).
% 12.19/8.19 tff(3441,plain,
% 12.19/8.19 ((~![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_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))),
% 12.19/8.19 inference(modus_ponens,[status(thm)],[3440, 3439])).
% 12.19/8.19 tff(3442,plain,
% 12.19/8.19 (m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3441, 77, 3435])).
% 12.19/8.19 tff(3443,plain,
% 12.19/8.19 (~node1(c_bit0, s52)),
% 12.19/8.19 inference(unit_resolution,[status(thm)],[3442, 3384])).
% 12.19/8.19 tff(3444,plain,
% 12.19/8.19 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3445,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit0, s52, s53))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3446,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit0, s52, s53)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3445, 3444])).
% 12.19/8.20 tff(3447,plain,
% 12.19/8.20 (node3(c_bit0, s52, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3446, 21, 3419])).
% 12.19/8.20 tff(3448,plain,
% 12.19/8.20 (((~![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, 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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3449,plain,
% 12.19/8.20 ((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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3450,plain,
% 12.19/8.20 (((~![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))))),
% 12.19/8.20 inference(monotonicity,[status(thm)],[3449])).
% 12.19/8.20 tff(3451,plain,
% 12.19/8.20 (((~![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)))),
% 12.19/8.20 inference(transitivity,[status(thm)],[3450, 3448])).
% 12.19/8.20 tff(3452,plain,
% 12.19/8.20 ((~![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))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3453,plain,
% 12.19/8.20 ((~![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, s53) | node1(c_bit0, s52) | (~node3(c_bit0, s52, s53))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3452, 3451])).
% 12.19/8.20 tff(3454,plain,
% 12.19/8.20 (m_counter_cell_v_value(c_bit0, s53) | node1(c_bit0, s52)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3453, 106, 3447])).
% 12.19/8.20 tff(3455,plain,
% 12.19/8.20 (m_counter_cell_v_value(c_bit0, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3454, 3443])).
% 12.19/8.20 tff(3456,assumption,(~m_counter_cell_v_carry_in(c_bit0, s53)), introduced(assumption)).
% 12.19/8.20 tff(3457,plain,
% 12.19/8.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s53)),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3458,plain,
% 12.19/8.20 ($false),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3457, 65, 3456])).
% 12.19/8.20 tff(3459,plain,(m_counter_cell_v_carry_in(c_bit0, s53)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.20 tff(3460,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3461,plain,
% 12.19/8.20 ((~![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))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3462,plain,
% 12.19/8.20 ((~![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)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 12.19/8.20 tff(3463,plain,
% 12.19/8.20 ((~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3462, 1368, 3459])).
% 12.19/8.20 tff(3464,plain,
% 12.19/8.20 (m_counter_cell_v_carry_out(c_bit0, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3463, 3455])).
% 12.19/8.20 tff(3465,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3466,plain,
% 12.19/8.20 ((~![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))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3467,plain,
% 12.19/8.20 ((~![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)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3466, 3465])).
% 12.19/8.20 tff(3468,plain,
% 12.19/8.20 (m_counter_cell_v_carry_in(c_bit1, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3467, 1383, 3464])).
% 12.19/8.20 tff(3469,plain,
% 12.19/8.20 (((~![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_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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3470,plain,
% 12.19/8.20 (((~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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3471,plain,
% 12.19/8.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 12.19/8.20 inference(monotonicity,[status(thm)],[3470])).
% 12.19/8.20 tff(3472,plain,
% 12.19/8.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 12.19/8.20 inference(transitivity,[status(thm)],[3471, 3469])).
% 12.19/8.20 tff(3473,plain,
% 12.19/8.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s53)) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3474,plain,
% 12.19/8.20 ((~![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_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3473, 3472])).
% 12.19/8.20 tff(3475,plain,
% 12.19/8.20 (m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3474, 77, 3468])).
% 12.19/8.20 tff(3476,plain,
% 12.19/8.20 (~node1(c_bit1, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3475, 3431])).
% 12.19/8.20 tff(3477,plain,
% 12.19/8.20 (succ(s53, s54) <=> succ(s53, s54)),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3478,axiom,(succ(s53, s54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound54')).
% 12.19/8.20 tff(3479,plain,
% 12.19/8.20 (succ(s53, s54)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3478, 3477])).
% 12.19/8.20 tff(3480,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3481,plain,
% 12.19/8.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3482,plain,
% 12.19/8.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 12.19/8.20 tff(3483,plain,
% 12.19/8.20 (trans(s53, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3482, 3479, 7])).
% 12.19/8.20 tff(3484,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3485,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit1, s53, s54))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3486,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit1, s53, s54)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3485, 3484])).
% 12.19/8.20 tff(3487,plain,
% 12.19/8.20 (node3(c_bit1, s53, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3486, 21, 3483])).
% 12.19/8.20 tff(3488,plain,
% 12.19/8.20 (((~![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_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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3489,plain,
% 12.19/8.20 ((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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3490,plain,
% 12.19/8.20 (((~![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))))),
% 12.19/8.20 inference(monotonicity,[status(thm)],[3489])).
% 12.19/8.20 tff(3491,plain,
% 12.19/8.20 (((~![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)))),
% 12.19/8.20 inference(transitivity,[status(thm)],[3490, 3488])).
% 12.19/8.20 tff(3492,plain,
% 12.19/8.20 ((~![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))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3493,plain,
% 12.19/8.20 ((~![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_bit1, s54) | node1(c_bit1, s53) | (~node3(c_bit1, s53, s54))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3492, 3491])).
% 12.19/8.20 tff(3494,plain,
% 12.19/8.20 (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3493, 106, 3487])).
% 12.19/8.20 tff(3495,plain,
% 12.19/8.20 (m_counter_cell_v_value(c_bit1, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3494, 3476])).
% 12.19/8.20 tff(3496,plain,
% 12.19/8.20 (((~![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, 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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3497,plain,
% 12.19/8.20 ((~![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, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53)))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3498,plain,
% 12.19/8.20 ((~![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, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3497, 3496])).
% 12.19/8.20 tff(3499,plain,
% 12.19/8.20 ((~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53))),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3498, 126, 3459])).
% 12.19/8.20 tff(3500,plain,
% 12.19/8.20 (~node2(c_bit0, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3499, 3455])).
% 12.19/8.20 tff(3501,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3502,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit0, s53, s54))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3503,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit0, s53, s54)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3502, 3501])).
% 12.19/8.20 tff(3504,plain,
% 12.19/8.20 (node3(c_bit0, s53, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3503, 21, 3483])).
% 12.19/8.20 tff(3505,plain,
% 12.19/8.20 (((~![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, 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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3506,plain,
% 12.19/8.20 ((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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3507,plain,
% 12.19/8.20 (((~![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))))),
% 12.19/8.20 inference(monotonicity,[status(thm)],[3506])).
% 12.19/8.20 tff(3508,plain,
% 12.19/8.20 (((~![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)))),
% 12.19/8.20 inference(transitivity,[status(thm)],[3507, 3505])).
% 12.19/8.20 tff(3509,plain,
% 12.19/8.20 ((~![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)))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3510,plain,
% 12.19/8.20 ((~![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, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 12.19/8.20 tff(3511,plain,
% 12.19/8.20 ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3510, 141, 3504])).
% 12.19/8.20 tff(3512,plain,
% 12.19/8.20 (~m_counter_cell_v_value(c_bit0, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3511, 3500])).
% 12.19/8.20 tff(3513,plain,
% 12.19/8.20 (((~![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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3514,plain,
% 12.19/8.20 ((~![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)))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3515,plain,
% 12.19/8.20 ((~![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))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3514, 3513])).
% 12.19/8.20 tff(3516,plain,
% 12.19/8.20 (~node4(c_bit0, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3515, 1221, 3512])).
% 12.19/8.20 tff(3517,assumption,(m_counter_cell_v_carry_out(c_bit0, s54)), introduced(assumption)).
% 12.19/8.20 tff(3518,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3519,plain,
% 12.19/8.20 ((~![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))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3520,plain,
% 12.19/8.20 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3519, 3518])).
% 12.19/8.20 tff(3521,plain,
% 12.19/8.20 ($false),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3520, 1235, 3517, 3516])).
% 12.19/8.20 tff(3522,plain,(~m_counter_cell_v_carry_out(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.20 tff(3523,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3524,plain,
% 12.19/8.20 ((~![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))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3525,plain,
% 12.19/8.20 ((~![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)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3524, 3523])).
% 12.19/8.20 tff(3526,plain,
% 12.19/8.20 (~m_counter_cell_v_carry_in(c_bit1, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3525, 1249, 3522])).
% 12.19/8.20 tff(3527,assumption,(node1(c_bit1, s54)), introduced(assumption)).
% 12.19/8.20 tff(3528,assumption,(m_counter_cell_v_value(c_bit1, s54)), introduced(assumption)).
% 12.19/8.20 tff(3529,plain,
% 12.19/8.20 (((~![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_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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3530,plain,
% 12.19/8.20 (((~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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3531,plain,
% 12.19/8.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_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))))),
% 12.19/8.20 inference(monotonicity,[status(thm)],[3530])).
% 12.19/8.20 tff(3532,plain,
% 12.19/8.20 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_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)))),
% 12.19/8.20 inference(transitivity,[status(thm)],[3531, 3529])).
% 12.19/8.20 tff(3533,plain,
% 12.19/8.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s54)) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3534,plain,
% 12.19/8.20 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3533, 3532])).
% 12.19/8.20 tff(3535,plain,
% 12.19/8.20 ($false),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3534, 1517, 3528, 3527, 3526])).
% 12.19/8.20 tff(3536,plain,((~node1(c_bit1, s54)) | (~m_counter_cell_v_value(c_bit1, s54))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.20 tff(3537,plain,
% 12.19/8.20 (~node1(c_bit1, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3536, 3495])).
% 12.19/8.20 tff(3538,plain,
% 12.19/8.20 (succ(s54, s55) <=> succ(s54, s55)),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3539,axiom,(succ(s54, s55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound55')).
% 12.19/8.20 tff(3540,plain,
% 12.19/8.20 (succ(s54, s55)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3539, 3538])).
% 12.19/8.20 tff(3541,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3542,plain,
% 12.19/8.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3543,plain,
% 12.19/8.20 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3542, 3541])).
% 12.19/8.20 tff(3544,plain,
% 12.19/8.20 (trans(s54, s55)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3543, 3540, 7])).
% 12.19/8.20 tff(3545,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3546,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit1, s54, s55))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3547,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit1, s54, s55)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 12.19/8.20 tff(3548,plain,
% 12.19/8.20 (node3(c_bit1, s54, s55)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3547, 21, 3544])).
% 12.19/8.20 tff(3549,plain,
% 12.19/8.20 (((~![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_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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3550,plain,
% 12.19/8.20 ((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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3551,plain,
% 12.19/8.20 (((~![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))))),
% 12.19/8.20 inference(monotonicity,[status(thm)],[3550])).
% 12.19/8.20 tff(3552,plain,
% 12.19/8.20 (((~![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)))),
% 12.19/8.20 inference(transitivity,[status(thm)],[3551, 3549])).
% 12.19/8.20 tff(3553,plain,
% 12.19/8.20 ((~![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))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3554,plain,
% 12.19/8.20 ((~![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_bit1, s55) | node1(c_bit1, s54) | (~node3(c_bit1, s54, s55))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3553, 3552])).
% 12.19/8.20 tff(3555,plain,
% 12.19/8.20 (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3554, 106, 3548])).
% 12.19/8.20 tff(3556,plain,
% 12.19/8.20 (m_counter_cell_v_value(c_bit1, s55)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3555, 3537])).
% 12.19/8.20 tff(3557,assumption,(~m_counter_cell_v_carry_in(c_bit0, s54)), introduced(assumption)).
% 12.19/8.20 tff(3558,plain,
% 12.19/8.20 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s54)),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3559,plain,
% 12.19/8.20 ($false),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3558, 65, 3557])).
% 12.19/8.20 tff(3560,plain,(m_counter_cell_v_carry_in(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.20 tff(3561,plain,
% 12.19/8.20 (((~![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, 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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3562,plain,
% 12.19/8.20 (((~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)))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3563,plain,
% 12.19/8.20 (((~![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, 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))))),
% 12.19/8.20 inference(monotonicity,[status(thm)],[3562])).
% 12.19/8.20 tff(3564,plain,
% 12.19/8.20 (((~![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, 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)))),
% 12.19/8.20 inference(transitivity,[status(thm)],[3563, 3561])).
% 12.19/8.20 tff(3565,plain,
% 12.19/8.20 ((~![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, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3566,plain,
% 12.19/8.20 ((~![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, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3565, 3564])).
% 12.19/8.20 tff(3567,plain,
% 12.19/8.20 (m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3566, 77, 3560])).
% 12.19/8.20 tff(3568,plain,
% 12.19/8.20 (~node1(c_bit0, s54)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3567, 3512])).
% 12.19/8.20 tff(3569,plain,
% 12.19/8.20 (((~![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))),
% 12.19/8.20 inference(rewrite,[status(thm)],[])).
% 12.19/8.20 tff(3570,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit0, s54, s55))),
% 12.19/8.20 inference(quant_inst,[status(thm)],[])).
% 12.19/8.20 tff(3571,plain,
% 12.19/8.20 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit0, s54, s55)),
% 12.19/8.20 inference(modus_ponens,[status(thm)],[3570, 3569])).
% 12.19/8.20 tff(3572,plain,
% 12.19/8.20 (node3(c_bit0, s54, s55)),
% 12.19/8.20 inference(unit_resolution,[status(thm)],[3571, 21, 3544])).
% 12.19/8.20 tff(3573,plain,
% 12.19/8.20 (((~![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, 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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3574,plain,
% 12.19/8.21 ((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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3575,plain,
% 12.19/8.21 (((~![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))))),
% 12.19/8.21 inference(monotonicity,[status(thm)],[3574])).
% 12.19/8.21 tff(3576,plain,
% 12.19/8.21 (((~![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)))),
% 12.19/8.21 inference(transitivity,[status(thm)],[3575, 3573])).
% 12.19/8.21 tff(3577,plain,
% 12.19/8.21 ((~![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))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3578,plain,
% 12.19/8.21 ((~![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, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3577, 3576])).
% 12.19/8.21 tff(3579,plain,
% 12.19/8.21 (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3578, 106, 3572])).
% 12.19/8.21 tff(3580,plain,
% 12.19/8.21 (m_counter_cell_v_value(c_bit0, s55)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3579, 3568])).
% 12.19/8.21 tff(3581,assumption,(~m_counter_cell_v_carry_in(c_bit0, s55)), introduced(assumption)).
% 12.19/8.21 tff(3582,plain,
% 12.19/8.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s55)),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3583,plain,
% 12.19/8.21 ($false),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3582, 65, 3581])).
% 12.19/8.21 tff(3584,plain,(m_counter_cell_v_carry_in(c_bit0, s55)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.21 tff(3585,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3586,plain,
% 12.19/8.21 ((~![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))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3587,plain,
% 12.19/8.21 ((~![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)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3586, 3585])).
% 12.19/8.21 tff(3588,plain,
% 12.19/8.21 ((~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3587, 1368, 3584])).
% 12.19/8.21 tff(3589,plain,
% 12.19/8.21 (m_counter_cell_v_carry_out(c_bit0, s55)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3588, 3580])).
% 12.19/8.21 tff(3590,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3591,plain,
% 12.19/8.21 ((~![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))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3592,plain,
% 12.19/8.21 ((~![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)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3591, 3590])).
% 12.19/8.21 tff(3593,plain,
% 12.19/8.21 (m_counter_cell_v_carry_in(c_bit1, s55)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3592, 1383, 3589])).
% 12.19/8.21 tff(3594,plain,
% 12.19/8.21 (((~![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_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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3595,plain,
% 12.19/8.21 ((~![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_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55)))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3596,plain,
% 12.19/8.21 ((~![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_bit1, s55)) | (~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3595, 3594])).
% 12.19/8.21 tff(3597,plain,
% 12.19/8.21 ((~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55))),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3596, 126, 3593])).
% 12.19/8.21 tff(3598,plain,
% 12.19/8.21 (~node2(c_bit1, s55)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3597, 3556])).
% 12.19/8.21 tff(3599,plain,
% 12.19/8.21 (succ(s55, s56) <=> succ(s55, s56)),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3600,axiom,(succ(s55, s56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound56')).
% 12.19/8.21 tff(3601,plain,
% 12.19/8.21 (succ(s55, s56)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3600, 3599])).
% 12.19/8.21 tff(3602,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3603,plain,
% 12.19/8.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3604,plain,
% 12.19/8.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3603, 3602])).
% 12.19/8.21 tff(3605,plain,
% 12.19/8.21 (trans(s55, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3604, 3601, 7])).
% 12.19/8.21 tff(3606,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3607,plain,
% 12.19/8.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit1, s55, s56))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3608,plain,
% 12.19/8.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit1, s55, s56)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3607, 3606])).
% 12.19/8.21 tff(3609,plain,
% 12.19/8.21 (node3(c_bit1, s55, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3608, 21, 3605])).
% 12.19/8.21 tff(3610,plain,
% 12.19/8.21 (((~![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_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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3611,plain,
% 12.19/8.21 ((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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3612,plain,
% 12.19/8.21 (((~![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))))),
% 12.19/8.21 inference(monotonicity,[status(thm)],[3611])).
% 12.19/8.21 tff(3613,plain,
% 12.19/8.21 (((~![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)))),
% 12.19/8.21 inference(transitivity,[status(thm)],[3612, 3610])).
% 12.19/8.21 tff(3614,plain,
% 12.19/8.21 ((~![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)))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3615,plain,
% 12.19/8.21 ((~![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_bit1, s56)) | node2(c_bit1, s55) | (~node3(c_bit1, s55, s56))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3614, 3613])).
% 12.19/8.21 tff(3616,plain,
% 12.19/8.21 ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3615, 141, 3609])).
% 12.19/8.21 tff(3617,plain,
% 12.19/8.21 (~m_counter_cell_v_value(c_bit1, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3616, 3598])).
% 12.19/8.21 tff(3618,plain,
% 12.19/8.21 (((~![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, 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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3619,plain,
% 12.19/8.21 ((~![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, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55)))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3620,plain,
% 12.19/8.21 ((~![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, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3619, 3618])).
% 12.19/8.21 tff(3621,plain,
% 12.19/8.21 ((~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55))),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3620, 126, 3584])).
% 12.19/8.21 tff(3622,plain,
% 12.19/8.21 (~node2(c_bit0, s55)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3621, 3580])).
% 12.19/8.21 tff(3623,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3624,plain,
% 12.19/8.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit0, s55, s56))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3625,plain,
% 12.19/8.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit0, s55, s56)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3624, 3623])).
% 12.19/8.21 tff(3626,plain,
% 12.19/8.21 (node3(c_bit0, s55, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3625, 21, 3605])).
% 12.19/8.21 tff(3627,plain,
% 12.19/8.21 (((~![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, 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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3628,plain,
% 12.19/8.21 ((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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3629,plain,
% 12.19/8.21 (((~![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))))),
% 12.19/8.21 inference(monotonicity,[status(thm)],[3628])).
% 12.19/8.21 tff(3630,plain,
% 12.19/8.21 (((~![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)))),
% 12.19/8.21 inference(transitivity,[status(thm)],[3629, 3627])).
% 12.19/8.21 tff(3631,plain,
% 12.19/8.21 ((~![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)))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3632,plain,
% 12.19/8.21 ((~![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, s56)) | node2(c_bit0, s55) | (~node3(c_bit0, s55, s56))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3631, 3630])).
% 12.19/8.21 tff(3633,plain,
% 12.19/8.21 ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3632, 141, 3626])).
% 12.19/8.21 tff(3634,plain,
% 12.19/8.21 (~m_counter_cell_v_value(c_bit0, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3633, 3622])).
% 12.19/8.21 tff(3635,plain,
% 12.19/8.21 (((~![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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3636,plain,
% 12.19/8.21 ((~![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)))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3637,plain,
% 12.19/8.21 ((~![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))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 12.19/8.21 tff(3638,plain,
% 12.19/8.21 (~node4(c_bit0, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3637, 1221, 3634])).
% 12.19/8.21 tff(3639,assumption,(m_counter_cell_v_carry_out(c_bit0, s56)), introduced(assumption)).
% 12.19/8.21 tff(3640,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3641,plain,
% 12.19/8.21 ((~![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))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3642,plain,
% 12.19/8.21 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3641, 3640])).
% 12.19/8.21 tff(3643,plain,
% 12.19/8.21 ($false),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3642, 1235, 3639, 3638])).
% 12.19/8.21 tff(3644,plain,(~m_counter_cell_v_carry_out(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.21 tff(3645,assumption,(m_counter_cell_v_carry_in(c_bit1, s56)), introduced(assumption)).
% 12.19/8.21 tff(3646,assumption,(~m_counter_cell_v_carry_out(c_bit0, s56)), introduced(assumption)).
% 12.19/8.21 tff(3647,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3648,plain,
% 12.19/8.21 ((~![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))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3649,plain,
% 12.19/8.21 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3648, 3647])).
% 12.19/8.21 tff(3650,plain,
% 12.19/8.21 ($false),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3649, 1249, 3646, 3645])).
% 12.19/8.21 tff(3651,plain,(m_counter_cell_v_carry_out(c_bit0, s56) | (~m_counter_cell_v_carry_in(c_bit1, s56))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.21 tff(3652,plain,
% 12.19/8.21 (~m_counter_cell_v_carry_in(c_bit1, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3651, 3644])).
% 12.19/8.21 tff(3653,assumption,(node2(c_bit1, s56)), introduced(assumption)).
% 12.19/8.21 tff(3654,assumption,(~m_counter_cell_v_value(c_bit1, s56)), introduced(assumption)).
% 12.19/8.21 tff(3655,plain,
% 12.19/8.21 (((~![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_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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3656,plain,
% 12.19/8.21 ((~![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_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56)))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3657,plain,
% 12.19/8.21 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3656, 3655])).
% 12.19/8.21 tff(3658,plain,
% 12.19/8.21 ($false),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3657, 1449, 3654, 3653, 3652])).
% 12.19/8.21 tff(3659,plain,(m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56))), inference(lemma,lemma(discharge,[]))).
% 12.19/8.21 tff(3660,plain,
% 12.19/8.21 (~node2(c_bit1, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3659, 3617])).
% 12.19/8.21 tff(3661,plain,
% 12.19/8.21 (succ(s56, s57) <=> succ(s56, s57)),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3662,axiom,(succ(s56, s57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound57')).
% 12.19/8.21 tff(3663,plain,
% 12.19/8.21 (succ(s56, s57)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3662, 3661])).
% 12.19/8.21 tff(3664,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3665,plain,
% 12.19/8.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3666,plain,
% 12.19/8.21 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3665, 3664])).
% 12.19/8.21 tff(3667,plain,
% 12.19/8.21 (trans(s56, s57)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3666, 3663, 7])).
% 12.19/8.21 tff(3668,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3669,plain,
% 12.19/8.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit1, s56, s57))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3670,plain,
% 12.19/8.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit1, s56, s57)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 12.19/8.21 tff(3671,plain,
% 12.19/8.21 (node3(c_bit1, s56, s57)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3670, 21, 3667])).
% 12.19/8.21 tff(3672,plain,
% 12.19/8.21 (((~![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_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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3673,plain,
% 12.19/8.21 ((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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3674,plain,
% 12.19/8.21 (((~![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))))),
% 12.19/8.21 inference(monotonicity,[status(thm)],[3673])).
% 12.19/8.21 tff(3675,plain,
% 12.19/8.21 (((~![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)))),
% 12.19/8.21 inference(transitivity,[status(thm)],[3674, 3672])).
% 12.19/8.21 tff(3676,plain,
% 12.19/8.21 ((~![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)))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3677,plain,
% 12.19/8.21 ((~![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_bit1, s57)) | node2(c_bit1, s56) | (~node3(c_bit1, s56, s57))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3676, 3675])).
% 12.19/8.21 tff(3678,plain,
% 12.19/8.21 ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3677, 141, 3671])).
% 12.19/8.21 tff(3679,plain,
% 12.19/8.21 (~m_counter_cell_v_value(c_bit1, s57)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3678, 3660])).
% 12.19/8.21 tff(3680,assumption,(node1(c_bit1, s57)), introduced(assumption)).
% 12.19/8.21 tff(3681,assumption,(~m_counter_cell_v_carry_in(c_bit0, s56)), introduced(assumption)).
% 12.19/8.21 tff(3682,plain,
% 12.19/8.21 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s56)),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3683,plain,
% 12.19/8.21 ($false),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3682, 65, 3681])).
% 12.19/8.21 tff(3684,plain,(m_counter_cell_v_carry_in(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.21 tff(3685,plain,
% 12.19/8.21 (((~![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, 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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3686,plain,
% 12.19/8.21 (((~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)))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3687,plain,
% 12.19/8.21 (((~![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, 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))))),
% 12.19/8.21 inference(monotonicity,[status(thm)],[3686])).
% 12.19/8.21 tff(3688,plain,
% 12.19/8.21 (((~![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, 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)))),
% 12.19/8.21 inference(transitivity,[status(thm)],[3687, 3685])).
% 12.19/8.21 tff(3689,plain,
% 12.19/8.21 ((~![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, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3690,plain,
% 12.19/8.21 ((~![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, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3689, 3688])).
% 12.19/8.21 tff(3691,plain,
% 12.19/8.21 (m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3690, 77, 3684])).
% 12.19/8.21 tff(3692,plain,
% 12.19/8.21 (~node1(c_bit0, s56)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3691, 3634])).
% 12.19/8.21 tff(3693,plain,
% 12.19/8.21 (((~![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))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3694,plain,
% 12.19/8.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit0, s56, s57))),
% 12.19/8.21 inference(quant_inst,[status(thm)],[])).
% 12.19/8.21 tff(3695,plain,
% 12.19/8.21 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit0, s56, s57)),
% 12.19/8.21 inference(modus_ponens,[status(thm)],[3694, 3693])).
% 12.19/8.21 tff(3696,plain,
% 12.19/8.21 (node3(c_bit0, s56, s57)),
% 12.19/8.21 inference(unit_resolution,[status(thm)],[3695, 21, 3667])).
% 12.19/8.21 tff(3697,plain,
% 12.19/8.21 (((~![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, s57) | (~node3(c_bit0, s56, s57)) | node1(c_bit0, 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_bit0, s57) | (~node3(c_bit0, s56, s57)) | node1(c_bit0, s56))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3698,plain,
% 12.19/8.21 ((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) | (~node3(c_bit0, s56, s57)) | node1(c_bit0, s56))),
% 12.19/8.21 inference(rewrite,[status(thm)],[])).
% 12.19/8.21 tff(3699,plain,
% 12.19/8.21 (((~![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) | (~node3(c_bit0, s56, s57)) | node1(c_bit0, s56)))),
% 12.19/8.21 inference(monotonicity,[status(thm)],[3698])).
% 12.19/8.22 tff(3700,plain,
% 12.19/8.22 (((~![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) | (~node3(c_bit0, s56, s57)) | node1(c_bit0, s56))),
% 12.19/8.22 inference(transitivity,[status(thm)],[3699, 3697])).
% 12.19/8.22 tff(3701,plain,
% 12.19/8.22 ((~![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))),
% 12.19/8.22 inference(quant_inst,[status(thm)],[])).
% 12.19/8.22 tff(3702,plain,
% 12.19/8.22 ((~![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, s57) | (~node3(c_bit0, s56, s57)) | node1(c_bit0, s56)),
% 12.19/8.22 inference(modus_ponens,[status(thm)],[3701, 3700])).
% 12.19/8.22 tff(3703,plain,
% 12.19/8.22 (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56)),
% 12.19/8.22 inference(unit_resolution,[status(thm)],[3702, 106, 3696])).
% 12.19/8.22 tff(3704,plain,
% 12.19/8.22 (m_counter_cell_v_value(c_bit0, s57)),
% 12.19/8.22 inference(unit_resolution,[status(thm)],[3703, 3692])).
% 12.19/8.22 tff(3705,assumption,(~m_counter_cell_v_carry_in(c_bit0, s57)), introduced(assumption)).
% 12.19/8.22 tff(3706,plain,
% 12.19/8.22 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s57)),
% 12.19/8.22 inference(quant_inst,[status(thm)],[])).
% 12.19/8.22 tff(3707,plain,
% 12.19/8.22 ($false),
% 12.19/8.22 inference(unit_resolution,[status(thm)],[3706, 65, 3705])).
% 12.19/8.22 tff(3708,plain,(m_counter_cell_v_carry_in(c_bit0, s57)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.22 tff(3709,plain,
% 12.19/8.22 (((~![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))),
% 12.19/8.22 inference(rewrite,[status(thm)],[])).
% 12.19/8.22 tff(3710,plain,
% 12.19/8.22 ((~![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))),
% 12.19/8.22 inference(quant_inst,[status(thm)],[])).
% 12.19/8.22 tff(3711,plain,
% 12.19/8.22 ((~![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)),
% 12.19/8.22 inference(modus_ponens,[status(thm)],[3710, 3709])).
% 12.19/8.22 tff(3712,plain,
% 12.19/8.22 ((~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57)),
% 12.19/8.22 inference(unit_resolution,[status(thm)],[3711, 1368, 3708])).
% 12.19/8.22 tff(3713,plain,
% 12.19/8.22 (m_counter_cell_v_carry_out(c_bit0, s57)),
% 12.19/8.22 inference(unit_resolution,[status(thm)],[3712, 3704])).
% 12.19/8.22 tff(3714,plain,
% 12.19/8.22 (((~![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))),
% 12.19/8.22 inference(rewrite,[status(thm)],[])).
% 12.19/8.22 tff(3715,plain,
% 12.19/8.22 ((~![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))),
% 12.19/8.22 inference(quant_inst,[status(thm)],[])).
% 12.19/8.22 tff(3716,plain,
% 12.19/8.22 ((~![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)),
% 12.19/8.22 inference(modus_ponens,[status(thm)],[3715, 3714])).
% 12.19/8.22 tff(3717,plain,
% 12.19/8.22 (m_counter_cell_v_carry_in(c_bit1, s57)),
% 12.19/8.22 inference(unit_resolution,[status(thm)],[3716, 1383, 3713])).
% 12.19/8.22 tff(3718,assumption,(~m_counter_cell_v_value(c_bit1, s57)), introduced(assumption)).
% 12.19/8.22 tff(3719,plain,
% 12.19/8.22 (((~![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_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)))),
% 12.19/8.22 inference(rewrite,[status(thm)],[])).
% 12.19/8.22 tff(3720,plain,
% 12.19/8.22 (((~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)))),
% 12.19/8.22 inference(rewrite,[status(thm)],[])).
% 12.19/8.22 tff(3721,plain,
% 12.19/8.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 12.19/8.22 inference(monotonicity,[status(thm)],[3720])).
% 12.19/8.22 tff(3722,plain,
% 12.19/8.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 12.19/8.22 inference(transitivity,[status(thm)],[3721, 3719])).
% 12.19/8.22 tff(3723,plain,
% 12.19/8.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s57)) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57))),
% 12.19/8.22 inference(quant_inst,[status(thm)],[])).
% 12.19/8.22 tff(3724,plain,
% 12.19/8.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57))),
% 12.19/8.22 inference(modus_ponens,[status(thm)],[3723, 3722])).
% 12.19/8.22 tff(3725,plain,
% 12.19/8.22 ($false),
% 12.19/8.22 inference(unit_resolution,[status(thm)],[3724, 77, 3718, 3717, 3680])).
% 12.19/8.22 tff(3726,plain,((~node1(c_bit1, s57)) | m_counter_cell_v_value(c_bit1, s57)), inference(lemma,lemma(discharge,[]))).
% 12.19/8.22 tff(3727,plain,
% 12.19/8.22 (~node1(c_bit1, s57)),
% 12.19/8.22 inference(unit_resolution,[status(thm)],[3726, 3679])).
% 12.19/8.22 tff(3728,plain,
% 12.19/8.22 (succ(s57, s58) <=> succ(s57, s58)),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3729,axiom,(succ(s57, s58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound58')).
% 12.29/8.22 tff(3730,plain,
% 12.29/8.22 (succ(s57, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3729, 3728])).
% 12.29/8.22 tff(3731,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3732,plain,
% 12.29/8.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3733,plain,
% 12.29/8.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 12.29/8.22 tff(3734,plain,
% 12.29/8.22 (trans(s57, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3733, 3730, 7])).
% 12.29/8.22 tff(3735,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3736,plain,
% 12.29/8.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit1, s57, s58))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3737,plain,
% 12.29/8.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit1, s57, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3736, 3735])).
% 12.29/8.22 tff(3738,plain,
% 12.29/8.22 (node3(c_bit1, s57, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3737, 21, 3734])).
% 12.29/8.22 tff(3739,plain,
% 12.29/8.22 (((~![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_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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3740,plain,
% 12.29/8.22 ((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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3741,plain,
% 12.29/8.22 (((~![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))))),
% 12.29/8.22 inference(monotonicity,[status(thm)],[3740])).
% 12.29/8.22 tff(3742,plain,
% 12.29/8.22 (((~![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)))),
% 12.29/8.22 inference(transitivity,[status(thm)],[3741, 3739])).
% 12.29/8.22 tff(3743,plain,
% 12.29/8.22 ((~![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))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3744,plain,
% 12.29/8.22 ((~![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_bit1, s58) | node1(c_bit1, s57) | (~node3(c_bit1, s57, s58))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3743, 3742])).
% 12.29/8.22 tff(3745,plain,
% 12.29/8.22 (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3744, 106, 3738])).
% 12.29/8.22 tff(3746,plain,
% 12.29/8.22 (m_counter_cell_v_value(c_bit1, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3745, 3727])).
% 12.29/8.22 tff(3747,plain,
% 12.29/8.22 (((~![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, 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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3748,plain,
% 12.29/8.22 ((~![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, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57)))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3749,plain,
% 12.29/8.22 ((~![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, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3748, 3747])).
% 12.29/8.22 tff(3750,plain,
% 12.29/8.22 ((~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57))),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3749, 126, 3708])).
% 12.29/8.22 tff(3751,plain,
% 12.29/8.22 (~node2(c_bit0, s57)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3750, 3704])).
% 12.29/8.22 tff(3752,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3753,plain,
% 12.29/8.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit0, s57, s58))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3754,plain,
% 12.29/8.22 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit0, s57, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3753, 3752])).
% 12.29/8.22 tff(3755,plain,
% 12.29/8.22 (node3(c_bit0, s57, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3754, 21, 3734])).
% 12.29/8.22 tff(3756,plain,
% 12.29/8.22 (((~![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, 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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3757,plain,
% 12.29/8.22 ((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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3758,plain,
% 12.29/8.22 (((~![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))))),
% 12.29/8.22 inference(monotonicity,[status(thm)],[3757])).
% 12.29/8.22 tff(3759,plain,
% 12.29/8.22 (((~![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)))),
% 12.29/8.22 inference(transitivity,[status(thm)],[3758, 3756])).
% 12.29/8.22 tff(3760,plain,
% 12.29/8.22 ((~![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)))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3761,plain,
% 12.29/8.22 ((~![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, s58)) | node2(c_bit0, s57) | (~node3(c_bit0, s57, s58))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3760, 3759])).
% 12.29/8.22 tff(3762,plain,
% 12.29/8.22 ((~m_counter_cell_v_value(c_bit0, s58)) | node2(c_bit0, s57)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3761, 141, 3755])).
% 12.29/8.22 tff(3763,plain,
% 12.29/8.22 (~m_counter_cell_v_value(c_bit0, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3762, 3751])).
% 12.29/8.22 tff(3764,plain,
% 12.29/8.22 (((~![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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3765,plain,
% 12.29/8.22 ((~![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)))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3766,plain,
% 12.29/8.22 ((~![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))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3765, 3764])).
% 12.29/8.22 tff(3767,plain,
% 12.29/8.22 (~node4(c_bit0, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3766, 1221, 3763])).
% 12.29/8.22 tff(3768,assumption,(m_counter_cell_v_carry_out(c_bit0, s58)), introduced(assumption)).
% 12.29/8.22 tff(3769,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3770,plain,
% 12.29/8.22 ((~![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))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3771,plain,
% 12.29/8.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3770, 3769])).
% 12.29/8.22 tff(3772,plain,
% 12.29/8.22 ($false),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3771, 1235, 3768, 3767])).
% 12.29/8.22 tff(3773,plain,(~m_counter_cell_v_carry_out(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 12.29/8.22 tff(3774,assumption,(m_counter_cell_v_carry_in(c_bit1, s58)), introduced(assumption)).
% 12.29/8.22 tff(3775,assumption,(~m_counter_cell_v_carry_out(c_bit0, s58)), introduced(assumption)).
% 12.29/8.22 tff(3776,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3777,plain,
% 12.29/8.22 ((~![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))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3778,plain,
% 12.29/8.22 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3777, 3776])).
% 12.29/8.22 tff(3779,plain,
% 12.29/8.22 ($false),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3778, 1249, 3775, 3774])).
% 12.29/8.22 tff(3780,plain,((~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 12.29/8.22 tff(3781,plain,
% 12.29/8.22 (~m_counter_cell_v_carry_in(c_bit1, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3780, 3773])).
% 12.29/8.22 tff(3782,assumption,(~m_counter_cell_v_carry_in(c_bit1, s58)), introduced(assumption)).
% 12.29/8.22 tff(3783,plain,
% 12.29/8.22 (((~![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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3784,plain,
% 12.29/8.22 ((~![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)))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3785,plain,
% 12.29/8.22 ((~![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))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3784, 3783])).
% 12.29/8.22 tff(3786,plain,
% 12.29/8.22 (~node4(c_bit1, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3785, 3055, 3782])).
% 12.29/8.22 tff(3787,assumption,(m_counter_cell_v_carry_out(c_bit1, s58)), introduced(assumption)).
% 12.29/8.22 tff(3788,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3789,plain,
% 12.29/8.22 ((~![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))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3790,plain,
% 12.29/8.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s58)) | node4(c_bit1, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3789, 3788])).
% 12.29/8.22 tff(3791,plain,
% 12.29/8.22 ($false),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3790, 1235, 3787, 3786])).
% 12.29/8.22 tff(3792,plain,((~m_counter_cell_v_carry_out(c_bit1, s58)) | m_counter_cell_v_carry_in(c_bit1, s58)), inference(lemma,lemma(discharge,[]))).
% 12.29/8.22 tff(3793,plain,
% 12.29/8.22 (~m_counter_cell_v_carry_out(c_bit1, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3792, 3781])).
% 12.29/8.22 tff(3794,assumption,(m_counter_cell_v_carry_in(c_bit2, s58)), introduced(assumption)).
% 12.29/8.22 tff(3795,assumption,(~m_counter_cell_v_carry_out(c_bit1, s58)), introduced(assumption)).
% 12.29/8.22 tff(3796,plain,
% 12.29/8.22 (^[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)))),
% 12.29/8.22 inference(bind,[status(th)],[])).
% 12.29/8.22 tff(3797,plain,
% 12.29/8.22 (![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))),
% 12.29/8.22 inference(quant_intro,[status(thm)],[3796])).
% 12.29/8.22 tff(3798,plain,
% 12.29/8.22 (![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3799,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')).
% 12.29/8.22 tff(3800,plain,
% 12.29/8.22 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3799, 3798])).
% 12.29/8.22 tff(3801,plain,(
% 12.29/8.22 ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 12.29/8.22 inference(skolemize,[status(sab)],[3800])).
% 12.29/8.22 tff(3802,plain,
% 12.29/8.22 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3801, 3797])).
% 12.29/8.22 tff(3803,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3804,plain,
% 12.29/8.22 ((~![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))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3805,plain,
% 12.29/8.22 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit1, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3804, 3803])).
% 12.29/8.22 tff(3806,plain,
% 12.29/8.22 ($false),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3805, 3802, 3795, 3794])).
% 12.29/8.22 tff(3807,plain,((~m_counter_cell_v_carry_in(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit1, s58)), inference(lemma,lemma(discharge,[]))).
% 12.29/8.22 tff(3808,plain,
% 12.29/8.22 (~m_counter_cell_v_carry_in(c_bit2, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3807, 3793])).
% 12.29/8.22 tff(3809,plain,
% 12.29/8.22 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s58) | (~node4(c_bit2, s58)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s58) | (~node4(c_bit2, s58)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3810,plain,
% 12.29/8.22 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s58) | (~node4(c_bit2, s58)))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3811,plain,
% 12.29/8.22 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s58) | (~node4(c_bit2, s58))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 12.29/8.22 tff(3812,plain,
% 12.29/8.22 (~node4(c_bit2, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3811, 3055, 3808])).
% 12.29/8.22 tff(3813,plain,
% 12.29/8.22 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit2, s58)) | node4(c_bit2, s58))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit2, s58)) | node4(c_bit2, s58))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3814,plain,
% 12.29/8.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit2, s58)) | node4(c_bit2, s58))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3815,plain,
% 12.29/8.22 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit2, s58)) | node4(c_bit2, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3814, 3813])).
% 12.29/8.22 tff(3816,plain,
% 12.29/8.22 (~m_counter_cell_v_carry_out(c_bit2, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3815, 1235, 3812])).
% 12.29/8.22 tff(3817,assumption,(m_counter_cell_v_value(c_bit2, s58)), introduced(assumption)).
% 12.29/8.22 tff(3818,assumption,(~m_counter_cell_v_carry_out(c_bit2, s58)), introduced(assumption)).
% 12.29/8.22 tff(3819,plain,
% 12.29/8.22 (((~![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, s58)) | (~m_counter_cell_v_value(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit2, 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_bit2, s58)) | (~m_counter_cell_v_value(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit2, s58))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3820,plain,
% 12.29/8.22 ((~![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, s58)) | (~m_counter_cell_v_value(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit2, s58))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3821,plain,
% 12.29/8.22 ((~![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, s58)) | (~m_counter_cell_v_value(c_bit2, s58)) | m_counter_cell_v_carry_out(c_bit2, s58)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3820, 3819])).
% 12.29/8.22 tff(3822,plain,
% 12.29/8.22 ((~m_counter_cell_v_carry_in(c_bit2, s58)) | (~m_counter_cell_v_value(c_bit2, s58))),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3821, 1368, 3818])).
% 12.29/8.22 tff(3823,plain,
% 12.29/8.22 (~m_counter_cell_v_carry_in(c_bit2, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3822, 3817])).
% 12.29/8.22 tff(3824,plain,
% 12.29/8.22 (((~![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_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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3825,plain,
% 12.29/8.22 (((~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)))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3826,plain,
% 12.29/8.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_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))))),
% 12.29/8.22 inference(monotonicity,[status(thm)],[3825])).
% 12.29/8.22 tff(3827,plain,
% 12.29/8.22 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_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)))),
% 12.29/8.22 inference(transitivity,[status(thm)],[3826, 3824])).
% 12.29/8.22 tff(3828,plain,
% 12.29/8.22 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s58)) | m_counter_cell_v_carry_in(c_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3829,plain,
% 12.29/8.22 ((~![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_bit2, s58) | (~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58))),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3828, 3827])).
% 12.29/8.22 tff(3830,plain,
% 12.29/8.22 (~node1(c_bit2, s58)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3829, 1517, 3817, 3823])).
% 12.29/8.22 tff(3831,plain,
% 12.29/8.22 (succ(s58, s59) <=> succ(s58, s59)),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3832,axiom,(succ(s58, s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound59')).
% 12.29/8.22 tff(3833,plain,
% 12.29/8.22 (succ(s58, s59)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3832, 3831])).
% 12.29/8.22 tff(3834,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.22 inference(rewrite,[status(thm)],[])).
% 12.29/8.22 tff(3835,plain,
% 12.29/8.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))),
% 12.29/8.22 inference(quant_inst,[status(thm)],[])).
% 12.29/8.22 tff(3836,plain,
% 12.29/8.22 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59)),
% 12.29/8.22 inference(modus_ponens,[status(thm)],[3835, 3834])).
% 12.29/8.22 tff(3837,plain,
% 12.29/8.22 (trans(s58, s59)),
% 12.29/8.22 inference(unit_resolution,[status(thm)],[3836, 3833, 7])).
% 12.29/8.22 tff(3838,plain,
% 12.29/8.22 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3839,plain,
% 12.29/8.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit2, s58, s59))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3840,plain,
% 12.29/8.23 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit2, s58, s59)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 12.29/8.23 tff(3841,plain,
% 12.29/8.23 (node3(c_bit2, s58, s59)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3840, 21, 3837])).
% 12.29/8.23 tff(3842,plain,
% 12.29/8.23 (((~![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_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)))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3843,plain,
% 12.29/8.23 ((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)))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3844,plain,
% 12.29/8.23 (((~![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))))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3843])).
% 12.29/8.23 tff(3845,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3844, 3842])).
% 12.29/8.23 tff(3846,plain,
% 12.29/8.23 ((~![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))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3847,plain,
% 12.29/8.23 ((~![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_bit2, s59) | node1(c_bit2, s58) | (~node3(c_bit2, s58, s59))),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3846, 3845])).
% 12.29/8.23 tff(3848,plain,
% 12.29/8.23 (m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s58)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3847, 106, 3841])).
% 12.29/8.23 tff(3849,plain,
% 12.29/8.23 (m_counter_cell_v_value(c_bit2, s59)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3848, 3830])).
% 12.29/8.23 tff(3850,assumption,(~always5(s59)), introduced(assumption)).
% 12.29/8.23 tff(3851,plain,
% 12.29/8.23 (^[Y: $i, X: $i] : refl(((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ((~always5(X)) | (~trans(X, Y)) | always5(Y)))),
% 12.29/8.23 inference(bind,[status(th)],[])).
% 12.29/8.23 tff(3852,plain,
% 12.29/8.23 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 12.29/8.23 inference(quant_intro,[status(thm)],[3851])).
% 12.29/8.23 tff(3853,plain,
% 12.29/8.23 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3854,plain,
% 12.29/8.23 (^[Y: $i, X: $i] : rewrite(((always5(Y) | (~trans(X, Y))) | (~always5(X))) <=> ((~always5(X)) | (~trans(X, Y)) | always5(Y)))),
% 12.29/8.23 inference(bind,[status(th)],[])).
% 12.29/8.23 tff(3855,plain,
% 12.29/8.23 (![Y: $i, X: $i] : ((always5(Y) | (~trans(X, Y))) | (~always5(X))) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 12.29/8.23 inference(quant_intro,[status(thm)],[3854])).
% 12.29/8.23 tff(3856,axiom,(![Y: $i, X: $i] : ((always5(Y) | (~trans(X, Y))) | (~always5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty2')).
% 12.29/8.23 tff(3857,plain,
% 12.29/8.23 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3856, 3855])).
% 12.29/8.23 tff(3858,plain,
% 12.29/8.23 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3857, 3853])).
% 12.29/8.23 tff(3859,plain,(
% 12.29/8.23 ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 12.29/8.23 inference(skolemize,[status(sab)],[3858])).
% 12.29/8.23 tff(3860,plain,
% 12.29/8.23 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3859, 3852])).
% 12.29/8.23 tff(3861,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3862,plain,
% 12.29/8.23 (((~always5(s58)) | (~trans(s58, s59)) | always5(s59)) <=> (always5(s59) | (~trans(s58, s59)) | (~always5(s58)))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3863,plain,
% 12.29/8.23 (((~![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))))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3862])).
% 12.29/8.23 tff(3864,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3863, 3861])).
% 12.29/8.23 tff(3865,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s58)) | (~trans(s58, s59)) | always5(s59))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3866,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s59) | (~trans(s58, s59)) | (~always5(s58))),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3865, 3864])).
% 12.29/8.23 tff(3867,plain,
% 12.29/8.23 (always5(s59) | (~always5(s58))),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3866, 3860, 3837])).
% 12.29/8.23 tff(3868,plain,
% 12.29/8.23 (~always5(s58)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3867, 3850])).
% 12.29/8.23 tff(3869,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3870,plain,
% 12.29/8.23 (((~always5(s57)) | (~trans(s57, s58)) | always5(s58)) <=> ((~trans(s57, s58)) | (~always5(s57)) | always5(s58))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3871,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3870])).
% 12.29/8.23 tff(3872,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3871, 3869])).
% 12.29/8.23 tff(3873,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s57)) | (~trans(s57, s58)) | always5(s58))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3874,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s57, s58)) | (~always5(s57)) | always5(s58)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3873, 3872])).
% 12.29/8.23 tff(3875,plain,
% 12.29/8.23 ((~always5(s57)) | always5(s58)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3874, 3860, 3734])).
% 12.29/8.23 tff(3876,plain,
% 12.29/8.23 (~always5(s57)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3875, 3868])).
% 12.29/8.23 tff(3877,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3878,plain,
% 12.29/8.23 (((~always5(s56)) | (~trans(s56, s57)) | always5(s57)) <=> ((~trans(s56, s57)) | (~always5(s56)) | always5(s57))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3879,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3878])).
% 12.29/8.23 tff(3880,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3879, 3877])).
% 12.29/8.23 tff(3881,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s56)) | (~trans(s56, s57)) | always5(s57))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3882,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s56, s57)) | (~always5(s56)) | always5(s57)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3881, 3880])).
% 12.29/8.23 tff(3883,plain,
% 12.29/8.23 ((~always5(s56)) | always5(s57)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3882, 3860, 3667])).
% 12.29/8.23 tff(3884,plain,
% 12.29/8.23 (~always5(s56)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3883, 3876])).
% 12.29/8.23 tff(3885,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3886,plain,
% 12.29/8.23 (((~always5(s55)) | (~trans(s55, s56)) | always5(s56)) <=> ((~trans(s55, s56)) | (~always5(s55)) | always5(s56))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3887,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3886])).
% 12.29/8.23 tff(3888,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3887, 3885])).
% 12.29/8.23 tff(3889,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s55)) | (~trans(s55, s56)) | always5(s56))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3890,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s55, s56)) | (~always5(s55)) | always5(s56)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3889, 3888])).
% 12.29/8.23 tff(3891,plain,
% 12.29/8.23 ((~always5(s55)) | always5(s56)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3890, 3860, 3605])).
% 12.29/8.23 tff(3892,plain,
% 12.29/8.23 (~always5(s55)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3891, 3884])).
% 12.29/8.23 tff(3893,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3894,plain,
% 12.29/8.23 (((~always5(s54)) | (~trans(s54, s55)) | always5(s55)) <=> ((~trans(s54, s55)) | (~always5(s54)) | always5(s55))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3895,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3894])).
% 12.29/8.23 tff(3896,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3895, 3893])).
% 12.29/8.23 tff(3897,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s54)) | (~trans(s54, s55)) | always5(s55))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3898,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s54, s55)) | (~always5(s54)) | always5(s55)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3897, 3896])).
% 12.29/8.23 tff(3899,plain,
% 12.29/8.23 ((~always5(s54)) | always5(s55)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3898, 3860, 3544])).
% 12.29/8.23 tff(3900,plain,
% 12.29/8.23 (~always5(s54)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3899, 3892])).
% 12.29/8.23 tff(3901,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3902,plain,
% 12.29/8.23 (((~always5(s53)) | (~trans(s53, s54)) | always5(s54)) <=> ((~trans(s53, s54)) | (~always5(s53)) | always5(s54))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3903,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3902])).
% 12.29/8.23 tff(3904,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3903, 3901])).
% 12.29/8.23 tff(3905,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s53)) | (~trans(s53, s54)) | always5(s54))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3906,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s53, s54)) | (~always5(s53)) | always5(s54)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 12.29/8.23 tff(3907,plain,
% 12.29/8.23 ((~always5(s53)) | always5(s54)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3906, 3860, 3483])).
% 12.29/8.23 tff(3908,plain,
% 12.29/8.23 (~always5(s53)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3907, 3900])).
% 12.29/8.23 tff(3909,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3910,plain,
% 12.29/8.23 (((~always5(s52)) | (~trans(s52, s53)) | always5(s53)) <=> ((~trans(s52, s53)) | (~always5(s52)) | always5(s53))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3911,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3910])).
% 12.29/8.23 tff(3912,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3911, 3909])).
% 12.29/8.23 tff(3913,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s52)) | (~trans(s52, s53)) | always5(s53))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3914,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s52, s53)) | (~always5(s52)) | always5(s53)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3913, 3912])).
% 12.29/8.23 tff(3915,plain,
% 12.29/8.23 ((~always5(s52)) | always5(s53)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3914, 3860, 3419])).
% 12.29/8.23 tff(3916,plain,
% 12.29/8.23 (~always5(s52)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3915, 3908])).
% 12.29/8.23 tff(3917,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3918,plain,
% 12.29/8.23 (((~always5(s51)) | (~trans(s51, s52)) | always5(s52)) <=> ((~trans(s51, s52)) | (~always5(s51)) | always5(s52))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3919,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3918])).
% 12.29/8.23 tff(3920,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3919, 3917])).
% 12.29/8.23 tff(3921,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s51)) | (~trans(s51, s52)) | always5(s52))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3922,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s51, s52)) | (~always5(s51)) | always5(s52)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3921, 3920])).
% 12.29/8.23 tff(3923,plain,
% 12.29/8.23 ((~always5(s51)) | always5(s52)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3922, 3860, 3355])).
% 12.29/8.23 tff(3924,plain,
% 12.29/8.23 (~always5(s51)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3923, 3916])).
% 12.29/8.23 tff(3925,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3926,plain,
% 12.29/8.23 (((~always5(s50)) | (~trans(s50, s51)) | always5(s51)) <=> ((~trans(s50, s51)) | (~always5(s50)) | always5(s51))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3927,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3926])).
% 12.29/8.23 tff(3928,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3927, 3925])).
% 12.29/8.23 tff(3929,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s50)) | (~trans(s50, s51)) | always5(s51))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3930,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s50, s51)) | (~always5(s50)) | always5(s51)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3929, 3928])).
% 12.29/8.23 tff(3931,plain,
% 12.29/8.23 ((~always5(s50)) | always5(s51)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3930, 3860, 3289])).
% 12.29/8.23 tff(3932,plain,
% 12.29/8.23 (~always5(s50)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3931, 3924])).
% 12.29/8.23 tff(3933,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3934,plain,
% 12.29/8.23 (((~always5(s49)) | (~trans(s49, s50)) | always5(s50)) <=> ((~trans(s49, s50)) | (~always5(s49)) | always5(s50))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3935,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3934])).
% 12.29/8.23 tff(3936,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3935, 3933])).
% 12.29/8.23 tff(3937,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s49)) | (~trans(s49, s50)) | always5(s50))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3938,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s49, s50)) | (~always5(s49)) | always5(s50)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3937, 3936])).
% 12.29/8.23 tff(3939,plain,
% 12.29/8.23 ((~always5(s49)) | always5(s50)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3938, 3860, 3203])).
% 12.29/8.23 tff(3940,plain,
% 12.29/8.23 (~always5(s49)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3939, 3932])).
% 12.29/8.23 tff(3941,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3942,plain,
% 12.29/8.23 (((~always5(s48)) | (~trans(s48, s49)) | always5(s49)) <=> ((~trans(s48, s49)) | (~always5(s48)) | always5(s49))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3943,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3942])).
% 12.29/8.23 tff(3944,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3943, 3941])).
% 12.29/8.23 tff(3945,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s48)) | (~trans(s48, s49)) | always5(s49))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3946,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s48, s49)) | (~always5(s48)) | always5(s49)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3945, 3944])).
% 12.29/8.23 tff(3947,plain,
% 12.29/8.23 ((~always5(s48)) | always5(s49)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3946, 3860, 3134])).
% 12.29/8.23 tff(3948,plain,
% 12.29/8.23 (~always5(s48)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3947, 3940])).
% 12.29/8.23 tff(3949,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3950,plain,
% 12.29/8.23 (((~always5(s47)) | (~trans(s47, s48)) | always5(s48)) <=> ((~trans(s47, s48)) | (~always5(s47)) | always5(s48))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3951,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3950])).
% 12.29/8.23 tff(3952,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3951, 3949])).
% 12.29/8.23 tff(3953,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s47)) | (~trans(s47, s48)) | always5(s48))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3954,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s47, s48)) | (~always5(s47)) | always5(s48)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3953, 3952])).
% 12.29/8.23 tff(3955,plain,
% 12.29/8.23 ((~always5(s47)) | always5(s48)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3954, 3860, 3074])).
% 12.29/8.23 tff(3956,plain,
% 12.29/8.23 (~always5(s47)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3955, 3948])).
% 12.29/8.23 tff(3957,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3958,plain,
% 12.29/8.23 (((~always5(s46)) | (~trans(s46, s47)) | always5(s47)) <=> ((~trans(s46, s47)) | (~always5(s46)) | always5(s47))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3959,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3958])).
% 12.29/8.23 tff(3960,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3959, 3957])).
% 12.29/8.23 tff(3961,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s46)) | (~trans(s46, s47)) | always5(s47))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3962,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s46, s47)) | (~always5(s46)) | always5(s47)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3961, 3960])).
% 12.29/8.23 tff(3963,plain,
% 12.29/8.23 ((~always5(s46)) | always5(s47)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3962, 3860, 2976])).
% 12.29/8.23 tff(3964,plain,
% 12.29/8.23 (~always5(s46)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3963, 3956])).
% 12.29/8.23 tff(3965,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3966,plain,
% 12.29/8.23 (((~always5(s45)) | (~trans(s45, s46)) | always5(s46)) <=> ((~trans(s45, s46)) | (~always5(s45)) | always5(s46))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3967,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3966])).
% 12.29/8.23 tff(3968,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3967, 3965])).
% 12.29/8.23 tff(3969,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s45)) | (~trans(s45, s46)) | always5(s46))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3970,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s45, s46)) | (~always5(s45)) | always5(s46)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3969, 3968])).
% 12.29/8.23 tff(3971,plain,
% 12.29/8.23 ((~always5(s45)) | always5(s46)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3970, 3860, 2909])).
% 12.29/8.23 tff(3972,plain,
% 12.29/8.23 (~always5(s45)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3971, 3964])).
% 12.29/8.23 tff(3973,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3974,plain,
% 12.29/8.23 (((~always5(s44)) | (~trans(s44, s45)) | always5(s45)) <=> ((~trans(s44, s45)) | (~always5(s44)) | always5(s45))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3975,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3974])).
% 12.29/8.23 tff(3976,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3975, 3973])).
% 12.29/8.23 tff(3977,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s44)) | (~trans(s44, s45)) | always5(s45))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3978,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s44, s45)) | (~always5(s44)) | always5(s45)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3977, 3976])).
% 12.29/8.23 tff(3979,plain,
% 12.29/8.23 ((~always5(s44)) | always5(s45)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3978, 3860, 2845])).
% 12.29/8.23 tff(3980,plain,
% 12.29/8.23 (~always5(s44)),
% 12.29/8.23 inference(unit_resolution,[status(thm)],[3979, 3972])).
% 12.29/8.23 tff(3981,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3982,plain,
% 12.29/8.23 (((~always5(s43)) | (~trans(s43, s44)) | always5(s44)) <=> ((~trans(s43, s44)) | (~always5(s43)) | always5(s44))),
% 12.29/8.23 inference(rewrite,[status(thm)],[])).
% 12.29/8.23 tff(3983,plain,
% 12.29/8.23 (((~![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)))),
% 12.29/8.23 inference(monotonicity,[status(thm)],[3982])).
% 12.29/8.23 tff(3984,plain,
% 12.29/8.23 (((~![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))),
% 12.29/8.23 inference(transitivity,[status(thm)],[3983, 3981])).
% 12.29/8.23 tff(3985,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s43)) | (~trans(s43, s44)) | always5(s44))),
% 12.29/8.23 inference(quant_inst,[status(thm)],[])).
% 12.29/8.23 tff(3986,plain,
% 12.29/8.23 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s43, s44)) | (~always5(s43)) | always5(s44)),
% 12.29/8.23 inference(modus_ponens,[status(thm)],[3985, 3984])).
% 12.29/8.23 tff(3987,plain,
% 12.29/8.23 ((~always5(s43)) | always5(s44)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[3986, 3860, 2779])).
% 12.29/8.24 tff(3988,plain,
% 12.29/8.24 (~always5(s43)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[3987, 3980])).
% 12.29/8.24 tff(3989,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(3990,plain,
% 12.29/8.24 (((~always5(s42)) | (~trans(s42, s43)) | always5(s43)) <=> ((~trans(s42, s43)) | (~always5(s42)) | always5(s43))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(3991,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[3990])).
% 12.29/8.24 tff(3992,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[3991, 3989])).
% 12.29/8.24 tff(3993,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s42)) | (~trans(s42, s43)) | always5(s43))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(3994,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s42, s43)) | (~always5(s42)) | always5(s43)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[3993, 3992])).
% 12.29/8.24 tff(3995,plain,
% 12.29/8.24 ((~always5(s42)) | always5(s43)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[3994, 3860, 2718])).
% 12.29/8.24 tff(3996,plain,
% 12.29/8.24 (~always5(s42)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[3995, 3988])).
% 12.29/8.24 tff(3997,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(3998,plain,
% 12.29/8.24 (((~always5(s41)) | (~trans(s41, s42)) | always5(s42)) <=> ((~trans(s41, s42)) | (~always5(s41)) | always5(s42))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(3999,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[3998])).
% 12.29/8.24 tff(4000,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[3999, 3997])).
% 12.29/8.24 tff(4001,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s41)) | (~trans(s41, s42)) | always5(s42))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4002,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s41, s42)) | (~always5(s41)) | always5(s42)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4001, 4000])).
% 12.29/8.24 tff(4003,plain,
% 12.29/8.24 ((~always5(s41)) | always5(s42)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4002, 3860, 2651])).
% 12.29/8.24 tff(4004,plain,
% 12.29/8.24 (~always5(s41)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4003, 3996])).
% 12.29/8.24 tff(4005,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4006,plain,
% 12.29/8.24 (((~always5(s40)) | (~trans(s40, s41)) | always5(s41)) <=> ((~trans(s40, s41)) | (~always5(s40)) | always5(s41))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4007,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4006])).
% 12.29/8.24 tff(4008,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4007, 4005])).
% 12.29/8.24 tff(4009,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s40)) | (~trans(s40, s41)) | always5(s41))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4010,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s40, s41)) | (~always5(s40)) | always5(s41)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4009, 4008])).
% 12.29/8.24 tff(4011,plain,
% 12.29/8.24 ((~always5(s40)) | always5(s41)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4010, 3860, 2587])).
% 12.29/8.24 tff(4012,plain,
% 12.29/8.24 (~always5(s40)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4011, 4004])).
% 12.29/8.24 tff(4013,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4014,plain,
% 12.29/8.24 (((~always5(s39)) | (~trans(s39, s40)) | always5(s40)) <=> ((~trans(s39, s40)) | (~always5(s39)) | always5(s40))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4015,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4014])).
% 12.29/8.24 tff(4016,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4015, 4013])).
% 12.29/8.24 tff(4017,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s39)) | (~trans(s39, s40)) | always5(s40))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4018,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s39, s40)) | (~always5(s39)) | always5(s40)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4017, 4016])).
% 12.29/8.24 tff(4019,plain,
% 12.29/8.24 ((~always5(s39)) | always5(s40)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4018, 3860, 1200])).
% 12.29/8.24 tff(4020,plain,
% 12.29/8.24 (~always5(s39)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4019, 4012])).
% 12.29/8.24 tff(4021,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4022,plain,
% 12.29/8.24 (((~always5(s38)) | (~trans(s38, s39)) | always5(s39)) <=> ((~trans(s38, s39)) | (~always5(s38)) | always5(s39))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4023,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4022])).
% 12.29/8.24 tff(4024,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4023, 4021])).
% 12.29/8.24 tff(4025,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s38)) | (~trans(s38, s39)) | always5(s39))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4026,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s38, s39)) | (~always5(s38)) | always5(s39)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4025, 4024])).
% 12.29/8.24 tff(4027,plain,
% 12.29/8.24 ((~always5(s38)) | always5(s39)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4026, 3860, 1172])).
% 12.29/8.24 tff(4028,plain,
% 12.29/8.24 (~always5(s38)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4027, 4020])).
% 12.29/8.24 tff(4029,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4030,plain,
% 12.29/8.24 (((~always5(s37)) | (~trans(s37, s38)) | always5(s38)) <=> ((~trans(s37, s38)) | (~always5(s37)) | always5(s38))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4031,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4030])).
% 12.29/8.24 tff(4032,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4031, 4029])).
% 12.29/8.24 tff(4033,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s37)) | (~trans(s37, s38)) | always5(s38))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4034,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s37, s38)) | (~always5(s37)) | always5(s38)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4033, 4032])).
% 12.29/8.24 tff(4035,plain,
% 12.29/8.24 ((~always5(s37)) | always5(s38)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4034, 3860, 1141])).
% 12.29/8.24 tff(4036,plain,
% 12.29/8.24 (~always5(s37)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4035, 4028])).
% 12.29/8.24 tff(4037,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4038,plain,
% 12.29/8.24 (((~always5(s36)) | (~trans(s36, s37)) | always5(s37)) <=> ((~trans(s36, s37)) | (~always5(s36)) | always5(s37))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4039,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4038])).
% 12.29/8.24 tff(4040,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4039, 4037])).
% 12.29/8.24 tff(4041,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s36)) | (~trans(s36, s37)) | always5(s37))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4042,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s36, s37)) | (~always5(s36)) | always5(s37)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4041, 4040])).
% 12.29/8.24 tff(4043,plain,
% 12.29/8.24 ((~always5(s36)) | always5(s37)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4042, 3860, 1113])).
% 12.29/8.24 tff(4044,plain,
% 12.29/8.24 (~always5(s36)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4043, 4036])).
% 12.29/8.24 tff(4045,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4046,plain,
% 12.29/8.24 (((~always5(s35)) | (~trans(s35, s36)) | always5(s36)) <=> ((~trans(s35, s36)) | (~always5(s35)) | always5(s36))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4047,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4046])).
% 12.29/8.24 tff(4048,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4047, 4045])).
% 12.29/8.24 tff(4049,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s35)) | (~trans(s35, s36)) | always5(s36))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4050,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s35, s36)) | (~always5(s35)) | always5(s36)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4049, 4048])).
% 12.29/8.24 tff(4051,plain,
% 12.29/8.24 ((~always5(s35)) | always5(s36)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4050, 3860, 1082])).
% 12.29/8.24 tff(4052,plain,
% 12.29/8.24 (~always5(s35)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4051, 4044])).
% 12.29/8.24 tff(4053,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4054,plain,
% 12.29/8.24 (((~always5(s34)) | (~trans(s34, s35)) | always5(s35)) <=> ((~trans(s34, s35)) | (~always5(s34)) | always5(s35))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4055,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4054])).
% 12.29/8.24 tff(4056,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4055, 4053])).
% 12.29/8.24 tff(4057,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s34)) | (~trans(s34, s35)) | always5(s35))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4058,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s34, s35)) | (~always5(s34)) | always5(s35)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4057, 4056])).
% 12.29/8.24 tff(4059,plain,
% 12.29/8.24 ((~always5(s34)) | always5(s35)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4058, 3860, 1054])).
% 12.29/8.24 tff(4060,plain,
% 12.29/8.24 (~always5(s34)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4059, 4052])).
% 12.29/8.24 tff(4061,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4062,plain,
% 12.29/8.24 (((~always5(s33)) | (~trans(s33, s34)) | always5(s34)) <=> ((~trans(s33, s34)) | (~always5(s33)) | always5(s34))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4063,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4062])).
% 12.29/8.24 tff(4064,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4063, 4061])).
% 12.29/8.24 tff(4065,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s33)) | (~trans(s33, s34)) | always5(s34))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4066,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s33, s34)) | (~always5(s33)) | always5(s34)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4065, 4064])).
% 12.29/8.24 tff(4067,plain,
% 12.29/8.24 ((~always5(s33)) | always5(s34)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4066, 3860, 1023])).
% 12.29/8.24 tff(4068,plain,
% 12.29/8.24 (~always5(s33)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4067, 4060])).
% 12.29/8.24 tff(4069,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4070,plain,
% 12.29/8.24 (((~always5(s32)) | (~trans(s32, s33)) | always5(s33)) <=> ((~trans(s32, s33)) | (~always5(s32)) | always5(s33))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4071,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4070])).
% 12.29/8.24 tff(4072,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4071, 4069])).
% 12.29/8.24 tff(4073,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s32)) | (~trans(s32, s33)) | always5(s33))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4074,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s32, s33)) | (~always5(s32)) | always5(s33)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4073, 4072])).
% 12.29/8.24 tff(4075,plain,
% 12.29/8.24 ((~always5(s32)) | always5(s33)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4074, 3860, 995])).
% 12.29/8.24 tff(4076,plain,
% 12.29/8.24 (~always5(s32)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4075, 4068])).
% 12.29/8.24 tff(4077,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4078,plain,
% 12.29/8.24 (((~always5(s31)) | (~trans(s31, s32)) | always5(s32)) <=> ((~trans(s31, s32)) | (~always5(s31)) | always5(s32))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4079,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4078])).
% 12.29/8.24 tff(4080,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4079, 4077])).
% 12.29/8.24 tff(4081,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s31)) | (~trans(s31, s32)) | always5(s32))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4082,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s31, s32)) | (~always5(s31)) | always5(s32)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4081, 4080])).
% 12.29/8.24 tff(4083,plain,
% 12.29/8.24 ((~always5(s31)) | always5(s32)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4082, 3860, 964])).
% 12.29/8.24 tff(4084,plain,
% 12.29/8.24 (~always5(s31)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4083, 4076])).
% 12.29/8.24 tff(4085,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4086,plain,
% 12.29/8.24 (((~always5(s30)) | (~trans(s30, s31)) | always5(s31)) <=> ((~trans(s30, s31)) | (~always5(s30)) | always5(s31))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4087,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4086])).
% 12.29/8.24 tff(4088,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4087, 4085])).
% 12.29/8.24 tff(4089,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s30)) | (~trans(s30, s31)) | always5(s31))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4090,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s30, s31)) | (~always5(s30)) | always5(s31)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4089, 4088])).
% 12.29/8.24 tff(4091,plain,
% 12.29/8.24 ((~always5(s30)) | always5(s31)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4090, 3860, 936])).
% 12.29/8.24 tff(4092,plain,
% 12.29/8.24 (~always5(s30)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4091, 4084])).
% 12.29/8.24 tff(4093,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4094,plain,
% 12.29/8.24 (((~always5(s29)) | (~trans(s29, s30)) | always5(s30)) <=> ((~trans(s29, s30)) | (~always5(s29)) | always5(s30))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4095,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4094])).
% 12.29/8.24 tff(4096,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4095, 4093])).
% 12.29/8.24 tff(4097,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s29)) | (~trans(s29, s30)) | always5(s30))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4098,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s29, s30)) | (~always5(s29)) | always5(s30)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4097, 4096])).
% 12.29/8.24 tff(4099,plain,
% 12.29/8.24 ((~always5(s29)) | always5(s30)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4098, 3860, 905])).
% 12.29/8.24 tff(4100,plain,
% 12.29/8.24 (~always5(s29)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4099, 4092])).
% 12.29/8.24 tff(4101,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4102,plain,
% 12.29/8.24 (((~always5(s28)) | (~trans(s28, s29)) | always5(s29)) <=> ((~trans(s28, s29)) | (~always5(s28)) | always5(s29))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4103,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4102])).
% 12.29/8.24 tff(4104,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4103, 4101])).
% 12.29/8.24 tff(4105,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s28)) | (~trans(s28, s29)) | always5(s29))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4106,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s28, s29)) | (~always5(s28)) | always5(s29)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4105, 4104])).
% 12.29/8.24 tff(4107,plain,
% 12.29/8.24 ((~always5(s28)) | always5(s29)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4106, 3860, 877])).
% 12.29/8.24 tff(4108,plain,
% 12.29/8.24 (~always5(s28)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4107, 4100])).
% 12.29/8.24 tff(4109,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4110,plain,
% 12.29/8.24 (((~always5(s27)) | (~trans(s27, s28)) | always5(s28)) <=> ((~trans(s27, s28)) | (~always5(s27)) | always5(s28))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.24 tff(4111,plain,
% 12.29/8.24 (((~![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)))),
% 12.29/8.24 inference(monotonicity,[status(thm)],[4110])).
% 12.29/8.24 tff(4112,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(transitivity,[status(thm)],[4111, 4109])).
% 12.29/8.24 tff(4113,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s27)) | (~trans(s27, s28)) | always5(s28))),
% 12.29/8.24 inference(quant_inst,[status(thm)],[])).
% 12.29/8.24 tff(4114,plain,
% 12.29/8.24 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s27, s28)) | (~always5(s27)) | always5(s28)),
% 12.29/8.24 inference(modus_ponens,[status(thm)],[4113, 4112])).
% 12.29/8.24 tff(4115,plain,
% 12.29/8.24 ((~always5(s27)) | always5(s28)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4114, 3860, 846])).
% 12.29/8.24 tff(4116,plain,
% 12.29/8.24 (~always5(s27)),
% 12.29/8.24 inference(unit_resolution,[status(thm)],[4115, 4108])).
% 12.29/8.24 tff(4117,plain,
% 12.29/8.24 (((~![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))),
% 12.29/8.24 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4118,plain,
% 12.29/8.25 (((~always5(s26)) | (~trans(s26, s27)) | always5(s27)) <=> ((~trans(s26, s27)) | (~always5(s26)) | always5(s27))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4119,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4118])).
% 12.29/8.25 tff(4120,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4119, 4117])).
% 12.29/8.25 tff(4121,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s26)) | (~trans(s26, s27)) | always5(s27))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4122,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s26, s27)) | (~always5(s26)) | always5(s27)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4121, 4120])).
% 12.29/8.25 tff(4123,plain,
% 12.29/8.25 ((~always5(s26)) | always5(s27)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4122, 3860, 818])).
% 12.29/8.25 tff(4124,plain,
% 12.29/8.25 (~always5(s26)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4123, 4116])).
% 12.29/8.25 tff(4125,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4126,plain,
% 12.29/8.25 (((~always5(s25)) | (~trans(s25, s26)) | always5(s26)) <=> ((~trans(s25, s26)) | (~always5(s25)) | always5(s26))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4127,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4126])).
% 12.29/8.25 tff(4128,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4127, 4125])).
% 12.29/8.25 tff(4129,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s25)) | (~trans(s25, s26)) | always5(s26))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4130,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s25, s26)) | (~always5(s25)) | always5(s26)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4129, 4128])).
% 12.29/8.25 tff(4131,plain,
% 12.29/8.25 ((~always5(s25)) | always5(s26)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4130, 3860, 787])).
% 12.29/8.25 tff(4132,plain,
% 12.29/8.25 (~always5(s25)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4131, 4124])).
% 12.29/8.25 tff(4133,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4134,plain,
% 12.29/8.25 (((~always5(s24)) | (~trans(s24, s25)) | always5(s25)) <=> ((~trans(s24, s25)) | (~always5(s24)) | always5(s25))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4135,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4134])).
% 12.29/8.25 tff(4136,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4135, 4133])).
% 12.29/8.25 tff(4137,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s24)) | (~trans(s24, s25)) | always5(s25))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4138,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s24, s25)) | (~always5(s24)) | always5(s25)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4137, 4136])).
% 12.29/8.25 tff(4139,plain,
% 12.29/8.25 ((~always5(s24)) | always5(s25)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4138, 3860, 759])).
% 12.29/8.25 tff(4140,plain,
% 12.29/8.25 (~always5(s24)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4139, 4132])).
% 12.29/8.25 tff(4141,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4142,plain,
% 12.29/8.25 (((~always5(s23)) | (~trans(s23, s24)) | always5(s24)) <=> ((~trans(s23, s24)) | (~always5(s23)) | always5(s24))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4143,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4142])).
% 12.29/8.25 tff(4144,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4143, 4141])).
% 12.29/8.25 tff(4145,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s23)) | (~trans(s23, s24)) | always5(s24))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4146,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s23, s24)) | (~always5(s23)) | always5(s24)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4145, 4144])).
% 12.29/8.25 tff(4147,plain,
% 12.29/8.25 ((~always5(s23)) | always5(s24)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4146, 3860, 728])).
% 12.29/8.25 tff(4148,plain,
% 12.29/8.25 (~always5(s23)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4147, 4140])).
% 12.29/8.25 tff(4149,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4150,plain,
% 12.29/8.25 (((~always5(s22)) | (~trans(s22, s23)) | always5(s23)) <=> ((~trans(s22, s23)) | (~always5(s22)) | always5(s23))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4151,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4150])).
% 12.29/8.25 tff(4152,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4151, 4149])).
% 12.29/8.25 tff(4153,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s22)) | (~trans(s22, s23)) | always5(s23))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4154,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s22, s23)) | (~always5(s22)) | always5(s23)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4153, 4152])).
% 12.29/8.25 tff(4155,plain,
% 12.29/8.25 ((~always5(s22)) | always5(s23)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4154, 3860, 700])).
% 12.29/8.25 tff(4156,plain,
% 12.29/8.25 (~always5(s22)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4155, 4148])).
% 12.29/8.25 tff(4157,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4158,plain,
% 12.29/8.25 (((~always5(s21)) | (~trans(s21, s22)) | always5(s22)) <=> ((~trans(s21, s22)) | (~always5(s21)) | always5(s22))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4159,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4158])).
% 12.29/8.25 tff(4160,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4159, 4157])).
% 12.29/8.25 tff(4161,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s21)) | (~trans(s21, s22)) | always5(s22))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4162,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s21, s22)) | (~always5(s21)) | always5(s22)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4161, 4160])).
% 12.29/8.25 tff(4163,plain,
% 12.29/8.25 ((~always5(s21)) | always5(s22)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4162, 3860, 669])).
% 12.29/8.25 tff(4164,plain,
% 12.29/8.25 (~always5(s21)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4163, 4156])).
% 12.29/8.25 tff(4165,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4166,plain,
% 12.29/8.25 (((~always5(s20)) | (~trans(s20, s21)) | always5(s21)) <=> ((~trans(s20, s21)) | (~always5(s20)) | always5(s21))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4167,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4166])).
% 12.29/8.25 tff(4168,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4167, 4165])).
% 12.29/8.25 tff(4169,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s20)) | (~trans(s20, s21)) | always5(s21))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4170,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s20, s21)) | (~always5(s20)) | always5(s21)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4169, 4168])).
% 12.29/8.25 tff(4171,plain,
% 12.29/8.25 ((~always5(s20)) | always5(s21)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4170, 3860, 641])).
% 12.29/8.25 tff(4172,plain,
% 12.29/8.25 (~always5(s20)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4171, 4164])).
% 12.29/8.25 tff(4173,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4174,plain,
% 12.29/8.25 (((~always5(s19)) | (~trans(s19, s20)) | always5(s20)) <=> ((~trans(s19, s20)) | (~always5(s19)) | always5(s20))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4175,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4174])).
% 12.29/8.25 tff(4176,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4175, 4173])).
% 12.29/8.25 tff(4177,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s19)) | (~trans(s19, s20)) | always5(s20))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4178,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s19, s20)) | (~always5(s19)) | always5(s20)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4177, 4176])).
% 12.29/8.25 tff(4179,plain,
% 12.29/8.25 ((~always5(s19)) | always5(s20)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4178, 3860, 610])).
% 12.29/8.25 tff(4180,plain,
% 12.29/8.25 (~always5(s19)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4179, 4172])).
% 12.29/8.25 tff(4181,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4182,plain,
% 12.29/8.25 (((~always5(s18)) | (~trans(s18, s19)) | always5(s19)) <=> ((~trans(s18, s19)) | (~always5(s18)) | always5(s19))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4183,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4182])).
% 12.29/8.25 tff(4184,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4183, 4181])).
% 12.29/8.25 tff(4185,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s18)) | (~trans(s18, s19)) | always5(s19))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4186,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s18, s19)) | (~always5(s18)) | always5(s19)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4185, 4184])).
% 12.29/8.25 tff(4187,plain,
% 12.29/8.25 ((~always5(s18)) | always5(s19)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4186, 3860, 582])).
% 12.29/8.25 tff(4188,plain,
% 12.29/8.25 (~always5(s18)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4187, 4180])).
% 12.29/8.25 tff(4189,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4190,plain,
% 12.29/8.25 (((~always5(s17)) | (~trans(s17, s18)) | always5(s18)) <=> ((~trans(s17, s18)) | (~always5(s17)) | always5(s18))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4191,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4190])).
% 12.29/8.25 tff(4192,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4191, 4189])).
% 12.29/8.25 tff(4193,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s17)) | (~trans(s17, s18)) | always5(s18))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4194,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s17, s18)) | (~always5(s17)) | always5(s18)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4193, 4192])).
% 12.29/8.25 tff(4195,plain,
% 12.29/8.25 ((~always5(s17)) | always5(s18)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4194, 3860, 551])).
% 12.29/8.25 tff(4196,plain,
% 12.29/8.25 (~always5(s17)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4195, 4188])).
% 12.29/8.25 tff(4197,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4198,plain,
% 12.29/8.25 (((~always5(s16)) | (~trans(s16, s17)) | always5(s17)) <=> ((~trans(s16, s17)) | (~always5(s16)) | always5(s17))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4199,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4198])).
% 12.29/8.25 tff(4200,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4199, 4197])).
% 12.29/8.25 tff(4201,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s16)) | (~trans(s16, s17)) | always5(s17))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4202,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s16, s17)) | (~always5(s16)) | always5(s17)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4201, 4200])).
% 12.29/8.25 tff(4203,plain,
% 12.29/8.25 ((~always5(s16)) | always5(s17)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4202, 3860, 523])).
% 12.29/8.25 tff(4204,plain,
% 12.29/8.25 (~always5(s16)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4203, 4196])).
% 12.29/8.25 tff(4205,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4206,plain,
% 12.29/8.25 (((~always5(s15)) | (~trans(s15, s16)) | always5(s16)) <=> ((~trans(s15, s16)) | (~always5(s15)) | always5(s16))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4207,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4206])).
% 12.29/8.25 tff(4208,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4207, 4205])).
% 12.29/8.25 tff(4209,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s15)) | (~trans(s15, s16)) | always5(s16))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4210,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s15, s16)) | (~always5(s15)) | always5(s16)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4209, 4208])).
% 12.29/8.25 tff(4211,plain,
% 12.29/8.25 ((~always5(s15)) | always5(s16)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4210, 3860, 494])).
% 12.29/8.25 tff(4212,plain,
% 12.29/8.25 (~always5(s15)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4211, 4204])).
% 12.29/8.25 tff(4213,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4214,plain,
% 12.29/8.25 (((~always5(s14)) | (~trans(s14, s15)) | always5(s15)) <=> ((~trans(s14, s15)) | (~always5(s14)) | always5(s15))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4215,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4214])).
% 12.29/8.25 tff(4216,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4215, 4213])).
% 12.29/8.25 tff(4217,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s14)) | (~trans(s14, s15)) | always5(s15))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4218,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s14, s15)) | (~always5(s14)) | always5(s15)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4217, 4216])).
% 12.29/8.25 tff(4219,plain,
% 12.29/8.25 ((~always5(s14)) | always5(s15)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4218, 3860, 468])).
% 12.29/8.25 tff(4220,plain,
% 12.29/8.25 (~always5(s14)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4219, 4212])).
% 12.29/8.25 tff(4221,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4222,plain,
% 12.29/8.25 (((~always5(s13)) | (~trans(s13, s14)) | always5(s14)) <=> ((~trans(s13, s14)) | (~always5(s13)) | always5(s14))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4223,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4222])).
% 12.29/8.25 tff(4224,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4223, 4221])).
% 12.29/8.25 tff(4225,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s13)) | (~trans(s13, s14)) | always5(s14))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4226,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s13, s14)) | (~always5(s13)) | always5(s14)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4225, 4224])).
% 12.29/8.25 tff(4227,plain,
% 12.29/8.25 ((~always5(s13)) | always5(s14)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4226, 3860, 439])).
% 12.29/8.25 tff(4228,plain,
% 12.29/8.25 (~always5(s13)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4227, 4220])).
% 12.29/8.25 tff(4229,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4230,plain,
% 12.29/8.25 (((~always5(s12)) | (~trans(s12, s13)) | always5(s13)) <=> ((~trans(s12, s13)) | (~always5(s12)) | always5(s13))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4231,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4230])).
% 12.29/8.25 tff(4232,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4231, 4229])).
% 12.29/8.25 tff(4233,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s12)) | (~trans(s12, s13)) | always5(s13))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4234,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s12, s13)) | (~always5(s12)) | always5(s13)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 12.29/8.25 tff(4235,plain,
% 12.29/8.25 ((~always5(s12)) | always5(s13)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4234, 3860, 14])).
% 12.29/8.25 tff(4236,plain,
% 12.29/8.25 (~always5(s12)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4235, 4228])).
% 12.29/8.25 tff(4237,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4238,plain,
% 12.29/8.25 (((~always5(s11)) | (~trans(s11, s12)) | always5(s12)) <=> ((~trans(s11, s12)) | (~always5(s11)) | always5(s12))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4239,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.25 inference(monotonicity,[status(thm)],[4238])).
% 12.29/8.25 tff(4240,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(transitivity,[status(thm)],[4239, 4237])).
% 12.29/8.25 tff(4241,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s11)) | (~trans(s11, s12)) | always5(s12))),
% 12.29/8.25 inference(quant_inst,[status(thm)],[])).
% 12.29/8.25 tff(4242,plain,
% 12.29/8.25 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s11, s12)) | (~always5(s11)) | always5(s12)),
% 12.29/8.25 inference(modus_ponens,[status(thm)],[4241, 4240])).
% 12.29/8.25 tff(4243,plain,
% 12.29/8.25 ((~always5(s11)) | always5(s12)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4242, 3860, 396])).
% 12.29/8.25 tff(4244,plain,
% 12.29/8.25 (~always5(s11)),
% 12.29/8.25 inference(unit_resolution,[status(thm)],[4243, 4236])).
% 12.29/8.25 tff(4245,plain,
% 12.29/8.25 (((~![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))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4246,plain,
% 12.29/8.25 (((~always5(s10)) | (~trans(s10, s11)) | always5(s11)) <=> ((~trans(s10, s11)) | (~always5(s10)) | always5(s11))),
% 12.29/8.25 inference(rewrite,[status(thm)],[])).
% 12.29/8.25 tff(4247,plain,
% 12.29/8.25 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4246])).
% 12.29/8.26 tff(4248,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4247, 4245])).
% 12.29/8.26 tff(4249,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s10)) | (~trans(s10, s11)) | always5(s11))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4250,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s10, s11)) | (~always5(s10)) | always5(s11)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4249, 4248])).
% 12.29/8.26 tff(4251,plain,
% 12.29/8.26 ((~always5(s10)) | always5(s11)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4250, 3860, 370])).
% 12.29/8.26 tff(4252,plain,
% 12.29/8.26 (~always5(s10)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4251, 4244])).
% 12.29/8.26 tff(4253,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4254,plain,
% 12.29/8.26 (((~always5(s9)) | (~trans(s9, s10)) | always5(s10)) <=> ((~trans(s9, s10)) | (~always5(s9)) | always5(s10))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4255,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4254])).
% 12.29/8.26 tff(4256,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4255, 4253])).
% 12.29/8.26 tff(4257,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s9)) | (~trans(s9, s10)) | always5(s10))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4258,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s9, s10)) | (~always5(s9)) | always5(s10)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4257, 4256])).
% 12.29/8.26 tff(4259,plain,
% 12.29/8.26 ((~always5(s9)) | always5(s10)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4258, 3860, 341])).
% 12.29/8.26 tff(4260,plain,
% 12.29/8.26 (~always5(s9)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4259, 4252])).
% 12.29/8.26 tff(4261,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4262,plain,
% 12.29/8.26 (((~always5(s8)) | (~trans(s8, s9)) | always5(s9)) <=> ((~trans(s8, s9)) | (~always5(s8)) | always5(s9))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4263,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4262])).
% 12.29/8.26 tff(4264,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4263, 4261])).
% 12.29/8.26 tff(4265,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s8)) | (~trans(s8, s9)) | always5(s9))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4266,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s8, s9)) | (~always5(s8)) | always5(s9)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4265, 4264])).
% 12.29/8.26 tff(4267,plain,
% 12.29/8.26 ((~always5(s8)) | always5(s9)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4266, 3860, 315])).
% 12.29/8.26 tff(4268,plain,
% 12.29/8.26 (~always5(s8)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4267, 4260])).
% 12.29/8.26 tff(4269,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4270,plain,
% 12.29/8.26 (((~always5(s7)) | (~trans(s7, s8)) | always5(s8)) <=> ((~trans(s7, s8)) | (~always5(s7)) | always5(s8))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4271,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4270])).
% 12.29/8.26 tff(4272,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4271, 4269])).
% 12.29/8.26 tff(4273,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s7)) | (~trans(s7, s8)) | always5(s8))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4274,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s7, s8)) | (~always5(s7)) | always5(s8)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 12.29/8.26 tff(4275,plain,
% 12.29/8.26 ((~always5(s7)) | always5(s8)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4274, 3860, 32])).
% 12.29/8.26 tff(4276,plain,
% 12.29/8.26 (~always5(s7)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4275, 4268])).
% 12.29/8.26 tff(4277,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4278,plain,
% 12.29/8.26 (((~always5(s6)) | (~trans(s6, s7)) | always5(s7)) <=> ((~trans(s6, s7)) | (~always5(s6)) | always5(s7))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4279,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4278])).
% 12.29/8.26 tff(4280,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4279, 4277])).
% 12.29/8.26 tff(4281,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s6)) | (~trans(s6, s7)) | always5(s7))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4282,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s6, s7)) | (~always5(s6)) | always5(s7)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4281, 4280])).
% 12.29/8.26 tff(4283,plain,
% 12.29/8.26 ((~always5(s6)) | always5(s7)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4282, 3860, 272])).
% 12.29/8.26 tff(4284,plain,
% 12.29/8.26 (~always5(s6)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4283, 4276])).
% 12.29/8.26 tff(4285,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4286,plain,
% 12.29/8.26 (((~always5(s5)) | (~trans(s5, s6)) | always5(s6)) <=> ((~trans(s5, s6)) | (~always5(s5)) | always5(s6))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4287,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4286])).
% 12.29/8.26 tff(4288,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4287, 4285])).
% 12.29/8.26 tff(4289,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s5)) | (~trans(s5, s6)) | always5(s6))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4290,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s5, s6)) | (~always5(s5)) | always5(s6)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4289, 4288])).
% 12.29/8.26 tff(4291,plain,
% 12.29/8.26 ((~always5(s5)) | always5(s6)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4290, 3860, 246])).
% 12.29/8.26 tff(4292,plain,
% 12.29/8.26 (~always5(s5)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4291, 4284])).
% 12.29/8.26 tff(4293,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4294,plain,
% 12.29/8.26 (((~always5(s4)) | (~trans(s4, s5)) | always5(s5)) <=> ((~trans(s4, s5)) | (~always5(s4)) | always5(s5))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4295,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4294])).
% 12.29/8.26 tff(4296,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4295, 4293])).
% 12.29/8.26 tff(4297,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s4)) | (~trans(s4, s5)) | always5(s5))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4298,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s4, s5)) | (~always5(s4)) | always5(s5)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4297, 4296])).
% 12.29/8.26 tff(4299,plain,
% 12.29/8.26 ((~always5(s4)) | always5(s5)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4298, 3860, 220])).
% 12.29/8.26 tff(4300,plain,
% 12.29/8.26 (~always5(s4)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4299, 4292])).
% 12.29/8.26 tff(4301,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4302,plain,
% 12.29/8.26 (((~always5(s3)) | (~trans(s3, s4)) | always5(s4)) <=> ((~trans(s3, s4)) | (~always5(s3)) | always5(s4))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4303,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4302])).
% 12.29/8.26 tff(4304,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4303, 4301])).
% 12.29/8.26 tff(4305,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s3)) | (~trans(s3, s4)) | always5(s4))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4306,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s3, s4)) | (~always5(s3)) | always5(s4)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4305, 4304])).
% 12.29/8.26 tff(4307,plain,
% 12.29/8.26 ((~always5(s3)) | always5(s4)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4306, 3860, 191])).
% 12.29/8.26 tff(4308,plain,
% 12.29/8.26 (~always5(s3)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4307, 4300])).
% 12.29/8.26 tff(4309,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4310,plain,
% 12.29/8.26 (((~always5(s2)) | (~trans(s2, s3)) | always5(s3)) <=> ((~trans(s2, s3)) | (~always5(s2)) | always5(s3))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4311,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4310])).
% 12.29/8.26 tff(4312,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4311, 4309])).
% 12.29/8.26 tff(4313,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s2)) | (~trans(s2, s3)) | always5(s3))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4314,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s2, s3)) | (~always5(s2)) | always5(s3)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4313, 4312])).
% 12.29/8.26 tff(4315,plain,
% 12.29/8.26 ((~always5(s2)) | always5(s3)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4314, 3860, 165])).
% 12.29/8.26 tff(4316,plain,
% 12.29/8.26 (~always5(s2)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4315, 4308])).
% 12.29/8.26 tff(4317,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4318,plain,
% 12.29/8.26 (((~always5(s1)) | (~trans(s1, s2)) | always5(s2)) <=> ((~trans(s1, s2)) | (~always5(s1)) | always5(s2))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4319,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4318])).
% 12.29/8.26 tff(4320,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4319, 4317])).
% 12.29/8.26 tff(4321,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s1)) | (~trans(s1, s2)) | always5(s2))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4322,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s1, s2)) | (~always5(s1)) | always5(s2)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4321, 4320])).
% 12.29/8.26 tff(4323,plain,
% 12.29/8.26 ((~always5(s1)) | always5(s2)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4322, 3860, 43])).
% 12.29/8.26 tff(4324,plain,
% 12.29/8.26 (~always5(s1)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4323, 4316])).
% 12.29/8.26 tff(4325,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4326,plain,
% 12.29/8.26 (((~always5(s0)) | (~trans(s0, s1)) | always5(s1)) <=> ((~trans(s0, s1)) | (~always5(s0)) | always5(s1))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4327,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4326])).
% 12.29/8.26 tff(4328,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4327, 4325])).
% 12.29/8.26 tff(4329,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s0)) | (~trans(s0, s1)) | always5(s1))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4330,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s0, s1)) | (~always5(s0)) | always5(s1)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4329, 4328])).
% 12.29/8.26 tff(4331,plain,
% 12.29/8.26 ((~always5(s0)) | always5(s1)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4330, 3860, 92])).
% 12.29/8.26 tff(4332,plain,
% 12.29/8.26 (~always5(s0)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4331, 4324])).
% 12.29/8.26 tff(4333,plain,
% 12.29/8.26 (until6(s0) <=> until6(s0)),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4334,axiom,(until6(s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty11')).
% 12.29/8.26 tff(4335,plain,
% 12.29/8.26 (until6(s0)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4334, 4333])).
% 12.29/8.26 tff(4336,plain,
% 12.29/8.26 (^[X: $i] : refl((always5(X) | (~until6(X)) | xuntil7(X)) <=> (always5(X) | (~until6(X)) | xuntil7(X)))),
% 12.29/8.26 inference(bind,[status(th)],[])).
% 12.29/8.26 tff(4337,plain,
% 12.29/8.26 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X)) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 12.29/8.26 inference(quant_intro,[status(thm)],[4336])).
% 12.29/8.26 tff(4338,plain,
% 12.29/8.26 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X)) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4339,plain,
% 12.29/8.26 (^[X: $i] : rewrite(((always5(X) | xuntil7(X)) | (~until6(X))) <=> (always5(X) | (~until6(X)) | xuntil7(X)))),
% 12.29/8.26 inference(bind,[status(th)],[])).
% 12.29/8.26 tff(4340,plain,
% 12.29/8.26 (![X: $i] : ((always5(X) | xuntil7(X)) | (~until6(X))) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 12.29/8.26 inference(quant_intro,[status(thm)],[4339])).
% 12.29/8.26 tff(4341,axiom,(![X: $i] : ((always5(X) | xuntil7(X)) | (~until6(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty4')).
% 12.29/8.26 tff(4342,plain,
% 12.29/8.26 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4341, 4340])).
% 12.29/8.26 tff(4343,plain,
% 12.29/8.26 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4342, 4338])).
% 12.29/8.26 tff(4344,plain,(
% 12.29/8.26 ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 12.29/8.26 inference(skolemize,[status(sab)],[4343])).
% 12.29/8.26 tff(4345,plain,
% 12.29/8.26 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4344, 4337])).
% 12.29/8.26 tff(4346,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4347,plain,
% 12.29/8.26 ((always5(s0) | (~until6(s0)) | xuntil7(s0)) <=> (xuntil7(s0) | always5(s0) | (~until6(s0)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4348,plain,
% 12.29/8.26 (((~![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))))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4347])).
% 12.29/8.26 tff(4349,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4348, 4346])).
% 12.29/8.26 tff(4350,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s0) | (~until6(s0)) | xuntil7(s0))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4351,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s0) | always5(s0) | (~until6(s0))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4350, 4349])).
% 12.29/8.26 tff(4352,plain,
% 12.29/8.26 (xuntil7(s0) | always5(s0)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4351, 4345, 4335])).
% 12.29/8.26 tff(4353,plain,
% 12.29/8.26 (xuntil7(s0)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4352, 4332])).
% 12.29/8.26 tff(4354,plain,
% 12.29/8.26 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)))),
% 12.29/8.26 inference(bind,[status(th)],[])).
% 12.29/8.26 tff(4355,plain,
% 12.29/8.26 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 12.29/8.26 inference(quant_intro,[status(thm)],[4354])).
% 12.29/8.26 tff(4356,plain,
% 12.29/8.26 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4357,plain,
% 12.29/8.26 (^[Y: $i, X: $i] : rewrite(((until6(Y) | (~succ(X, Y))) | (~xuntil7(X))) <=> ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)))),
% 12.29/8.26 inference(bind,[status(th)],[])).
% 12.29/8.26 tff(4358,plain,
% 12.29/8.26 (![Y: $i, X: $i] : ((until6(Y) | (~succ(X, Y))) | (~xuntil7(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 12.29/8.26 inference(quant_intro,[status(thm)],[4357])).
% 12.29/8.26 tff(4359,axiom,(![Y: $i, X: $i] : ((until6(Y) | (~succ(X, Y))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty5')).
% 12.29/8.26 tff(4360,plain,
% 12.29/8.26 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4359, 4358])).
% 12.29/8.26 tff(4361,plain,
% 12.29/8.26 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4360, 4356])).
% 12.29/8.26 tff(4362,plain,(
% 12.29/8.26 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 12.29/8.26 inference(skolemize,[status(sab)],[4361])).
% 12.29/8.26 tff(4363,plain,
% 12.29/8.26 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4362, 4355])).
% 12.29/8.26 tff(4364,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4365,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4366,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4365, 4364])).
% 12.29/8.26 tff(4367,plain,
% 12.29/8.26 ((~xuntil7(s0)) | until6(s1)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4366, 88, 4363])).
% 12.29/8.26 tff(4368,plain,
% 12.29/8.26 (until6(s1)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4367, 4353])).
% 12.29/8.26 tff(4369,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4370,plain,
% 12.29/8.26 ((always5(s1) | (~until6(s1)) | xuntil7(s1)) <=> (xuntil7(s1) | always5(s1) | (~until6(s1)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4371,plain,
% 12.29/8.26 (((~![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))))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4370])).
% 12.29/8.26 tff(4372,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4371, 4369])).
% 12.29/8.26 tff(4373,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s1) | (~until6(s1)) | xuntil7(s1))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4374,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s1) | always5(s1) | (~until6(s1))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4373, 4372])).
% 12.29/8.26 tff(4375,plain,
% 12.29/8.26 (xuntil7(s1)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4374, 4345, 4368, 4324])).
% 12.29/8.26 tff(4376,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4377,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4378,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4377, 4376])).
% 12.29/8.26 tff(4379,plain,
% 12.29/8.26 ((~xuntil7(s1)) | until6(s2)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4378, 39, 4363])).
% 12.29/8.26 tff(4380,plain,
% 12.29/8.26 (until6(s2)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4379, 4375])).
% 12.29/8.26 tff(4381,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4382,plain,
% 12.29/8.26 ((always5(s2) | (~until6(s2)) | xuntil7(s2)) <=> (xuntil7(s2) | always5(s2) | (~until6(s2)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4383,plain,
% 12.29/8.26 (((~![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))))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4382])).
% 12.29/8.26 tff(4384,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4383, 4381])).
% 12.29/8.26 tff(4385,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s2) | (~until6(s2)) | xuntil7(s2))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4386,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s2) | always5(s2) | (~until6(s2))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4385, 4384])).
% 12.29/8.26 tff(4387,plain,
% 12.29/8.26 (xuntil7(s2) | (~until6(s2))),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4386, 4345, 4316])).
% 12.29/8.26 tff(4388,plain,
% 12.29/8.26 (xuntil7(s2)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4387, 4380])).
% 12.29/8.26 tff(4389,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4390,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4391,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4390, 4389])).
% 12.29/8.26 tff(4392,plain,
% 12.29/8.26 ((~xuntil7(s2)) | until6(s3)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4391, 161, 4363])).
% 12.29/8.26 tff(4393,plain,
% 12.29/8.26 (until6(s3)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4392, 4388])).
% 12.29/8.26 tff(4394,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4395,plain,
% 12.29/8.26 ((always5(s3) | (~until6(s3)) | xuntil7(s3)) <=> (xuntil7(s3) | always5(s3) | (~until6(s3)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4396,plain,
% 12.29/8.26 (((~![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))))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4395])).
% 12.29/8.26 tff(4397,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4396, 4394])).
% 12.29/8.26 tff(4398,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s3) | (~until6(s3)) | xuntil7(s3))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4399,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s3) | always5(s3) | (~until6(s3))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4398, 4397])).
% 12.29/8.26 tff(4400,plain,
% 12.29/8.26 (xuntil7(s3) | (~until6(s3))),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4399, 4345, 4308])).
% 12.29/8.26 tff(4401,plain,
% 12.29/8.26 (xuntil7(s3)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4400, 4393])).
% 12.29/8.26 tff(4402,plain,
% 12.29/8.26 (((~![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))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4403,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4404,plain,
% 12.29/8.26 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4)),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4403, 4402])).
% 12.29/8.26 tff(4405,plain,
% 12.29/8.26 ((~xuntil7(s3)) | until6(s4)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4404, 187, 4363])).
% 12.29/8.26 tff(4406,plain,
% 12.29/8.26 (until6(s4)),
% 12.29/8.26 inference(unit_resolution,[status(thm)],[4405, 4401])).
% 12.29/8.26 tff(4407,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4408,plain,
% 12.29/8.26 ((always5(s4) | (~until6(s4)) | xuntil7(s4)) <=> (xuntil7(s4) | always5(s4) | (~until6(s4)))),
% 12.29/8.26 inference(rewrite,[status(thm)],[])).
% 12.29/8.26 tff(4409,plain,
% 12.29/8.26 (((~![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))))),
% 12.29/8.26 inference(monotonicity,[status(thm)],[4408])).
% 12.29/8.26 tff(4410,plain,
% 12.29/8.26 (((~![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)))),
% 12.29/8.26 inference(transitivity,[status(thm)],[4409, 4407])).
% 12.29/8.26 tff(4411,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s4) | (~until6(s4)) | xuntil7(s4))),
% 12.29/8.26 inference(quant_inst,[status(thm)],[])).
% 12.29/8.26 tff(4412,plain,
% 12.29/8.26 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s4) | always5(s4) | (~until6(s4))),
% 12.29/8.26 inference(modus_ponens,[status(thm)],[4411, 4410])).
% 12.29/8.26 tff(4413,plain,
% 12.29/8.26 (xuntil7(s4) | (~until6(s4))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4412, 4345, 4300])).
% 12.29/8.27 tff(4414,plain,
% 12.29/8.27 (xuntil7(s4)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4413, 4406])).
% 12.29/8.27 tff(4415,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4416,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4417,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4416, 4415])).
% 12.29/8.27 tff(4418,plain,
% 12.29/8.27 ((~xuntil7(s4)) | until6(s5)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4417, 216, 4363])).
% 12.29/8.27 tff(4419,plain,
% 12.29/8.27 (until6(s5)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4418, 4414])).
% 12.29/8.27 tff(4420,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4421,plain,
% 12.29/8.27 ((always5(s5) | (~until6(s5)) | xuntil7(s5)) <=> (xuntil7(s5) | always5(s5) | (~until6(s5)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4422,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4421])).
% 12.29/8.27 tff(4423,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4422, 4420])).
% 12.29/8.27 tff(4424,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s5) | (~until6(s5)) | xuntil7(s5))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4425,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s5) | always5(s5) | (~until6(s5))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4424, 4423])).
% 12.29/8.27 tff(4426,plain,
% 12.29/8.27 (xuntil7(s5) | (~until6(s5))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4425, 4345, 4292])).
% 12.29/8.27 tff(4427,plain,
% 12.29/8.27 (xuntil7(s5)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4426, 4419])).
% 12.29/8.27 tff(4428,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4429,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4430,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4429, 4428])).
% 12.29/8.27 tff(4431,plain,
% 12.29/8.27 ((~xuntil7(s5)) | until6(s6)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4430, 242, 4363])).
% 12.29/8.27 tff(4432,plain,
% 12.29/8.27 (until6(s6)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4431, 4427])).
% 12.29/8.27 tff(4433,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4434,plain,
% 12.29/8.27 ((always5(s6) | (~until6(s6)) | xuntil7(s6)) <=> (xuntil7(s6) | always5(s6) | (~until6(s6)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4435,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4434])).
% 12.29/8.27 tff(4436,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4435, 4433])).
% 12.29/8.27 tff(4437,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s6) | (~until6(s6)) | xuntil7(s6))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4438,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s6) | always5(s6) | (~until6(s6))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4437, 4436])).
% 12.29/8.27 tff(4439,plain,
% 12.29/8.27 (xuntil7(s6) | (~until6(s6))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4438, 4345, 4284])).
% 12.29/8.27 tff(4440,plain,
% 12.29/8.27 (xuntil7(s6)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4439, 4432])).
% 12.29/8.27 tff(4441,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4442,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4443,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4442, 4441])).
% 12.29/8.27 tff(4444,plain,
% 12.29/8.27 ((~xuntil7(s6)) | until6(s7)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4443, 268, 4363])).
% 12.29/8.27 tff(4445,plain,
% 12.29/8.27 (until6(s7)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4444, 4440])).
% 12.29/8.27 tff(4446,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4447,plain,
% 12.29/8.27 ((always5(s7) | (~until6(s7)) | xuntil7(s7)) <=> (xuntil7(s7) | always5(s7) | (~until6(s7)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4448,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4447])).
% 12.29/8.27 tff(4449,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4448, 4446])).
% 12.29/8.27 tff(4450,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s7) | (~until6(s7)) | xuntil7(s7))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4451,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s7) | always5(s7) | (~until6(s7))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4450, 4449])).
% 12.29/8.27 tff(4452,plain,
% 12.29/8.27 (xuntil7(s7) | (~until6(s7))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4451, 4345, 4276])).
% 12.29/8.27 tff(4453,plain,
% 12.29/8.27 (xuntil7(s7)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4452, 4445])).
% 12.29/8.27 tff(4454,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4455,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4456,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4455, 4454])).
% 12.29/8.27 tff(4457,plain,
% 12.29/8.27 ((~xuntil7(s7)) | until6(s8)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4456, 28, 4363])).
% 12.29/8.27 tff(4458,plain,
% 12.29/8.27 (until6(s8)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4457, 4453])).
% 12.29/8.27 tff(4459,assumption,(~always5(s15)), introduced(assumption)).
% 12.29/8.27 tff(4460,plain,
% 12.29/8.27 (~always5(s14)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4219, 4459])).
% 12.29/8.27 tff(4461,assumption,(~xuntil7(s15)), introduced(assumption)).
% 12.29/8.27 tff(4462,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4463,plain,
% 12.29/8.27 ((always5(s15) | (~until6(s15)) | xuntil7(s15)) <=> (xuntil7(s15) | always5(s15) | (~until6(s15)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4464,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4463])).
% 12.29/8.27 tff(4465,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4464, 4462])).
% 12.29/8.27 tff(4466,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s15) | (~until6(s15)) | xuntil7(s15))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4467,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s15) | always5(s15) | (~until6(s15))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4466, 4465])).
% 12.29/8.27 tff(4468,plain,
% 12.29/8.27 (always5(s15) | (~until6(s15))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4467, 4345, 4461])).
% 12.29/8.27 tff(4469,plain,
% 12.29/8.27 (~until6(s15)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4468, 4459])).
% 12.29/8.27 tff(4470,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4471,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4472,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4471, 4470])).
% 12.29/8.27 tff(4473,plain,
% 12.29/8.27 ((~xuntil7(s14)) | until6(s15)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4472, 464, 4363])).
% 12.29/8.27 tff(4474,plain,
% 12.29/8.27 (~xuntil7(s14)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4473, 4469])).
% 12.29/8.27 tff(4475,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4476,plain,
% 12.29/8.27 ((always5(s14) | (~until6(s14)) | xuntil7(s14)) <=> (xuntil7(s14) | always5(s14) | (~until6(s14)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4477,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4476])).
% 12.29/8.27 tff(4478,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4477, 4475])).
% 12.29/8.27 tff(4479,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s14) | (~until6(s14)) | xuntil7(s14))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4480,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s14) | always5(s14) | (~until6(s14))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4479, 4478])).
% 12.29/8.27 tff(4481,plain,
% 12.29/8.27 (~until6(s14)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4480, 4345, 4474, 4460])).
% 12.29/8.27 tff(4482,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4483,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4484,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4483, 4482])).
% 12.29/8.27 tff(4485,plain,
% 12.29/8.27 ((~xuntil7(s13)) | until6(s14)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4484, 435, 4363])).
% 12.29/8.27 tff(4486,plain,
% 12.29/8.27 (~xuntil7(s13)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4485, 4481])).
% 12.29/8.27 tff(4487,plain,
% 12.29/8.27 (~always5(s13)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4227, 4460])).
% 12.29/8.27 tff(4488,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4489,plain,
% 12.29/8.27 ((always5(s13) | (~until6(s13)) | xuntil7(s13)) <=> (xuntil7(s13) | always5(s13) | (~until6(s13)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4490,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4489])).
% 12.29/8.27 tff(4491,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4490, 4488])).
% 12.29/8.27 tff(4492,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s13) | (~until6(s13)) | xuntil7(s13))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4493,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s13) | always5(s13) | (~until6(s13))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4492, 4491])).
% 12.29/8.27 tff(4494,plain,
% 12.29/8.27 (xuntil7(s13) | (~until6(s13))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4493, 4345, 4487])).
% 12.29/8.27 tff(4495,plain,
% 12.29/8.27 (~until6(s13)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4494, 4486])).
% 12.29/8.27 tff(4496,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4497,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4498,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4497, 4496])).
% 12.29/8.27 tff(4499,plain,
% 12.29/8.27 ((~xuntil7(s12)) | until6(s13)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4498, 10, 4363])).
% 12.29/8.27 tff(4500,plain,
% 12.29/8.27 (~xuntil7(s12)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4499, 4495])).
% 12.29/8.27 tff(4501,plain,
% 12.29/8.27 (~always5(s12)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4235, 4487])).
% 12.29/8.27 tff(4502,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4503,plain,
% 12.29/8.27 ((always5(s12) | (~until6(s12)) | xuntil7(s12)) <=> (xuntil7(s12) | always5(s12) | (~until6(s12)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4504,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4503])).
% 12.29/8.27 tff(4505,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4504, 4502])).
% 12.29/8.27 tff(4506,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s12) | (~until6(s12)) | xuntil7(s12))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4507,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s12) | always5(s12) | (~until6(s12))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4506, 4505])).
% 12.29/8.27 tff(4508,plain,
% 12.29/8.27 (xuntil7(s12) | (~until6(s12))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4507, 4345, 4501])).
% 12.29/8.27 tff(4509,plain,
% 12.29/8.27 (~until6(s12)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4508, 4500])).
% 12.29/8.27 tff(4510,plain,
% 12.29/8.27 (~always5(s11)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4243, 4501])).
% 12.29/8.27 tff(4511,plain,
% 12.29/8.27 (~always5(s10)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4251, 4510])).
% 12.29/8.27 tff(4512,plain,
% 12.29/8.27 (~always5(s9)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4259, 4511])).
% 12.29/8.27 tff(4513,plain,
% 12.29/8.27 (~always5(s8)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4267, 4512])).
% 12.29/8.27 tff(4514,assumption,(until6(s8)), introduced(assumption)).
% 12.29/8.27 tff(4515,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4516,plain,
% 12.29/8.27 ((always5(s8) | (~until6(s8)) | xuntil7(s8)) <=> (xuntil7(s8) | always5(s8) | (~until6(s8)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4517,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4516])).
% 12.29/8.27 tff(4518,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4517, 4515])).
% 12.29/8.27 tff(4519,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s8) | (~until6(s8)) | xuntil7(s8))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4520,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s8) | always5(s8) | (~until6(s8))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4519, 4518])).
% 12.29/8.27 tff(4521,plain,
% 12.29/8.27 (xuntil7(s8) | always5(s8)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4520, 4345, 4514])).
% 12.29/8.27 tff(4522,plain,
% 12.29/8.27 (xuntil7(s8)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4521, 4513])).
% 12.29/8.27 tff(4523,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4524,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4525,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4524, 4523])).
% 12.29/8.27 tff(4526,plain,
% 12.29/8.27 ((~xuntil7(s8)) | until6(s9)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4525, 311, 4363])).
% 12.29/8.27 tff(4527,plain,
% 12.29/8.27 (until6(s9)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4526, 4522])).
% 12.29/8.27 tff(4528,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4529,plain,
% 12.29/8.27 ((always5(s9) | (~until6(s9)) | xuntil7(s9)) <=> (xuntil7(s9) | always5(s9) | (~until6(s9)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4530,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4529])).
% 12.29/8.27 tff(4531,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4530, 4528])).
% 12.29/8.27 tff(4532,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s9) | (~until6(s9)) | xuntil7(s9))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4533,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s9) | always5(s9) | (~until6(s9))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4532, 4531])).
% 12.29/8.27 tff(4534,plain,
% 12.29/8.27 (xuntil7(s9)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4533, 4345, 4527, 4512])).
% 12.29/8.27 tff(4535,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4536,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s9, s10)) | (~xuntil7(s9)) | until6(s10))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4537,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s9, s10)) | (~xuntil7(s9)) | until6(s10)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4536, 4535])).
% 12.29/8.27 tff(4538,plain,
% 12.29/8.27 ((~xuntil7(s9)) | until6(s10)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4537, 337, 4363])).
% 12.29/8.27 tff(4539,plain,
% 12.29/8.27 (until6(s10)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4538, 4534])).
% 12.29/8.27 tff(4540,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4541,plain,
% 12.29/8.27 ((always5(s10) | (~until6(s10)) | xuntil7(s10)) <=> (xuntil7(s10) | always5(s10) | (~until6(s10)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4542,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4541])).
% 12.29/8.27 tff(4543,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4542, 4540])).
% 12.29/8.27 tff(4544,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s10) | (~until6(s10)) | xuntil7(s10))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4545,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s10) | always5(s10) | (~until6(s10))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4544, 4543])).
% 12.29/8.27 tff(4546,plain,
% 12.29/8.27 (xuntil7(s10) | (~until6(s10))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4545, 4345, 4511])).
% 12.29/8.27 tff(4547,plain,
% 12.29/8.27 (xuntil7(s10)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4546, 4539])).
% 12.29/8.27 tff(4548,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4549,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s10, s11)) | (~xuntil7(s10)) | until6(s11))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4550,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s10, s11)) | (~xuntil7(s10)) | until6(s11)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4549, 4548])).
% 12.29/8.27 tff(4551,plain,
% 12.29/8.27 ((~xuntil7(s10)) | until6(s11)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4550, 366, 4363])).
% 12.29/8.27 tff(4552,plain,
% 12.29/8.27 (until6(s11)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4551, 4547])).
% 12.29/8.27 tff(4553,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4554,plain,
% 12.29/8.27 ((always5(s11) | (~until6(s11)) | xuntil7(s11)) <=> (xuntil7(s11) | always5(s11) | (~until6(s11)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4555,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4554])).
% 12.29/8.27 tff(4556,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4555, 4553])).
% 12.29/8.27 tff(4557,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s11) | (~until6(s11)) | xuntil7(s11))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4558,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s11) | always5(s11) | (~until6(s11))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4557, 4556])).
% 12.29/8.27 tff(4559,plain,
% 12.29/8.27 (xuntil7(s11) | (~until6(s11))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4558, 4345, 4510])).
% 12.29/8.27 tff(4560,plain,
% 12.29/8.27 (xuntil7(s11)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4559, 4552])).
% 12.29/8.27 tff(4561,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4562,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s11, s12)) | (~xuntil7(s11)) | until6(s12))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4563,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s11, s12)) | (~xuntil7(s11)) | until6(s12)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4562, 4561])).
% 12.29/8.27 tff(4564,plain,
% 12.29/8.27 ((~xuntil7(s11)) | until6(s12)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4563, 392, 4363])).
% 12.29/8.27 tff(4565,plain,
% 12.29/8.27 ($false),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4564, 4560, 4509])).
% 12.29/8.27 tff(4566,plain,(always5(s15) | (~until6(s8)) | xuntil7(s15)), inference(lemma,lemma(discharge,[]))).
% 12.29/8.27 tff(4567,plain,
% 12.29/8.27 (xuntil7(s15)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4566, 4458, 4212])).
% 12.29/8.27 tff(4568,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4569,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4570,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4569, 4568])).
% 12.29/8.27 tff(4571,plain,
% 12.29/8.27 ((~xuntil7(s15)) | until6(s16)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4570, 490, 4363])).
% 12.29/8.27 tff(4572,plain,
% 12.29/8.27 (until6(s16)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4571, 4567])).
% 12.29/8.27 tff(4573,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4574,plain,
% 12.29/8.27 ((always5(s16) | (~until6(s16)) | xuntil7(s16)) <=> (xuntil7(s16) | always5(s16) | (~until6(s16)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4575,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4574])).
% 12.29/8.27 tff(4576,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4575, 4573])).
% 12.29/8.27 tff(4577,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s16) | (~until6(s16)) | xuntil7(s16))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4578,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s16) | always5(s16) | (~until6(s16))),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4577, 4576])).
% 12.29/8.27 tff(4579,plain,
% 12.29/8.27 (xuntil7(s16) | (~until6(s16))),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4578, 4345, 4204])).
% 12.29/8.27 tff(4580,plain,
% 12.29/8.27 (xuntil7(s16)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4579, 4572])).
% 12.29/8.27 tff(4581,plain,
% 12.29/8.27 (((~![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))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4582,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17))),
% 12.29/8.27 inference(quant_inst,[status(thm)],[])).
% 12.29/8.27 tff(4583,plain,
% 12.29/8.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17)),
% 12.29/8.27 inference(modus_ponens,[status(thm)],[4582, 4581])).
% 12.29/8.27 tff(4584,plain,
% 12.29/8.27 ((~xuntil7(s16)) | until6(s17)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4583, 519, 4363])).
% 12.29/8.27 tff(4585,plain,
% 12.29/8.27 (until6(s17)),
% 12.29/8.27 inference(unit_resolution,[status(thm)],[4584, 4580])).
% 12.29/8.27 tff(4586,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4587,plain,
% 12.29/8.27 ((always5(s17) | (~until6(s17)) | xuntil7(s17)) <=> (xuntil7(s17) | always5(s17) | (~until6(s17)))),
% 12.29/8.27 inference(rewrite,[status(thm)],[])).
% 12.29/8.27 tff(4588,plain,
% 12.29/8.27 (((~![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))))),
% 12.29/8.27 inference(monotonicity,[status(thm)],[4587])).
% 12.29/8.27 tff(4589,plain,
% 12.29/8.27 (((~![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)))),
% 12.29/8.27 inference(transitivity,[status(thm)],[4588, 4586])).
% 12.29/8.27 tff(4590,plain,
% 12.29/8.27 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s17) | (~until6(s17)) | xuntil7(s17))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4591,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s17) | always5(s17) | (~until6(s17))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4590, 4589])).
% 12.29/8.28 tff(4592,plain,
% 12.29/8.28 (xuntil7(s17) | (~until6(s17))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4591, 4345, 4196])).
% 12.29/8.28 tff(4593,plain,
% 12.29/8.28 (xuntil7(s17)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4592, 4585])).
% 12.29/8.28 tff(4594,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4595,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4596,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4595, 4594])).
% 12.29/8.28 tff(4597,plain,
% 12.29/8.28 ((~xuntil7(s17)) | until6(s18)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4596, 547, 4363])).
% 12.29/8.28 tff(4598,plain,
% 12.29/8.28 (until6(s18)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4597, 4593])).
% 12.29/8.28 tff(4599,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4600,plain,
% 12.29/8.28 ((always5(s18) | (~until6(s18)) | xuntil7(s18)) <=> (xuntil7(s18) | always5(s18) | (~until6(s18)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4601,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4600])).
% 12.29/8.28 tff(4602,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4601, 4599])).
% 12.29/8.28 tff(4603,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s18) | (~until6(s18)) | xuntil7(s18))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4604,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s18) | always5(s18) | (~until6(s18))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4603, 4602])).
% 12.29/8.28 tff(4605,plain,
% 12.29/8.28 (xuntil7(s18) | (~until6(s18))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4604, 4345, 4188])).
% 12.29/8.28 tff(4606,plain,
% 12.29/8.28 (xuntil7(s18)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4605, 4598])).
% 12.29/8.28 tff(4607,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4608,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4609,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4608, 4607])).
% 12.29/8.28 tff(4610,plain,
% 12.29/8.28 ((~xuntil7(s18)) | until6(s19)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4609, 578, 4363])).
% 12.29/8.28 tff(4611,plain,
% 12.29/8.28 (until6(s19)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4610, 4606])).
% 12.29/8.28 tff(4612,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4613,plain,
% 12.29/8.28 ((always5(s19) | (~until6(s19)) | xuntil7(s19)) <=> (xuntil7(s19) | always5(s19) | (~until6(s19)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4614,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4613])).
% 12.29/8.28 tff(4615,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4614, 4612])).
% 12.29/8.28 tff(4616,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s19) | (~until6(s19)) | xuntil7(s19))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4617,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s19) | always5(s19) | (~until6(s19))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4616, 4615])).
% 12.29/8.28 tff(4618,plain,
% 12.29/8.28 (xuntil7(s19) | (~until6(s19))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4617, 4345, 4180])).
% 12.29/8.28 tff(4619,plain,
% 12.29/8.28 (xuntil7(s19)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4618, 4611])).
% 12.29/8.28 tff(4620,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4621,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4622,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4621, 4620])).
% 12.29/8.28 tff(4623,plain,
% 12.29/8.28 ((~xuntil7(s19)) | until6(s20)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4622, 606, 4363])).
% 12.29/8.28 tff(4624,plain,
% 12.29/8.28 (until6(s20)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4623, 4619])).
% 12.29/8.28 tff(4625,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4626,plain,
% 12.29/8.28 ((always5(s20) | (~until6(s20)) | xuntil7(s20)) <=> (xuntil7(s20) | always5(s20) | (~until6(s20)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4627,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4626])).
% 12.29/8.28 tff(4628,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4627, 4625])).
% 12.29/8.28 tff(4629,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s20) | (~until6(s20)) | xuntil7(s20))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4630,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s20) | always5(s20) | (~until6(s20))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4629, 4628])).
% 12.29/8.28 tff(4631,plain,
% 12.29/8.28 (xuntil7(s20) | (~until6(s20))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4630, 4345, 4172])).
% 12.29/8.28 tff(4632,plain,
% 12.29/8.28 (xuntil7(s20)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4631, 4624])).
% 12.29/8.28 tff(4633,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4634,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4635,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4634, 4633])).
% 12.29/8.28 tff(4636,plain,
% 12.29/8.28 ((~xuntil7(s20)) | until6(s21)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4635, 637, 4363])).
% 12.29/8.28 tff(4637,plain,
% 12.29/8.28 (until6(s21)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4636, 4632])).
% 12.29/8.28 tff(4638,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4639,plain,
% 12.29/8.28 ((always5(s21) | (~until6(s21)) | xuntil7(s21)) <=> (xuntil7(s21) | always5(s21) | (~until6(s21)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4640,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4639])).
% 12.29/8.28 tff(4641,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4640, 4638])).
% 12.29/8.28 tff(4642,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s21) | (~until6(s21)) | xuntil7(s21))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4643,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s21) | always5(s21) | (~until6(s21))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4642, 4641])).
% 12.29/8.28 tff(4644,plain,
% 12.29/8.28 (xuntil7(s21) | (~until6(s21))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4643, 4345, 4164])).
% 12.29/8.28 tff(4645,plain,
% 12.29/8.28 (xuntil7(s21)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4644, 4637])).
% 12.29/8.28 tff(4646,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4647,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4648,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4647, 4646])).
% 12.29/8.28 tff(4649,plain,
% 12.29/8.28 ((~xuntil7(s21)) | until6(s22)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4648, 665, 4363])).
% 12.29/8.28 tff(4650,plain,
% 12.29/8.28 (until6(s22)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4649, 4645])).
% 12.29/8.28 tff(4651,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4652,plain,
% 12.29/8.28 ((always5(s22) | (~until6(s22)) | xuntil7(s22)) <=> (xuntil7(s22) | always5(s22) | (~until6(s22)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4653,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4652])).
% 12.29/8.28 tff(4654,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4653, 4651])).
% 12.29/8.28 tff(4655,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s22) | (~until6(s22)) | xuntil7(s22))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4656,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s22) | always5(s22) | (~until6(s22))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4655, 4654])).
% 12.29/8.28 tff(4657,plain,
% 12.29/8.28 (xuntil7(s22) | (~until6(s22))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4656, 4345, 4156])).
% 12.29/8.28 tff(4658,plain,
% 12.29/8.28 (xuntil7(s22)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4657, 4650])).
% 12.29/8.28 tff(4659,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4660,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4661,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4660, 4659])).
% 12.29/8.28 tff(4662,plain,
% 12.29/8.28 ((~xuntil7(s22)) | until6(s23)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4661, 696, 4363])).
% 12.29/8.28 tff(4663,plain,
% 12.29/8.28 (until6(s23)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4662, 4658])).
% 12.29/8.28 tff(4664,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4665,plain,
% 12.29/8.28 ((always5(s23) | (~until6(s23)) | xuntil7(s23)) <=> (xuntil7(s23) | always5(s23) | (~until6(s23)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4666,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4665])).
% 12.29/8.28 tff(4667,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4666, 4664])).
% 12.29/8.28 tff(4668,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s23) | (~until6(s23)) | xuntil7(s23))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4669,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s23) | always5(s23) | (~until6(s23))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4668, 4667])).
% 12.29/8.28 tff(4670,plain,
% 12.29/8.28 (xuntil7(s23) | (~until6(s23))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4669, 4345, 4148])).
% 12.29/8.28 tff(4671,plain,
% 12.29/8.28 (xuntil7(s23)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4670, 4663])).
% 12.29/8.28 tff(4672,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4673,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4674,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4673, 4672])).
% 12.29/8.28 tff(4675,plain,
% 12.29/8.28 ((~xuntil7(s23)) | until6(s24)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4674, 724, 4363])).
% 12.29/8.28 tff(4676,plain,
% 12.29/8.28 (until6(s24)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4675, 4671])).
% 12.29/8.28 tff(4677,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4678,plain,
% 12.29/8.28 ((always5(s24) | (~until6(s24)) | xuntil7(s24)) <=> (xuntil7(s24) | always5(s24) | (~until6(s24)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4679,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4678])).
% 12.29/8.28 tff(4680,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4679, 4677])).
% 12.29/8.28 tff(4681,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s24) | (~until6(s24)) | xuntil7(s24))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4682,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s24) | always5(s24) | (~until6(s24))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4681, 4680])).
% 12.29/8.28 tff(4683,plain,
% 12.29/8.28 (xuntil7(s24) | (~until6(s24))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4682, 4345, 4140])).
% 12.29/8.28 tff(4684,plain,
% 12.29/8.28 (xuntil7(s24)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4683, 4676])).
% 12.29/8.28 tff(4685,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4686,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4687,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4686, 4685])).
% 12.29/8.28 tff(4688,plain,
% 12.29/8.28 ((~xuntil7(s24)) | until6(s25)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4687, 755, 4363])).
% 12.29/8.28 tff(4689,plain,
% 12.29/8.28 (until6(s25)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4688, 4684])).
% 12.29/8.28 tff(4690,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4691,plain,
% 12.29/8.28 ((always5(s25) | (~until6(s25)) | xuntil7(s25)) <=> (xuntil7(s25) | always5(s25) | (~until6(s25)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4692,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4691])).
% 12.29/8.28 tff(4693,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4692, 4690])).
% 12.29/8.28 tff(4694,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s25) | (~until6(s25)) | xuntil7(s25))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4695,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s25) | always5(s25) | (~until6(s25))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4694, 4693])).
% 12.29/8.28 tff(4696,plain,
% 12.29/8.28 (xuntil7(s25) | (~until6(s25))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4695, 4345, 4132])).
% 12.29/8.28 tff(4697,plain,
% 12.29/8.28 (xuntil7(s25)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4696, 4689])).
% 12.29/8.28 tff(4698,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4699,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s25, s26)) | (~xuntil7(s25)) | until6(s26))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4700,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s25, s26)) | (~xuntil7(s25)) | until6(s26)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4699, 4698])).
% 12.29/8.28 tff(4701,plain,
% 12.29/8.28 ((~xuntil7(s25)) | until6(s26)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4700, 783, 4363])).
% 12.29/8.28 tff(4702,plain,
% 12.29/8.28 (until6(s26)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4701, 4697])).
% 12.29/8.28 tff(4703,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4704,plain,
% 12.29/8.28 ((always5(s26) | (~until6(s26)) | xuntil7(s26)) <=> (xuntil7(s26) | always5(s26) | (~until6(s26)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4705,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4704])).
% 12.29/8.28 tff(4706,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4705, 4703])).
% 12.29/8.28 tff(4707,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s26) | (~until6(s26)) | xuntil7(s26))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4708,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s26) | always5(s26) | (~until6(s26))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4707, 4706])).
% 12.29/8.28 tff(4709,plain,
% 12.29/8.28 (xuntil7(s26) | (~until6(s26))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4708, 4345, 4124])).
% 12.29/8.28 tff(4710,plain,
% 12.29/8.28 (xuntil7(s26)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4709, 4702])).
% 12.29/8.28 tff(4711,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4712,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s26, s27)) | (~xuntil7(s26)) | until6(s27))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4713,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s26, s27)) | (~xuntil7(s26)) | until6(s27)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4712, 4711])).
% 12.29/8.28 tff(4714,plain,
% 12.29/8.28 ((~xuntil7(s26)) | until6(s27)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4713, 814, 4363])).
% 12.29/8.28 tff(4715,plain,
% 12.29/8.28 (until6(s27)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4714, 4710])).
% 12.29/8.28 tff(4716,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4717,plain,
% 12.29/8.28 ((always5(s27) | (~until6(s27)) | xuntil7(s27)) <=> (xuntil7(s27) | always5(s27) | (~until6(s27)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4718,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4717])).
% 12.29/8.28 tff(4719,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4718, 4716])).
% 12.29/8.28 tff(4720,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s27) | (~until6(s27)) | xuntil7(s27))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4721,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s27) | always5(s27) | (~until6(s27))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4720, 4719])).
% 12.29/8.28 tff(4722,plain,
% 12.29/8.28 (xuntil7(s27) | (~until6(s27))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4721, 4345, 4116])).
% 12.29/8.28 tff(4723,plain,
% 12.29/8.28 (xuntil7(s27)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4722, 4715])).
% 12.29/8.28 tff(4724,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4725,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4726,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4725, 4724])).
% 12.29/8.28 tff(4727,plain,
% 12.29/8.28 ((~xuntil7(s27)) | until6(s28)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4726, 842, 4363])).
% 12.29/8.28 tff(4728,plain,
% 12.29/8.28 (until6(s28)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4727, 4723])).
% 12.29/8.28 tff(4729,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4730,plain,
% 12.29/8.28 ((always5(s28) | (~until6(s28)) | xuntil7(s28)) <=> (xuntil7(s28) | always5(s28) | (~until6(s28)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4731,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4730])).
% 12.29/8.28 tff(4732,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4731, 4729])).
% 12.29/8.28 tff(4733,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s28) | (~until6(s28)) | xuntil7(s28))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4734,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s28) | always5(s28) | (~until6(s28))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4733, 4732])).
% 12.29/8.28 tff(4735,plain,
% 12.29/8.28 (xuntil7(s28) | (~until6(s28))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4734, 4345, 4108])).
% 12.29/8.28 tff(4736,plain,
% 12.29/8.28 (xuntil7(s28)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4735, 4728])).
% 12.29/8.28 tff(4737,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4738,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4739,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4738, 4737])).
% 12.29/8.28 tff(4740,plain,
% 12.29/8.28 ((~xuntil7(s28)) | until6(s29)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4739, 873, 4363])).
% 12.29/8.28 tff(4741,plain,
% 12.29/8.28 (until6(s29)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4740, 4736])).
% 12.29/8.28 tff(4742,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4743,plain,
% 12.29/8.28 ((always5(s29) | (~until6(s29)) | xuntil7(s29)) <=> (xuntil7(s29) | always5(s29) | (~until6(s29)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4744,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4743])).
% 12.29/8.28 tff(4745,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4744, 4742])).
% 12.29/8.28 tff(4746,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s29) | (~until6(s29)) | xuntil7(s29))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4747,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s29) | always5(s29) | (~until6(s29))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4746, 4745])).
% 12.29/8.28 tff(4748,plain,
% 12.29/8.28 (xuntil7(s29) | (~until6(s29))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4747, 4345, 4100])).
% 12.29/8.28 tff(4749,plain,
% 12.29/8.28 (xuntil7(s29)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4748, 4741])).
% 12.29/8.28 tff(4750,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4751,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4752,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4751, 4750])).
% 12.29/8.28 tff(4753,plain,
% 12.29/8.28 ((~xuntil7(s29)) | until6(s30)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4752, 901, 4363])).
% 12.29/8.28 tff(4754,plain,
% 12.29/8.28 (until6(s30)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4753, 4749])).
% 12.29/8.28 tff(4755,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4756,plain,
% 12.29/8.28 ((always5(s30) | (~until6(s30)) | xuntil7(s30)) <=> (xuntil7(s30) | always5(s30) | (~until6(s30)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4757,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4756])).
% 12.29/8.28 tff(4758,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4757, 4755])).
% 12.29/8.28 tff(4759,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s30) | (~until6(s30)) | xuntil7(s30))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4760,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s30) | always5(s30) | (~until6(s30))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 12.29/8.28 tff(4761,plain,
% 12.29/8.28 (xuntil7(s30) | (~until6(s30))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4760, 4345, 4092])).
% 12.29/8.28 tff(4762,plain,
% 12.29/8.28 (xuntil7(s30)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4761, 4754])).
% 12.29/8.28 tff(4763,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4764,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4765,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4764, 4763])).
% 12.29/8.28 tff(4766,plain,
% 12.29/8.28 ((~xuntil7(s30)) | until6(s31)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4765, 932, 4363])).
% 12.29/8.28 tff(4767,plain,
% 12.29/8.28 (until6(s31)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4766, 4762])).
% 12.29/8.28 tff(4768,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4769,plain,
% 12.29/8.28 ((always5(s31) | (~until6(s31)) | xuntil7(s31)) <=> (xuntil7(s31) | always5(s31) | (~until6(s31)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4770,plain,
% 12.29/8.28 (((~![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))))),
% 12.29/8.28 inference(monotonicity,[status(thm)],[4769])).
% 12.29/8.28 tff(4771,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(transitivity,[status(thm)],[4770, 4768])).
% 12.29/8.28 tff(4772,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s31) | (~until6(s31)) | xuntil7(s31))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4773,plain,
% 12.29/8.28 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s31) | always5(s31) | (~until6(s31))),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4772, 4771])).
% 12.29/8.28 tff(4774,plain,
% 12.29/8.28 (xuntil7(s31) | (~until6(s31))),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4773, 4345, 4084])).
% 12.29/8.28 tff(4775,plain,
% 12.29/8.28 (xuntil7(s31)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4774, 4767])).
% 12.29/8.28 tff(4776,plain,
% 12.29/8.28 (((~![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))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4777,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32))),
% 12.29/8.28 inference(quant_inst,[status(thm)],[])).
% 12.29/8.28 tff(4778,plain,
% 12.29/8.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32)),
% 12.29/8.28 inference(modus_ponens,[status(thm)],[4777, 4776])).
% 12.29/8.28 tff(4779,plain,
% 12.29/8.28 ((~xuntil7(s31)) | until6(s32)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4778, 960, 4363])).
% 12.29/8.28 tff(4780,plain,
% 12.29/8.28 (until6(s32)),
% 12.29/8.28 inference(unit_resolution,[status(thm)],[4779, 4775])).
% 12.29/8.28 tff(4781,plain,
% 12.29/8.28 (((~![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)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.28 tff(4782,plain,
% 12.29/8.28 ((always5(s32) | (~until6(s32)) | xuntil7(s32)) <=> (xuntil7(s32) | always5(s32) | (~until6(s32)))),
% 12.29/8.28 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4783,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4782])).
% 12.29/8.29 tff(4784,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4783, 4781])).
% 12.29/8.29 tff(4785,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s32) | (~until6(s32)) | xuntil7(s32))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4786,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s32) | always5(s32) | (~until6(s32))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4785, 4784])).
% 12.29/8.29 tff(4787,plain,
% 12.29/8.29 (xuntil7(s32) | (~until6(s32))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4786, 4345, 4076])).
% 12.29/8.29 tff(4788,plain,
% 12.29/8.29 (xuntil7(s32)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4787, 4780])).
% 12.29/8.29 tff(4789,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4790,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4791,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4790, 4789])).
% 12.29/8.29 tff(4792,plain,
% 12.29/8.29 ((~xuntil7(s32)) | until6(s33)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4791, 991, 4363])).
% 12.29/8.29 tff(4793,plain,
% 12.29/8.29 (until6(s33)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4792, 4788])).
% 12.29/8.29 tff(4794,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4795,plain,
% 12.29/8.29 ((always5(s33) | (~until6(s33)) | xuntil7(s33)) <=> (xuntil7(s33) | always5(s33) | (~until6(s33)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4796,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4795])).
% 12.29/8.29 tff(4797,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4796, 4794])).
% 12.29/8.29 tff(4798,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s33) | (~until6(s33)) | xuntil7(s33))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4799,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s33) | always5(s33) | (~until6(s33))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4798, 4797])).
% 12.29/8.29 tff(4800,plain,
% 12.29/8.29 (xuntil7(s33) | (~until6(s33))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4799, 4345, 4068])).
% 12.29/8.29 tff(4801,plain,
% 12.29/8.29 (xuntil7(s33)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4800, 4793])).
% 12.29/8.29 tff(4802,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4803,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4804,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4803, 4802])).
% 12.29/8.29 tff(4805,plain,
% 12.29/8.29 ((~xuntil7(s33)) | until6(s34)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4804, 1019, 4363])).
% 12.29/8.29 tff(4806,plain,
% 12.29/8.29 (until6(s34)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4805, 4801])).
% 12.29/8.29 tff(4807,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4808,plain,
% 12.29/8.29 ((always5(s34) | (~until6(s34)) | xuntil7(s34)) <=> (xuntil7(s34) | always5(s34) | (~until6(s34)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4809,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4808])).
% 12.29/8.29 tff(4810,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4809, 4807])).
% 12.29/8.29 tff(4811,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s34) | (~until6(s34)) | xuntil7(s34))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4812,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s34) | always5(s34) | (~until6(s34))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4811, 4810])).
% 12.29/8.29 tff(4813,plain,
% 12.29/8.29 (xuntil7(s34) | (~until6(s34))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4812, 4345, 4060])).
% 12.29/8.29 tff(4814,plain,
% 12.29/8.29 (xuntil7(s34)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4813, 4806])).
% 12.29/8.29 tff(4815,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4816,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4817,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4816, 4815])).
% 12.29/8.29 tff(4818,plain,
% 12.29/8.29 ((~xuntil7(s34)) | until6(s35)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4817, 1050, 4363])).
% 12.29/8.29 tff(4819,plain,
% 12.29/8.29 (until6(s35)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4818, 4814])).
% 12.29/8.29 tff(4820,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4821,plain,
% 12.29/8.29 ((always5(s35) | (~until6(s35)) | xuntil7(s35)) <=> (xuntil7(s35) | always5(s35) | (~until6(s35)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4822,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4821])).
% 12.29/8.29 tff(4823,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4822, 4820])).
% 12.29/8.29 tff(4824,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s35) | (~until6(s35)) | xuntil7(s35))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4825,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s35) | always5(s35) | (~until6(s35))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4824, 4823])).
% 12.29/8.29 tff(4826,plain,
% 12.29/8.29 (xuntil7(s35) | (~until6(s35))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4825, 4345, 4052])).
% 12.29/8.29 tff(4827,plain,
% 12.29/8.29 (xuntil7(s35)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4826, 4819])).
% 12.29/8.29 tff(4828,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4829,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4830,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4829, 4828])).
% 12.29/8.29 tff(4831,plain,
% 12.29/8.29 ((~xuntil7(s35)) | until6(s36)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4830, 1078, 4363])).
% 12.29/8.29 tff(4832,plain,
% 12.29/8.29 (until6(s36)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4831, 4827])).
% 12.29/8.29 tff(4833,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4834,plain,
% 12.29/8.29 ((always5(s36) | (~until6(s36)) | xuntil7(s36)) <=> (xuntil7(s36) | always5(s36) | (~until6(s36)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4835,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4834])).
% 12.29/8.29 tff(4836,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4835, 4833])).
% 12.29/8.29 tff(4837,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s36) | (~until6(s36)) | xuntil7(s36))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4838,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s36) | always5(s36) | (~until6(s36))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4837, 4836])).
% 12.29/8.29 tff(4839,plain,
% 12.29/8.29 (xuntil7(s36) | (~until6(s36))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4838, 4345, 4044])).
% 12.29/8.29 tff(4840,plain,
% 12.29/8.29 (xuntil7(s36)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4839, 4832])).
% 12.29/8.29 tff(4841,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4842,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s36, s37)) | (~xuntil7(s36)) | until6(s37))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4843,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s36, s37)) | (~xuntil7(s36)) | until6(s37)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4842, 4841])).
% 12.29/8.29 tff(4844,plain,
% 12.29/8.29 ((~xuntil7(s36)) | until6(s37)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4843, 1109, 4363])).
% 12.29/8.29 tff(4845,plain,
% 12.29/8.29 (until6(s37)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4844, 4840])).
% 12.29/8.29 tff(4846,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4847,plain,
% 12.29/8.29 ((always5(s37) | (~until6(s37)) | xuntil7(s37)) <=> (xuntil7(s37) | always5(s37) | (~until6(s37)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4848,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4847])).
% 12.29/8.29 tff(4849,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4848, 4846])).
% 12.29/8.29 tff(4850,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s37) | (~until6(s37)) | xuntil7(s37))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4851,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s37) | always5(s37) | (~until6(s37))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4850, 4849])).
% 12.29/8.29 tff(4852,plain,
% 12.29/8.29 (xuntil7(s37) | (~until6(s37))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4851, 4345, 4036])).
% 12.29/8.29 tff(4853,plain,
% 12.29/8.29 (xuntil7(s37)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4852, 4845])).
% 12.29/8.29 tff(4854,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4855,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4856,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4855, 4854])).
% 12.29/8.29 tff(4857,plain,
% 12.29/8.29 ((~xuntil7(s37)) | until6(s38)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4856, 1137, 4363])).
% 12.29/8.29 tff(4858,plain,
% 12.29/8.29 (until6(s38)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4857, 4853])).
% 12.29/8.29 tff(4859,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4860,plain,
% 12.29/8.29 ((always5(s38) | (~until6(s38)) | xuntil7(s38)) <=> (xuntil7(s38) | always5(s38) | (~until6(s38)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4861,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4860])).
% 12.29/8.29 tff(4862,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4861, 4859])).
% 12.29/8.29 tff(4863,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s38) | (~until6(s38)) | xuntil7(s38))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4864,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s38) | always5(s38) | (~until6(s38))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4863, 4862])).
% 12.29/8.29 tff(4865,plain,
% 12.29/8.29 (xuntil7(s38) | (~until6(s38))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4864, 4345, 4028])).
% 12.29/8.29 tff(4866,plain,
% 12.29/8.29 (xuntil7(s38)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4865, 4858])).
% 12.29/8.29 tff(4867,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4868,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4869,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4868, 4867])).
% 12.29/8.29 tff(4870,plain,
% 12.29/8.29 ((~xuntil7(s38)) | until6(s39)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4869, 1168, 4363])).
% 12.29/8.29 tff(4871,plain,
% 12.29/8.29 (until6(s39)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4870, 4866])).
% 12.29/8.29 tff(4872,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4873,plain,
% 12.29/8.29 ((always5(s39) | (~until6(s39)) | xuntil7(s39)) <=> (xuntil7(s39) | always5(s39) | (~until6(s39)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4874,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4873])).
% 12.29/8.29 tff(4875,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4874, 4872])).
% 12.29/8.29 tff(4876,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s39) | (~until6(s39)) | xuntil7(s39))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4877,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s39) | always5(s39) | (~until6(s39))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4876, 4875])).
% 12.29/8.29 tff(4878,plain,
% 12.29/8.29 (xuntil7(s39) | (~until6(s39))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4877, 4345, 4020])).
% 12.29/8.29 tff(4879,plain,
% 12.29/8.29 (xuntil7(s39)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4878, 4871])).
% 12.29/8.29 tff(4880,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4881,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4882,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4881, 4880])).
% 12.29/8.29 tff(4883,plain,
% 12.29/8.29 ((~xuntil7(s39)) | until6(s40)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4882, 1196, 4363])).
% 12.29/8.29 tff(4884,plain,
% 12.29/8.29 (until6(s40)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4883, 4879])).
% 12.29/8.29 tff(4885,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4886,plain,
% 12.29/8.29 ((always5(s40) | (~until6(s40)) | xuntil7(s40)) <=> (xuntil7(s40) | always5(s40) | (~until6(s40)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4887,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4886])).
% 12.29/8.29 tff(4888,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4887, 4885])).
% 12.29/8.29 tff(4889,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s40) | (~until6(s40)) | xuntil7(s40))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4890,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s40) | always5(s40) | (~until6(s40))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4889, 4888])).
% 12.29/8.29 tff(4891,plain,
% 12.29/8.29 (xuntil7(s40) | (~until6(s40))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4890, 4345, 4012])).
% 12.29/8.29 tff(4892,plain,
% 12.29/8.29 (xuntil7(s40)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4891, 4884])).
% 12.29/8.29 tff(4893,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4894,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4895,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4894, 4893])).
% 12.29/8.29 tff(4896,plain,
% 12.29/8.29 ((~xuntil7(s40)) | until6(s41)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4895, 2583, 4363])).
% 12.29/8.29 tff(4897,plain,
% 12.29/8.29 (until6(s41)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4896, 4892])).
% 12.29/8.29 tff(4898,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4899,plain,
% 12.29/8.29 ((always5(s41) | (~until6(s41)) | xuntil7(s41)) <=> (xuntil7(s41) | always5(s41) | (~until6(s41)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4900,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4899])).
% 12.29/8.29 tff(4901,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4900, 4898])).
% 12.29/8.29 tff(4902,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s41) | (~until6(s41)) | xuntil7(s41))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4903,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s41) | always5(s41) | (~until6(s41))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 12.29/8.29 tff(4904,plain,
% 12.29/8.29 (xuntil7(s41) | (~until6(s41))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4903, 4345, 4004])).
% 12.29/8.29 tff(4905,plain,
% 12.29/8.29 (xuntil7(s41)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4904, 4897])).
% 12.29/8.29 tff(4906,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4907,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4908,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4907, 4906])).
% 12.29/8.29 tff(4909,plain,
% 12.29/8.29 ((~xuntil7(s41)) | until6(s42)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4908, 2647, 4363])).
% 12.29/8.29 tff(4910,plain,
% 12.29/8.29 (until6(s42)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4909, 4905])).
% 12.29/8.29 tff(4911,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4912,plain,
% 12.29/8.29 ((always5(s42) | (~until6(s42)) | xuntil7(s42)) <=> (xuntil7(s42) | always5(s42) | (~until6(s42)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4913,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4912])).
% 12.29/8.29 tff(4914,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4913, 4911])).
% 12.29/8.29 tff(4915,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s42) | (~until6(s42)) | xuntil7(s42))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4916,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s42) | always5(s42) | (~until6(s42))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4915, 4914])).
% 12.29/8.29 tff(4917,plain,
% 12.29/8.29 (xuntil7(s42) | (~until6(s42))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4916, 4345, 3996])).
% 12.29/8.29 tff(4918,plain,
% 12.29/8.29 (xuntil7(s42)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4917, 4910])).
% 12.29/8.29 tff(4919,plain,
% 12.29/8.29 (((~![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))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4920,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4921,plain,
% 12.29/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43)),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4920, 4919])).
% 12.29/8.29 tff(4922,plain,
% 12.29/8.29 ((~xuntil7(s42)) | until6(s43)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4921, 2714, 4363])).
% 12.29/8.29 tff(4923,plain,
% 12.29/8.29 (until6(s43)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4922, 4918])).
% 12.29/8.29 tff(4924,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4925,plain,
% 12.29/8.29 ((always5(s43) | (~until6(s43)) | xuntil7(s43)) <=> (xuntil7(s43) | always5(s43) | (~until6(s43)))),
% 12.29/8.29 inference(rewrite,[status(thm)],[])).
% 12.29/8.29 tff(4926,plain,
% 12.29/8.29 (((~![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))))),
% 12.29/8.29 inference(monotonicity,[status(thm)],[4925])).
% 12.29/8.29 tff(4927,plain,
% 12.29/8.29 (((~![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)))),
% 12.29/8.29 inference(transitivity,[status(thm)],[4926, 4924])).
% 12.29/8.29 tff(4928,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s43) | (~until6(s43)) | xuntil7(s43))),
% 12.29/8.29 inference(quant_inst,[status(thm)],[])).
% 12.29/8.29 tff(4929,plain,
% 12.29/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s43) | always5(s43) | (~until6(s43))),
% 12.29/8.29 inference(modus_ponens,[status(thm)],[4928, 4927])).
% 12.29/8.29 tff(4930,plain,
% 12.29/8.29 (xuntil7(s43) | (~until6(s43))),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4929, 4345, 3988])).
% 12.29/8.29 tff(4931,plain,
% 12.29/8.29 (xuntil7(s43)),
% 12.29/8.29 inference(unit_resolution,[status(thm)],[4930, 4923])).
% 12.37/8.29 tff(4932,plain,
% 12.37/8.29 (((~![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))),
% 12.37/8.29 inference(rewrite,[status(thm)],[])).
% 12.37/8.29 tff(4933,plain,
% 12.37/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44))),
% 12.37/8.29 inference(quant_inst,[status(thm)],[])).
% 12.37/8.29 tff(4934,plain,
% 12.37/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44)),
% 12.37/8.29 inference(modus_ponens,[status(thm)],[4933, 4932])).
% 12.37/8.29 tff(4935,plain,
% 12.37/8.29 ((~xuntil7(s43)) | until6(s44)),
% 12.37/8.29 inference(unit_resolution,[status(thm)],[4934, 2775, 4363])).
% 12.37/8.29 tff(4936,plain,
% 12.37/8.29 (until6(s44)),
% 12.37/8.29 inference(unit_resolution,[status(thm)],[4935, 4931])).
% 12.37/8.29 tff(4937,plain,
% 12.37/8.29 (((~![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)))),
% 12.37/8.29 inference(rewrite,[status(thm)],[])).
% 12.37/8.29 tff(4938,plain,
% 12.37/8.29 ((always5(s44) | (~until6(s44)) | xuntil7(s44)) <=> (xuntil7(s44) | always5(s44) | (~until6(s44)))),
% 12.37/8.29 inference(rewrite,[status(thm)],[])).
% 12.37/8.29 tff(4939,plain,
% 12.37/8.29 (((~![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))))),
% 12.37/8.29 inference(monotonicity,[status(thm)],[4938])).
% 12.37/8.29 tff(4940,plain,
% 12.37/8.29 (((~![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)))),
% 12.37/8.29 inference(transitivity,[status(thm)],[4939, 4937])).
% 12.37/8.29 tff(4941,plain,
% 12.37/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s44) | (~until6(s44)) | xuntil7(s44))),
% 12.37/8.29 inference(quant_inst,[status(thm)],[])).
% 12.37/8.29 tff(4942,plain,
% 12.37/8.29 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s44) | always5(s44) | (~until6(s44))),
% 12.37/8.29 inference(modus_ponens,[status(thm)],[4941, 4940])).
% 12.37/8.29 tff(4943,plain,
% 12.37/8.29 (xuntil7(s44) | (~until6(s44))),
% 12.37/8.29 inference(unit_resolution,[status(thm)],[4942, 4345, 3980])).
% 12.37/8.29 tff(4944,plain,
% 12.37/8.29 (xuntil7(s44)),
% 12.37/8.29 inference(unit_resolution,[status(thm)],[4943, 4936])).
% 12.37/8.29 tff(4945,plain,
% 12.37/8.29 (((~![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))),
% 12.37/8.29 inference(rewrite,[status(thm)],[])).
% 12.37/8.29 tff(4946,plain,
% 12.37/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45))),
% 12.37/8.29 inference(quant_inst,[status(thm)],[])).
% 12.37/8.29 tff(4947,plain,
% 12.37/8.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45)),
% 12.37/8.29 inference(modus_ponens,[status(thm)],[4946, 4945])).
% 12.37/8.29 tff(4948,plain,
% 12.37/8.29 ((~xuntil7(s44)) | until6(s45)),
% 12.37/8.29 inference(unit_resolution,[status(thm)],[4947, 2841, 4363])).
% 12.37/8.29 tff(4949,plain,
% 12.37/8.29 (until6(s45)),
% 12.37/8.29 inference(unit_resolution,[status(thm)],[4948, 4944])).
% 12.37/8.29 tff(4950,plain,
% 12.37/8.29 (((~![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)))),
% 12.37/8.29 inference(rewrite,[status(thm)],[])).
% 12.37/8.29 tff(4951,plain,
% 12.37/8.29 ((always5(s45) | (~until6(s45)) | xuntil7(s45)) <=> (xuntil7(s45) | always5(s45) | (~until6(s45)))),
% 12.37/8.29 inference(rewrite,[status(thm)],[])).
% 12.37/8.29 tff(4952,plain,
% 12.37/8.29 (((~![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))))),
% 12.37/8.29 inference(monotonicity,[status(thm)],[4951])).
% 12.37/8.30 tff(4953,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[4952, 4950])).
% 12.37/8.30 tff(4954,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s45) | (~until6(s45)) | xuntil7(s45))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(4955,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s45) | always5(s45) | (~until6(s45))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[4954, 4953])).
% 12.37/8.30 tff(4956,plain,
% 12.37/8.30 (xuntil7(s45) | (~until6(s45))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4955, 4345, 3972])).
% 12.37/8.30 tff(4957,plain,
% 12.37/8.30 (xuntil7(s45)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4956, 4949])).
% 12.37/8.30 tff(4958,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4959,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(4960,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[4959, 4958])).
% 12.37/8.30 tff(4961,plain,
% 12.37/8.30 ((~xuntil7(s45)) | until6(s46)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4960, 2905, 4363])).
% 12.37/8.30 tff(4962,plain,
% 12.37/8.30 (until6(s46)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4961, 4957])).
% 12.37/8.30 tff(4963,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4964,plain,
% 12.37/8.30 ((always5(s46) | (~until6(s46)) | xuntil7(s46)) <=> (xuntil7(s46) | always5(s46) | (~until6(s46)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4965,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[4964])).
% 12.37/8.30 tff(4966,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[4965, 4963])).
% 12.37/8.30 tff(4967,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s46) | (~until6(s46)) | xuntil7(s46))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(4968,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s46) | always5(s46) | (~until6(s46))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[4967, 4966])).
% 12.37/8.30 tff(4969,plain,
% 12.37/8.30 (xuntil7(s46) | (~until6(s46))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4968, 4345, 3964])).
% 12.37/8.30 tff(4970,plain,
% 12.37/8.30 (xuntil7(s46)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4969, 4962])).
% 12.37/8.30 tff(4971,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4972,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(4973,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[4972, 4971])).
% 12.37/8.30 tff(4974,plain,
% 12.37/8.30 ((~xuntil7(s46)) | until6(s47)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4973, 2972, 4363])).
% 12.37/8.30 tff(4975,plain,
% 12.37/8.30 (until6(s47)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4974, 4970])).
% 12.37/8.30 tff(4976,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4977,plain,
% 12.37/8.30 ((always5(s47) | (~until6(s47)) | xuntil7(s47)) <=> (xuntil7(s47) | always5(s47) | (~until6(s47)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4978,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[4977])).
% 12.37/8.30 tff(4979,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[4978, 4976])).
% 12.37/8.30 tff(4980,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s47) | (~until6(s47)) | xuntil7(s47))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(4981,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s47) | always5(s47) | (~until6(s47))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[4980, 4979])).
% 12.37/8.30 tff(4982,plain,
% 12.37/8.30 (xuntil7(s47) | (~until6(s47))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4981, 4345, 3956])).
% 12.37/8.30 tff(4983,plain,
% 12.37/8.30 (xuntil7(s47)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4982, 4975])).
% 12.37/8.30 tff(4984,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4985,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s47, s48)) | (~xuntil7(s47)) | until6(s48))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(4986,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s47, s48)) | (~xuntil7(s47)) | until6(s48)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[4985, 4984])).
% 12.37/8.30 tff(4987,plain,
% 12.37/8.30 ((~xuntil7(s47)) | until6(s48)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4986, 3070, 4363])).
% 12.37/8.30 tff(4988,plain,
% 12.37/8.30 (until6(s48)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4987, 4983])).
% 12.37/8.30 tff(4989,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4990,plain,
% 12.37/8.30 ((always5(s48) | (~until6(s48)) | xuntil7(s48)) <=> (xuntil7(s48) | always5(s48) | (~until6(s48)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4991,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[4990])).
% 12.37/8.30 tff(4992,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[4991, 4989])).
% 12.37/8.30 tff(4993,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s48) | (~until6(s48)) | xuntil7(s48))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(4994,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s48) | always5(s48) | (~until6(s48))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[4993, 4992])).
% 12.37/8.30 tff(4995,plain,
% 12.37/8.30 (xuntil7(s48) | (~until6(s48))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4994, 4345, 3948])).
% 12.37/8.30 tff(4996,plain,
% 12.37/8.30 (xuntil7(s48)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4995, 4988])).
% 12.37/8.30 tff(4997,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(4998,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(4999,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 12.37/8.30 tff(5000,plain,
% 12.37/8.30 ((~xuntil7(s48)) | until6(s49)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[4999, 3130, 4363])).
% 12.37/8.30 tff(5001,plain,
% 12.37/8.30 (until6(s49)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5000, 4996])).
% 12.37/8.30 tff(5002,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5003,plain,
% 12.37/8.30 ((always5(s49) | (~until6(s49)) | xuntil7(s49)) <=> (xuntil7(s49) | always5(s49) | (~until6(s49)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5004,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5003])).
% 12.37/8.30 tff(5005,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5004, 5002])).
% 12.37/8.30 tff(5006,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s49) | (~until6(s49)) | xuntil7(s49))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5007,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s49) | always5(s49) | (~until6(s49))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5006, 5005])).
% 12.37/8.30 tff(5008,plain,
% 12.37/8.30 (xuntil7(s49) | (~until6(s49))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5007, 4345, 3940])).
% 12.37/8.30 tff(5009,plain,
% 12.37/8.30 (xuntil7(s49)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5008, 5001])).
% 12.37/8.30 tff(5010,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5011,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5012,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5011, 5010])).
% 12.37/8.30 tff(5013,plain,
% 12.37/8.30 ((~xuntil7(s49)) | until6(s50)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5012, 3199, 4363])).
% 12.37/8.30 tff(5014,plain,
% 12.37/8.30 (until6(s50)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5013, 5009])).
% 12.37/8.30 tff(5015,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5016,plain,
% 12.37/8.30 ((always5(s50) | (~until6(s50)) | xuntil7(s50)) <=> (xuntil7(s50) | always5(s50) | (~until6(s50)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5017,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5016])).
% 12.37/8.30 tff(5018,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5017, 5015])).
% 12.37/8.30 tff(5019,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s50) | (~until6(s50)) | xuntil7(s50))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5020,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s50) | always5(s50) | (~until6(s50))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5019, 5018])).
% 12.37/8.30 tff(5021,plain,
% 12.37/8.30 (xuntil7(s50) | (~until6(s50))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5020, 4345, 3932])).
% 12.37/8.30 tff(5022,plain,
% 12.37/8.30 (xuntil7(s50)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5021, 5014])).
% 12.37/8.30 tff(5023,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5024,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5025,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5024, 5023])).
% 12.37/8.30 tff(5026,plain,
% 12.37/8.30 ((~xuntil7(s50)) | until6(s51)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5025, 3285, 4363])).
% 12.37/8.30 tff(5027,plain,
% 12.37/8.30 (until6(s51)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5026, 5022])).
% 12.37/8.30 tff(5028,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5029,plain,
% 12.37/8.30 ((always5(s51) | (~until6(s51)) | xuntil7(s51)) <=> (xuntil7(s51) | always5(s51) | (~until6(s51)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5030,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5029])).
% 12.37/8.30 tff(5031,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5030, 5028])).
% 12.37/8.30 tff(5032,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s51) | (~until6(s51)) | xuntil7(s51))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5033,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s51) | always5(s51) | (~until6(s51))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5032, 5031])).
% 12.37/8.30 tff(5034,plain,
% 12.37/8.30 (xuntil7(s51) | (~until6(s51))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5033, 4345, 3924])).
% 12.37/8.30 tff(5035,plain,
% 12.37/8.30 (xuntil7(s51)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5034, 5027])).
% 12.37/8.30 tff(5036,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5037,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5038,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5037, 5036])).
% 12.37/8.30 tff(5039,plain,
% 12.37/8.30 ((~xuntil7(s51)) | until6(s52)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5038, 3351, 4363])).
% 12.37/8.30 tff(5040,plain,
% 12.37/8.30 (until6(s52)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5039, 5035])).
% 12.37/8.30 tff(5041,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5042,plain,
% 12.37/8.30 ((always5(s52) | (~until6(s52)) | xuntil7(s52)) <=> (xuntil7(s52) | always5(s52) | (~until6(s52)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5043,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5042])).
% 12.37/8.30 tff(5044,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5043, 5041])).
% 12.37/8.30 tff(5045,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s52) | (~until6(s52)) | xuntil7(s52))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5046,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s52) | always5(s52) | (~until6(s52))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5045, 5044])).
% 12.37/8.30 tff(5047,plain,
% 12.37/8.30 (xuntil7(s52) | (~until6(s52))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5046, 4345, 3916])).
% 12.37/8.30 tff(5048,plain,
% 12.37/8.30 (xuntil7(s52)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5047, 5040])).
% 12.37/8.30 tff(5049,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5050,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5051,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5050, 5049])).
% 12.37/8.30 tff(5052,plain,
% 12.37/8.30 ((~xuntil7(s52)) | until6(s53)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5051, 3415, 4363])).
% 12.37/8.30 tff(5053,plain,
% 12.37/8.30 (until6(s53)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5052, 5048])).
% 12.37/8.30 tff(5054,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5055,plain,
% 12.37/8.30 ((always5(s53) | (~until6(s53)) | xuntil7(s53)) <=> (xuntil7(s53) | always5(s53) | (~until6(s53)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5056,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5055])).
% 12.37/8.30 tff(5057,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5056, 5054])).
% 12.37/8.30 tff(5058,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s53) | (~until6(s53)) | xuntil7(s53))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5059,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s53) | always5(s53) | (~until6(s53))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5058, 5057])).
% 12.37/8.30 tff(5060,plain,
% 12.37/8.30 (xuntil7(s53) | (~until6(s53))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5059, 4345, 3908])).
% 12.37/8.30 tff(5061,plain,
% 12.37/8.30 (xuntil7(s53)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5060, 5053])).
% 12.37/8.30 tff(5062,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5063,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5064,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5063, 5062])).
% 12.37/8.30 tff(5065,plain,
% 12.37/8.30 ((~xuntil7(s53)) | until6(s54)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5064, 3479, 4363])).
% 12.37/8.30 tff(5066,plain,
% 12.37/8.30 (until6(s54)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5065, 5061])).
% 12.37/8.30 tff(5067,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5068,plain,
% 12.37/8.30 ((always5(s54) | (~until6(s54)) | xuntil7(s54)) <=> (xuntil7(s54) | always5(s54) | (~until6(s54)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5069,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5068])).
% 12.37/8.30 tff(5070,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5069, 5067])).
% 12.37/8.30 tff(5071,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s54) | (~until6(s54)) | xuntil7(s54))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5072,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s54) | always5(s54) | (~until6(s54))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5071, 5070])).
% 12.37/8.30 tff(5073,plain,
% 12.37/8.30 (xuntil7(s54) | (~until6(s54))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5072, 4345, 3900])).
% 12.37/8.30 tff(5074,plain,
% 12.37/8.30 (xuntil7(s54)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5073, 5066])).
% 12.37/8.30 tff(5075,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5076,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5077,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5076, 5075])).
% 12.37/8.30 tff(5078,plain,
% 12.37/8.30 ((~xuntil7(s54)) | until6(s55)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5077, 3540, 4363])).
% 12.37/8.30 tff(5079,plain,
% 12.37/8.30 (until6(s55)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5078, 5074])).
% 12.37/8.30 tff(5080,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5081,plain,
% 12.37/8.30 ((always5(s55) | (~until6(s55)) | xuntil7(s55)) <=> (xuntil7(s55) | always5(s55) | (~until6(s55)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5082,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5081])).
% 12.37/8.30 tff(5083,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5082, 5080])).
% 12.37/8.30 tff(5084,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s55) | (~until6(s55)) | xuntil7(s55))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5085,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s55) | always5(s55) | (~until6(s55))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5084, 5083])).
% 12.37/8.30 tff(5086,plain,
% 12.37/8.30 (xuntil7(s55) | (~until6(s55))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5085, 4345, 3892])).
% 12.37/8.30 tff(5087,plain,
% 12.37/8.30 (xuntil7(s55)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5086, 5079])).
% 12.37/8.30 tff(5088,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5089,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5090,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5089, 5088])).
% 12.37/8.30 tff(5091,plain,
% 12.37/8.30 ((~xuntil7(s55)) | until6(s56)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5090, 3601, 4363])).
% 12.37/8.30 tff(5092,plain,
% 12.37/8.30 (until6(s56)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5091, 5087])).
% 12.37/8.30 tff(5093,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5094,plain,
% 12.37/8.30 ((always5(s56) | (~until6(s56)) | xuntil7(s56)) <=> (xuntil7(s56) | always5(s56) | (~until6(s56)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5095,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5094])).
% 12.37/8.30 tff(5096,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5095, 5093])).
% 12.37/8.30 tff(5097,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s56) | (~until6(s56)) | xuntil7(s56))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5098,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s56) | always5(s56) | (~until6(s56))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5097, 5096])).
% 12.37/8.30 tff(5099,plain,
% 12.37/8.30 (xuntil7(s56) | (~until6(s56))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5098, 4345, 3884])).
% 12.37/8.30 tff(5100,plain,
% 12.37/8.30 (xuntil7(s56)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5099, 5092])).
% 12.37/8.30 tff(5101,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5102,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s56, s57)) | (~xuntil7(s56)) | until6(s57))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5103,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s56, s57)) | (~xuntil7(s56)) | until6(s57)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5102, 5101])).
% 12.37/8.30 tff(5104,plain,
% 12.37/8.30 ((~xuntil7(s56)) | until6(s57)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5103, 3663, 4363])).
% 12.37/8.30 tff(5105,plain,
% 12.37/8.30 (until6(s57)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5104, 5100])).
% 12.37/8.30 tff(5106,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5107,plain,
% 12.37/8.30 ((always5(s57) | (~until6(s57)) | xuntil7(s57)) <=> (xuntil7(s57) | always5(s57) | (~until6(s57)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5108,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5107])).
% 12.37/8.30 tff(5109,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(transitivity,[status(thm)],[5108, 5106])).
% 12.37/8.30 tff(5110,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s57) | (~until6(s57)) | xuntil7(s57))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5111,plain,
% 12.37/8.30 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s57) | always5(s57) | (~until6(s57))),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5110, 5109])).
% 12.37/8.30 tff(5112,plain,
% 12.37/8.30 (xuntil7(s57) | (~until6(s57))),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5111, 4345, 3876])).
% 12.37/8.30 tff(5113,plain,
% 12.37/8.30 (xuntil7(s57)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5112, 5105])).
% 12.37/8.30 tff(5114,plain,
% 12.37/8.30 (((~![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))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5115,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s57, s58)) | (~xuntil7(s57)) | until6(s58))),
% 12.37/8.30 inference(quant_inst,[status(thm)],[])).
% 12.37/8.30 tff(5116,plain,
% 12.37/8.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s57, s58)) | (~xuntil7(s57)) | until6(s58)),
% 12.37/8.30 inference(modus_ponens,[status(thm)],[5115, 5114])).
% 12.37/8.30 tff(5117,plain,
% 12.37/8.30 ((~xuntil7(s57)) | until6(s58)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5116, 3730, 4363])).
% 12.37/8.30 tff(5118,plain,
% 12.37/8.30 (until6(s58)),
% 12.37/8.30 inference(unit_resolution,[status(thm)],[5117, 5113])).
% 12.37/8.30 tff(5119,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5120,plain,
% 12.37/8.30 ((always5(s58) | (~until6(s58)) | xuntil7(s58)) <=> (xuntil7(s58) | always5(s58) | (~until6(s58)))),
% 12.37/8.30 inference(rewrite,[status(thm)],[])).
% 12.37/8.30 tff(5121,plain,
% 12.37/8.30 (((~![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))))),
% 12.37/8.30 inference(monotonicity,[status(thm)],[5120])).
% 12.37/8.30 tff(5122,plain,
% 12.37/8.30 (((~![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)))),
% 12.37/8.31 inference(transitivity,[status(thm)],[5121, 5119])).
% 12.37/8.31 tff(5123,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s58) | (~until6(s58)) | xuntil7(s58))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5124,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s58) | always5(s58) | (~until6(s58))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5123, 5122])).
% 12.37/8.31 tff(5125,plain,
% 12.37/8.31 (xuntil7(s58) | (~until6(s58))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5124, 4345, 3868])).
% 12.37/8.31 tff(5126,plain,
% 12.37/8.31 (xuntil7(s58)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5125, 5118])).
% 12.37/8.31 tff(5127,plain,
% 12.37/8.31 (((~![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))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5128,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s58, s59)) | (~xuntil7(s58)) | until6(s59))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5129,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s58, s59)) | (~xuntil7(s58)) | until6(s59)),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5128, 5127])).
% 12.37/8.31 tff(5130,plain,
% 12.37/8.31 ((~xuntil7(s58)) | until6(s59)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5129, 3833, 4363])).
% 12.37/8.31 tff(5131,plain,
% 12.37/8.31 (until6(s59)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5130, 5126])).
% 12.37/8.31 tff(5132,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5133,plain,
% 12.37/8.31 ((always5(s59) | (~until6(s59)) | xuntil7(s59)) <=> (always5(s59) | xuntil7(s59) | (~until6(s59)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5134,plain,
% 12.37/8.31 (((~![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))))),
% 12.37/8.31 inference(monotonicity,[status(thm)],[5133])).
% 12.37/8.31 tff(5135,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(transitivity,[status(thm)],[5134, 5132])).
% 12.37/8.31 tff(5136,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | (~until6(s59)) | xuntil7(s59))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5137,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s59) | xuntil7(s59) | (~until6(s59))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5136, 5135])).
% 12.37/8.31 tff(5138,plain,
% 12.37/8.31 (xuntil7(s59)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5137, 4345, 5131, 3850])).
% 12.37/8.31 tff(5139,plain,
% 12.37/8.31 (^[X: $i] : refl(((~last(X)) | (~xuntil2p9(X))) <=> ((~last(X)) | (~xuntil2p9(X))))),
% 12.37/8.31 inference(bind,[status(th)],[])).
% 12.37/8.31 tff(5140,plain,
% 12.37/8.31 (![X: $i] : ((~last(X)) | (~xuntil2p9(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(quant_intro,[status(thm)],[5139])).
% 12.37/8.31 tff(5141,plain,
% 12.37/8.31 (![X: $i] : ((~last(X)) | (~xuntil2p9(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5142,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty10')).
% 12.37/8.31 tff(5143,plain,
% 12.37/8.31 (![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5142, 5141])).
% 12.37/8.31 tff(5144,plain,(
% 12.37/8.31 ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(skolemize,[status(sab)],[5143])).
% 12.37/8.31 tff(5145,plain,
% 12.37/8.31 (![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5144, 5140])).
% 12.37/8.31 tff(5146,plain,
% 12.37/8.31 (last(s59) <=> last(s59)),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5147,axiom,(last(s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound60')).
% 12.37/8.31 tff(5148,plain,
% 12.37/8.31 (last(s59)),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5147, 5146])).
% 12.37/8.31 tff(5149,plain,
% 12.37/8.31 (((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | ((~last(s59)) | (~xuntil2p9(s59)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | (~last(s59)) | (~xuntil2p9(s59)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5150,plain,
% 12.37/8.31 ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | ((~last(s59)) | (~xuntil2p9(s59)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5151,plain,
% 12.37/8.31 ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | (~last(s59)) | (~xuntil2p9(s59))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5150, 5149])).
% 12.37/8.31 tff(5152,plain,
% 12.37/8.31 (~xuntil2p9(s59)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5151, 5148, 5145])).
% 12.37/8.31 tff(5153,plain,
% 12.37/8.31 (^[X: $i] : refl((always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> (always5(X) | xuntil2p9(X) | (~until2p8(X))))),
% 12.37/8.31 inference(bind,[status(th)],[])).
% 12.37/8.31 tff(5154,plain,
% 12.37/8.31 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 12.37/8.31 inference(quant_intro,[status(thm)],[5153])).
% 12.37/8.31 tff(5155,plain,
% 12.37/8.31 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5156,plain,
% 12.37/8.31 (^[X: $i] : rewrite(((always5(X) | xuntil2p9(X)) | (~until2p8(X))) <=> (always5(X) | xuntil2p9(X) | (~until2p8(X))))),
% 12.37/8.31 inference(bind,[status(th)],[])).
% 12.37/8.31 tff(5157,plain,
% 12.37/8.31 (![X: $i] : ((always5(X) | xuntil2p9(X)) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 12.37/8.31 inference(quant_intro,[status(thm)],[5156])).
% 12.37/8.31 tff(5158,axiom,(![X: $i] : ((always5(X) | xuntil2p9(X)) | (~until2p8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty8')).
% 12.37/8.31 tff(5159,plain,
% 12.37/8.31 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5158, 5157])).
% 12.37/8.31 tff(5160,plain,
% 12.37/8.31 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5159, 5155])).
% 12.37/8.31 tff(5161,plain,(
% 12.37/8.31 ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 12.37/8.31 inference(skolemize,[status(sab)],[5160])).
% 12.37/8.31 tff(5162,plain,
% 12.37/8.31 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5161, 5154])).
% 12.37/8.31 tff(5163,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5164,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s59) | xuntil2p9(s59) | (~until2p8(s59)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5165,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s59) | xuntil2p9(s59) | (~until2p8(s59))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5164, 5163])).
% 12.37/8.31 tff(5166,plain,
% 12.37/8.31 (always5(s59) | (~until2p8(s59))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5165, 5162, 5152])).
% 12.37/8.31 tff(5167,plain,
% 12.37/8.31 (~until2p8(s59)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5166, 3850])).
% 12.37/8.31 tff(5168,plain,
% 12.37/8.31 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))))),
% 12.37/8.31 inference(bind,[status(th)],[])).
% 12.37/8.31 tff(5169,plain,
% 12.37/8.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(quant_intro,[status(thm)],[5168])).
% 12.37/8.31 tff(5170,plain,
% 12.37/8.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5171,plain,
% 12.37/8.31 (^[Y: $i, X: $i] : rewrite(((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X))) <=> ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))))),
% 12.37/8.31 inference(bind,[status(th)],[])).
% 12.37/8.31 tff(5172,plain,
% 12.37/8.31 (![Y: $i, X: $i] : ((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(quant_intro,[status(thm)],[5171])).
% 12.37/8.31 tff(5173,axiom,(![Y: $i, X: $i] : ((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty9')).
% 12.37/8.31 tff(5174,plain,
% 12.37/8.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5173, 5172])).
% 12.37/8.31 tff(5175,plain,
% 12.37/8.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5174, 5170])).
% 12.37/8.31 tff(5176,plain,(
% 12.37/8.31 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(skolemize,[status(sab)],[5175])).
% 12.37/8.31 tff(5177,plain,
% 12.37/8.31 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5176, 5169])).
% 12.37/8.31 tff(5178,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5179,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5180,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5179, 5178])).
% 12.37/8.31 tff(5181,plain,
% 12.37/8.31 (until2p8(s59) | (~xuntil2p9(s58))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5180, 3833, 5177])).
% 12.37/8.31 tff(5182,plain,
% 12.37/8.31 (~xuntil2p9(s58)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5181, 5167])).
% 12.37/8.31 tff(5183,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5184,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s58) | xuntil2p9(s58) | (~until2p8(s58)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5185,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s58) | xuntil2p9(s58) | (~until2p8(s58))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5184, 5183])).
% 12.37/8.31 tff(5186,plain,
% 12.37/8.31 (~until2p8(s58)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5185, 5162, 5182, 3868])).
% 12.37/8.31 tff(5187,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5188,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5189,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5188, 5187])).
% 12.37/8.31 tff(5190,plain,
% 12.37/8.31 (until2p8(s58) | (~xuntil2p9(s57))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5189, 3730, 5177])).
% 12.37/8.31 tff(5191,plain,
% 12.37/8.31 (~xuntil2p9(s57)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5190, 5186])).
% 12.37/8.31 tff(5192,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5193,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s57) | xuntil2p9(s57) | (~until2p8(s57)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5194,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s57) | xuntil2p9(s57) | (~until2p8(s57))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5193, 5192])).
% 12.37/8.31 tff(5195,plain,
% 12.37/8.31 (xuntil2p9(s57) | (~until2p8(s57))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5194, 5162, 3876])).
% 12.37/8.31 tff(5196,plain,
% 12.37/8.31 (~until2p8(s57)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5195, 5191])).
% 12.37/8.31 tff(5197,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5198,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5199,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5198, 5197])).
% 12.37/8.31 tff(5200,plain,
% 12.37/8.31 (until2p8(s57) | (~xuntil2p9(s56))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5199, 3663, 5177])).
% 12.37/8.31 tff(5201,plain,
% 12.37/8.31 (~xuntil2p9(s56)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5200, 5196])).
% 12.37/8.31 tff(5202,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5203,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s56) | xuntil2p9(s56) | (~until2p8(s56)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5204,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s56) | xuntil2p9(s56) | (~until2p8(s56))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5203, 5202])).
% 12.37/8.31 tff(5205,plain,
% 12.37/8.31 (xuntil2p9(s56) | (~until2p8(s56))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5204, 5162, 3884])).
% 12.37/8.31 tff(5206,plain,
% 12.37/8.31 (~until2p8(s56)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5205, 5201])).
% 12.37/8.31 tff(5207,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5208,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5209,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5208, 5207])).
% 12.37/8.31 tff(5210,plain,
% 12.37/8.31 (until2p8(s56) | (~xuntil2p9(s55))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5209, 3601, 5177])).
% 12.37/8.31 tff(5211,plain,
% 12.37/8.31 (~xuntil2p9(s55)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5210, 5206])).
% 12.37/8.31 tff(5212,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5213,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s55) | xuntil2p9(s55) | (~until2p8(s55)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5214,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s55) | xuntil2p9(s55) | (~until2p8(s55))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5213, 5212])).
% 12.37/8.31 tff(5215,plain,
% 12.37/8.31 (xuntil2p9(s55) | (~until2p8(s55))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5214, 5162, 3892])).
% 12.37/8.31 tff(5216,plain,
% 12.37/8.31 (~until2p8(s55)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5215, 5211])).
% 12.37/8.31 tff(5217,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5218,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5219,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5218, 5217])).
% 12.37/8.31 tff(5220,plain,
% 12.37/8.31 (until2p8(s55) | (~xuntil2p9(s54))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5219, 3540, 5177])).
% 12.37/8.31 tff(5221,plain,
% 12.37/8.31 (~xuntil2p9(s54)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5220, 5216])).
% 12.37/8.31 tff(5222,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5223,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s54) | xuntil2p9(s54) | (~until2p8(s54)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5224,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s54) | xuntil2p9(s54) | (~until2p8(s54))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 12.37/8.31 tff(5225,plain,
% 12.37/8.31 (xuntil2p9(s54) | (~until2p8(s54))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5224, 5162, 3900])).
% 12.37/8.31 tff(5226,plain,
% 12.37/8.31 (~until2p8(s54)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5225, 5221])).
% 12.37/8.31 tff(5227,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5228,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5229,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5228, 5227])).
% 12.37/8.31 tff(5230,plain,
% 12.37/8.31 (until2p8(s54) | (~xuntil2p9(s53))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5229, 3479, 5177])).
% 12.37/8.31 tff(5231,plain,
% 12.37/8.31 (~xuntil2p9(s53)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5230, 5226])).
% 12.37/8.31 tff(5232,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5233,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s53) | xuntil2p9(s53) | (~until2p8(s53)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5234,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s53) | xuntil2p9(s53) | (~until2p8(s53))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5233, 5232])).
% 12.37/8.31 tff(5235,plain,
% 12.37/8.31 (xuntil2p9(s53) | (~until2p8(s53))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5234, 5162, 3908])).
% 12.37/8.31 tff(5236,plain,
% 12.37/8.31 (~until2p8(s53)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5235, 5231])).
% 12.37/8.31 tff(5237,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5238,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5239,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5238, 5237])).
% 12.37/8.31 tff(5240,plain,
% 12.37/8.31 (until2p8(s53) | (~xuntil2p9(s52))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5239, 3415, 5177])).
% 12.37/8.31 tff(5241,plain,
% 12.37/8.31 (~xuntil2p9(s52)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5240, 5236])).
% 12.37/8.31 tff(5242,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5243,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s52) | xuntil2p9(s52) | (~until2p8(s52)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5244,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s52) | xuntil2p9(s52) | (~until2p8(s52))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5243, 5242])).
% 12.37/8.31 tff(5245,plain,
% 12.37/8.31 (xuntil2p9(s52) | (~until2p8(s52))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5244, 5162, 3916])).
% 12.37/8.31 tff(5246,plain,
% 12.37/8.31 (~until2p8(s52)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5245, 5241])).
% 12.37/8.31 tff(5247,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5248,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5249,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5248, 5247])).
% 12.37/8.31 tff(5250,plain,
% 12.37/8.31 (until2p8(s52) | (~xuntil2p9(s51))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5249, 3351, 5177])).
% 12.37/8.31 tff(5251,plain,
% 12.37/8.31 (~xuntil2p9(s51)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5250, 5246])).
% 12.37/8.31 tff(5252,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5253,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s51) | xuntil2p9(s51) | (~until2p8(s51)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5254,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s51) | xuntil2p9(s51) | (~until2p8(s51))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5253, 5252])).
% 12.37/8.31 tff(5255,plain,
% 12.37/8.31 (xuntil2p9(s51) | (~until2p8(s51))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5254, 5162, 3924])).
% 12.37/8.31 tff(5256,plain,
% 12.37/8.31 (~until2p8(s51)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5255, 5251])).
% 12.37/8.31 tff(5257,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5258,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5259,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5258, 5257])).
% 12.37/8.31 tff(5260,plain,
% 12.37/8.31 (until2p8(s51) | (~xuntil2p9(s50))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5259, 3285, 5177])).
% 12.37/8.31 tff(5261,plain,
% 12.37/8.31 (~xuntil2p9(s50)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5260, 5256])).
% 12.37/8.31 tff(5262,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5263,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s50) | xuntil2p9(s50) | (~until2p8(s50)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5264,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s50) | xuntil2p9(s50) | (~until2p8(s50))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5263, 5262])).
% 12.37/8.31 tff(5265,plain,
% 12.37/8.31 (xuntil2p9(s50) | (~until2p8(s50))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5264, 5162, 3932])).
% 12.37/8.31 tff(5266,plain,
% 12.37/8.31 (~until2p8(s50)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5265, 5261])).
% 12.37/8.31 tff(5267,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5268,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5269,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5268, 5267])).
% 12.37/8.31 tff(5270,plain,
% 12.37/8.31 (until2p8(s50) | (~xuntil2p9(s49))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5269, 3199, 5177])).
% 12.37/8.31 tff(5271,plain,
% 12.37/8.31 (~xuntil2p9(s49)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5270, 5266])).
% 12.37/8.31 tff(5272,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5273,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s49) | xuntil2p9(s49) | (~until2p8(s49)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5274,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s49) | xuntil2p9(s49) | (~until2p8(s49))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5273, 5272])).
% 12.37/8.31 tff(5275,plain,
% 12.37/8.31 (xuntil2p9(s49) | (~until2p8(s49))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5274, 5162, 3940])).
% 12.37/8.31 tff(5276,plain,
% 12.37/8.31 (~until2p8(s49)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5275, 5271])).
% 12.37/8.31 tff(5277,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5278,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5279,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5278, 5277])).
% 12.37/8.31 tff(5280,plain,
% 12.37/8.31 (until2p8(s49) | (~xuntil2p9(s48))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5279, 3130, 5177])).
% 12.37/8.31 tff(5281,plain,
% 12.37/8.31 (~xuntil2p9(s48)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5280, 5276])).
% 12.37/8.31 tff(5282,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5283,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s48) | xuntil2p9(s48) | (~until2p8(s48)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5284,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s48) | xuntil2p9(s48) | (~until2p8(s48))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5283, 5282])).
% 12.37/8.31 tff(5285,plain,
% 12.37/8.31 (xuntil2p9(s48) | (~until2p8(s48))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5284, 5162, 3948])).
% 12.37/8.31 tff(5286,plain,
% 12.37/8.31 (~until2p8(s48)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5285, 5281])).
% 12.37/8.31 tff(5287,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5288,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5289,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5288, 5287])).
% 12.37/8.31 tff(5290,plain,
% 12.37/8.31 (until2p8(s48) | (~xuntil2p9(s47))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5289, 3070, 5177])).
% 12.37/8.31 tff(5291,plain,
% 12.37/8.31 (~xuntil2p9(s47)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5290, 5286])).
% 12.37/8.31 tff(5292,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5293,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s47) | xuntil2p9(s47) | (~until2p8(s47)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5294,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s47) | xuntil2p9(s47) | (~until2p8(s47))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5293, 5292])).
% 12.37/8.31 tff(5295,plain,
% 12.37/8.31 (xuntil2p9(s47) | (~until2p8(s47))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5294, 5162, 3956])).
% 12.37/8.31 tff(5296,plain,
% 12.37/8.31 (~until2p8(s47)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5295, 5291])).
% 12.37/8.31 tff(5297,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5298,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5299,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5298, 5297])).
% 12.37/8.31 tff(5300,plain,
% 12.37/8.31 (until2p8(s47) | (~xuntil2p9(s46))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5299, 2972, 5177])).
% 12.37/8.31 tff(5301,plain,
% 12.37/8.31 (~xuntil2p9(s46)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5300, 5296])).
% 12.37/8.31 tff(5302,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5303,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s46) | xuntil2p9(s46) | (~until2p8(s46)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5304,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s46) | xuntil2p9(s46) | (~until2p8(s46))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5303, 5302])).
% 12.37/8.31 tff(5305,plain,
% 12.37/8.31 (xuntil2p9(s46) | (~until2p8(s46))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5304, 5162, 3964])).
% 12.37/8.31 tff(5306,plain,
% 12.37/8.31 (~until2p8(s46)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5305, 5301])).
% 12.37/8.31 tff(5307,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5308,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5309,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5308, 5307])).
% 12.37/8.31 tff(5310,plain,
% 12.37/8.31 (until2p8(s46) | (~xuntil2p9(s45))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5309, 2905, 5177])).
% 12.37/8.31 tff(5311,plain,
% 12.37/8.31 (~xuntil2p9(s45)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5310, 5306])).
% 12.37/8.31 tff(5312,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5313,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s45) | xuntil2p9(s45) | (~until2p8(s45)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5314,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s45) | xuntil2p9(s45) | (~until2p8(s45))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5313, 5312])).
% 12.37/8.31 tff(5315,plain,
% 12.37/8.31 (xuntil2p9(s45) | (~until2p8(s45))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5314, 5162, 3972])).
% 12.37/8.31 tff(5316,plain,
% 12.37/8.31 (~until2p8(s45)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5315, 5311])).
% 12.37/8.31 tff(5317,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5318,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5319,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5318, 5317])).
% 12.37/8.31 tff(5320,plain,
% 12.37/8.31 (until2p8(s45) | (~xuntil2p9(s44))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5319, 2841, 5177])).
% 12.37/8.31 tff(5321,plain,
% 12.37/8.31 (~xuntil2p9(s44)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5320, 5316])).
% 12.37/8.31 tff(5322,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5323,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s44) | xuntil2p9(s44) | (~until2p8(s44)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5324,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s44) | xuntil2p9(s44) | (~until2p8(s44))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5323, 5322])).
% 12.37/8.31 tff(5325,plain,
% 12.37/8.31 (xuntil2p9(s44) | (~until2p8(s44))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5324, 5162, 3980])).
% 12.37/8.31 tff(5326,plain,
% 12.37/8.31 (~until2p8(s44)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5325, 5321])).
% 12.37/8.31 tff(5327,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5328,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5329,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 12.37/8.31 tff(5330,plain,
% 12.37/8.31 (until2p8(s44) | (~xuntil2p9(s43))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5329, 2775, 5177])).
% 12.37/8.31 tff(5331,plain,
% 12.37/8.31 (~xuntil2p9(s43)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5330, 5326])).
% 12.37/8.31 tff(5332,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5333,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s43) | xuntil2p9(s43) | (~until2p8(s43)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5334,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s43) | xuntil2p9(s43) | (~until2p8(s43))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5333, 5332])).
% 12.37/8.31 tff(5335,plain,
% 12.37/8.31 (xuntil2p9(s43) | (~until2p8(s43))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5334, 5162, 3988])).
% 12.37/8.31 tff(5336,plain,
% 12.37/8.31 (~until2p8(s43)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5335, 5331])).
% 12.37/8.31 tff(5337,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5338,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5339,plain,
% 12.37/8.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 12.37/8.31 tff(5340,plain,
% 12.37/8.31 (until2p8(s43) | (~xuntil2p9(s42))),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5339, 2714, 5177])).
% 12.37/8.31 tff(5341,plain,
% 12.37/8.31 (~xuntil2p9(s42)),
% 12.37/8.31 inference(unit_resolution,[status(thm)],[5340, 5336])).
% 12.37/8.31 tff(5342,plain,
% 12.37/8.31 (((~![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)))),
% 12.37/8.31 inference(rewrite,[status(thm)],[])).
% 12.37/8.31 tff(5343,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s42) | xuntil2p9(s42) | (~until2p8(s42)))),
% 12.37/8.31 inference(quant_inst,[status(thm)],[])).
% 12.37/8.31 tff(5344,plain,
% 12.37/8.31 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s42) | xuntil2p9(s42) | (~until2p8(s42))),
% 12.37/8.31 inference(modus_ponens,[status(thm)],[5343, 5342])).
% 12.37/8.32 tff(5345,plain,
% 12.37/8.32 (xuntil2p9(s42) | (~until2p8(s42))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5344, 5162, 3996])).
% 12.37/8.32 tff(5346,plain,
% 12.37/8.32 (~until2p8(s42)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5345, 5341])).
% 12.37/8.32 tff(5347,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5348,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5349,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5348, 5347])).
% 12.37/8.32 tff(5350,plain,
% 12.37/8.32 (until2p8(s42) | (~xuntil2p9(s41))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5349, 2647, 5177])).
% 12.37/8.32 tff(5351,plain,
% 12.37/8.32 (~xuntil2p9(s41)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5350, 5346])).
% 12.37/8.32 tff(5352,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5353,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s41) | xuntil2p9(s41) | (~until2p8(s41)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5354,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s41) | xuntil2p9(s41) | (~until2p8(s41))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5353, 5352])).
% 12.37/8.32 tff(5355,plain,
% 12.37/8.32 (xuntil2p9(s41) | (~until2p8(s41))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5354, 5162, 4004])).
% 12.37/8.32 tff(5356,plain,
% 12.37/8.32 (~until2p8(s41)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5355, 5351])).
% 12.37/8.32 tff(5357,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5358,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5359,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5358, 5357])).
% 12.37/8.32 tff(5360,plain,
% 12.37/8.32 (until2p8(s41) | (~xuntil2p9(s40))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5359, 2583, 5177])).
% 12.37/8.32 tff(5361,plain,
% 12.37/8.32 (~xuntil2p9(s40)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5360, 5356])).
% 12.37/8.32 tff(5362,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5363,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s40) | xuntil2p9(s40) | (~until2p8(s40)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5364,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s40) | xuntil2p9(s40) | (~until2p8(s40))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5363, 5362])).
% 12.37/8.32 tff(5365,plain,
% 12.37/8.32 (xuntil2p9(s40) | (~until2p8(s40))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5364, 5162, 4012])).
% 12.37/8.32 tff(5366,plain,
% 12.37/8.32 (~until2p8(s40)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5365, 5361])).
% 12.37/8.32 tff(5367,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5368,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5369,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5368, 5367])).
% 12.37/8.32 tff(5370,plain,
% 12.37/8.32 (until2p8(s40) | (~xuntil2p9(s39))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5369, 1196, 5177])).
% 12.37/8.32 tff(5371,plain,
% 12.37/8.32 (~xuntil2p9(s39)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5370, 5366])).
% 12.37/8.32 tff(5372,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5373,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s39) | xuntil2p9(s39) | (~until2p8(s39)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5374,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s39) | xuntil2p9(s39) | (~until2p8(s39))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5373, 5372])).
% 12.37/8.32 tff(5375,plain,
% 12.37/8.32 (xuntil2p9(s39) | (~until2p8(s39))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5374, 5162, 4020])).
% 12.37/8.32 tff(5376,plain,
% 12.37/8.32 (~until2p8(s39)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5375, 5371])).
% 12.37/8.32 tff(5377,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5378,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5379,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5378, 5377])).
% 12.37/8.32 tff(5380,plain,
% 12.37/8.32 (until2p8(s39) | (~xuntil2p9(s38))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5379, 1168, 5177])).
% 12.37/8.32 tff(5381,plain,
% 12.37/8.32 (~xuntil2p9(s38)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5380, 5376])).
% 12.37/8.32 tff(5382,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5383,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s38) | xuntil2p9(s38) | (~until2p8(s38)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5384,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s38) | xuntil2p9(s38) | (~until2p8(s38))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 12.37/8.32 tff(5385,plain,
% 12.37/8.32 (xuntil2p9(s38) | (~until2p8(s38))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5384, 5162, 4028])).
% 12.37/8.32 tff(5386,plain,
% 12.37/8.32 (~until2p8(s38)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5385, 5381])).
% 12.37/8.32 tff(5387,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5388,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5389,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5388, 5387])).
% 12.37/8.32 tff(5390,plain,
% 12.37/8.32 (until2p8(s38) | (~xuntil2p9(s37))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5389, 1137, 5177])).
% 12.37/8.32 tff(5391,plain,
% 12.37/8.32 (~xuntil2p9(s37)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5390, 5386])).
% 12.37/8.32 tff(5392,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5393,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s37) | xuntil2p9(s37) | (~until2p8(s37)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5394,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s37) | xuntil2p9(s37) | (~until2p8(s37))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5393, 5392])).
% 12.37/8.32 tff(5395,plain,
% 12.37/8.32 (xuntil2p9(s37) | (~until2p8(s37))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5394, 5162, 4036])).
% 12.37/8.32 tff(5396,plain,
% 12.37/8.32 (~until2p8(s37)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5395, 5391])).
% 12.37/8.32 tff(5397,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5398,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5399,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5398, 5397])).
% 12.37/8.32 tff(5400,plain,
% 12.37/8.32 (until2p8(s37) | (~xuntil2p9(s36))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5399, 1109, 5177])).
% 12.37/8.32 tff(5401,plain,
% 12.37/8.32 (~xuntil2p9(s36)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5400, 5396])).
% 12.37/8.32 tff(5402,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5403,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s36) | xuntil2p9(s36) | (~until2p8(s36)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5404,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s36) | xuntil2p9(s36) | (~until2p8(s36))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5403, 5402])).
% 12.37/8.32 tff(5405,plain,
% 12.37/8.32 (xuntil2p9(s36) | (~until2p8(s36))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5404, 5162, 4044])).
% 12.37/8.32 tff(5406,plain,
% 12.37/8.32 (~until2p8(s36)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5405, 5401])).
% 12.37/8.32 tff(5407,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5408,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5409,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5408, 5407])).
% 12.37/8.32 tff(5410,plain,
% 12.37/8.32 (until2p8(s36) | (~xuntil2p9(s35))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5409, 1078, 5177])).
% 12.37/8.32 tff(5411,plain,
% 12.37/8.32 (~xuntil2p9(s35)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5410, 5406])).
% 12.37/8.32 tff(5412,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5413,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s35) | xuntil2p9(s35) | (~until2p8(s35)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5414,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s35) | xuntil2p9(s35) | (~until2p8(s35))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5413, 5412])).
% 12.37/8.32 tff(5415,plain,
% 12.37/8.32 (xuntil2p9(s35) | (~until2p8(s35))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5414, 5162, 4052])).
% 12.37/8.32 tff(5416,plain,
% 12.37/8.32 (~until2p8(s35)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5415, 5411])).
% 12.37/8.32 tff(5417,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5418,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5419,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5418, 5417])).
% 12.37/8.32 tff(5420,plain,
% 12.37/8.32 (until2p8(s35) | (~xuntil2p9(s34))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5419, 1050, 5177])).
% 12.37/8.32 tff(5421,plain,
% 12.37/8.32 (~xuntil2p9(s34)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5420, 5416])).
% 12.37/8.32 tff(5422,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5423,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s34) | xuntil2p9(s34) | (~until2p8(s34)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5424,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s34) | xuntil2p9(s34) | (~until2p8(s34))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5423, 5422])).
% 12.37/8.32 tff(5425,plain,
% 12.37/8.32 (xuntil2p9(s34) | (~until2p8(s34))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5424, 5162, 4060])).
% 12.37/8.32 tff(5426,plain,
% 12.37/8.32 (~until2p8(s34)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5425, 5421])).
% 12.37/8.32 tff(5427,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5428,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5429,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5428, 5427])).
% 12.37/8.32 tff(5430,plain,
% 12.37/8.32 (until2p8(s34) | (~xuntil2p9(s33))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5429, 1019, 5177])).
% 12.37/8.32 tff(5431,plain,
% 12.37/8.32 (~xuntil2p9(s33)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5430, 5426])).
% 12.37/8.32 tff(5432,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5433,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s33) | xuntil2p9(s33) | (~until2p8(s33)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5434,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s33) | xuntil2p9(s33) | (~until2p8(s33))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5433, 5432])).
% 12.37/8.32 tff(5435,plain,
% 12.37/8.32 (xuntil2p9(s33) | (~until2p8(s33))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5434, 5162, 4068])).
% 12.37/8.32 tff(5436,plain,
% 12.37/8.32 (~until2p8(s33)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5435, 5431])).
% 12.37/8.32 tff(5437,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5438,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5439,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5438, 5437])).
% 12.37/8.32 tff(5440,plain,
% 12.37/8.32 (until2p8(s33) | (~xuntil2p9(s32))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5439, 991, 5177])).
% 12.37/8.32 tff(5441,plain,
% 12.37/8.32 (~xuntil2p9(s32)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5440, 5436])).
% 12.37/8.32 tff(5442,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5443,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s32) | xuntil2p9(s32) | (~until2p8(s32)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5444,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s32) | xuntil2p9(s32) | (~until2p8(s32))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5443, 5442])).
% 12.37/8.32 tff(5445,plain,
% 12.37/8.32 (xuntil2p9(s32) | (~until2p8(s32))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5444, 5162, 4076])).
% 12.37/8.32 tff(5446,plain,
% 12.37/8.32 (~until2p8(s32)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5445, 5441])).
% 12.37/8.32 tff(5447,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5448,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5449,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5448, 5447])).
% 12.37/8.32 tff(5450,plain,
% 12.37/8.32 (until2p8(s32) | (~xuntil2p9(s31))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5449, 960, 5177])).
% 12.37/8.32 tff(5451,plain,
% 12.37/8.32 (~xuntil2p9(s31)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5450, 5446])).
% 12.37/8.32 tff(5452,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5453,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s31) | xuntil2p9(s31) | (~until2p8(s31)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5454,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s31) | xuntil2p9(s31) | (~until2p8(s31))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5453, 5452])).
% 12.37/8.32 tff(5455,plain,
% 12.37/8.32 (xuntil2p9(s31) | (~until2p8(s31))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5454, 5162, 4084])).
% 12.37/8.32 tff(5456,plain,
% 12.37/8.32 (~until2p8(s31)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5455, 5451])).
% 12.37/8.32 tff(5457,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5458,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5459,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5458, 5457])).
% 12.37/8.32 tff(5460,plain,
% 12.37/8.32 (until2p8(s31) | (~xuntil2p9(s30))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5459, 932, 5177])).
% 12.37/8.32 tff(5461,plain,
% 12.37/8.32 (~xuntil2p9(s30)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5460, 5456])).
% 12.37/8.32 tff(5462,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5463,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s30) | xuntil2p9(s30) | (~until2p8(s30)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5464,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s30) | xuntil2p9(s30) | (~until2p8(s30))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5463, 5462])).
% 12.37/8.32 tff(5465,plain,
% 12.37/8.32 (xuntil2p9(s30) | (~until2p8(s30))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5464, 5162, 4092])).
% 12.37/8.32 tff(5466,plain,
% 12.37/8.32 (~until2p8(s30)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5465, 5461])).
% 12.37/8.32 tff(5467,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5468,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5469,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5468, 5467])).
% 12.37/8.32 tff(5470,plain,
% 12.37/8.32 (until2p8(s30) | (~xuntil2p9(s29))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5469, 901, 5177])).
% 12.37/8.32 tff(5471,plain,
% 12.37/8.32 (~xuntil2p9(s29)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5470, 5466])).
% 12.37/8.32 tff(5472,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5473,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s29) | xuntil2p9(s29) | (~until2p8(s29)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5474,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s29) | xuntil2p9(s29) | (~until2p8(s29))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5473, 5472])).
% 12.37/8.32 tff(5475,plain,
% 12.37/8.32 (xuntil2p9(s29) | (~until2p8(s29))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5474, 5162, 4100])).
% 12.37/8.32 tff(5476,plain,
% 12.37/8.32 (~until2p8(s29)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5475, 5471])).
% 12.37/8.32 tff(5477,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5478,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5479,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5478, 5477])).
% 12.37/8.32 tff(5480,plain,
% 12.37/8.32 (until2p8(s29) | (~xuntil2p9(s28))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5479, 873, 5177])).
% 12.37/8.32 tff(5481,plain,
% 12.37/8.32 (~xuntil2p9(s28)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5480, 5476])).
% 12.37/8.32 tff(5482,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5483,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s28) | xuntil2p9(s28) | (~until2p8(s28)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5484,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s28) | xuntil2p9(s28) | (~until2p8(s28))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5483, 5482])).
% 12.37/8.32 tff(5485,plain,
% 12.37/8.32 (xuntil2p9(s28) | (~until2p8(s28))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5484, 5162, 4108])).
% 12.37/8.32 tff(5486,plain,
% 12.37/8.32 (~until2p8(s28)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5485, 5481])).
% 12.37/8.32 tff(5487,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5488,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5489,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5488, 5487])).
% 12.37/8.32 tff(5490,plain,
% 12.37/8.32 (until2p8(s28) | (~xuntil2p9(s27))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5489, 842, 5177])).
% 12.37/8.32 tff(5491,plain,
% 12.37/8.32 (~xuntil2p9(s27)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5490, 5486])).
% 12.37/8.32 tff(5492,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5493,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s27) | xuntil2p9(s27) | (~until2p8(s27)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5494,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s27) | xuntil2p9(s27) | (~until2p8(s27))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5493, 5492])).
% 12.37/8.32 tff(5495,plain,
% 12.37/8.32 (xuntil2p9(s27) | (~until2p8(s27))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5494, 5162, 4116])).
% 12.37/8.32 tff(5496,plain,
% 12.37/8.32 (~until2p8(s27)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5495, 5491])).
% 12.37/8.32 tff(5497,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5498,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5499,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5498, 5497])).
% 12.37/8.32 tff(5500,plain,
% 12.37/8.32 (until2p8(s27) | (~xuntil2p9(s26))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5499, 814, 5177])).
% 12.37/8.32 tff(5501,plain,
% 12.37/8.32 (~xuntil2p9(s26)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5500, 5496])).
% 12.37/8.32 tff(5502,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5503,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s26) | xuntil2p9(s26) | (~until2p8(s26)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5504,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s26) | xuntil2p9(s26) | (~until2p8(s26))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5503, 5502])).
% 12.37/8.32 tff(5505,plain,
% 12.37/8.32 (xuntil2p9(s26) | (~until2p8(s26))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5504, 5162, 4124])).
% 12.37/8.32 tff(5506,plain,
% 12.37/8.32 (~until2p8(s26)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5505, 5501])).
% 12.37/8.32 tff(5507,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5508,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5509,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5508, 5507])).
% 12.37/8.32 tff(5510,plain,
% 12.37/8.32 (until2p8(s26) | (~xuntil2p9(s25))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5509, 783, 5177])).
% 12.37/8.32 tff(5511,plain,
% 12.37/8.32 (~xuntil2p9(s25)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5510, 5506])).
% 12.37/8.32 tff(5512,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5513,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s25) | xuntil2p9(s25) | (~until2p8(s25)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5514,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s25) | xuntil2p9(s25) | (~until2p8(s25))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5513, 5512])).
% 12.37/8.32 tff(5515,plain,
% 12.37/8.32 (xuntil2p9(s25) | (~until2p8(s25))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5514, 5162, 4132])).
% 12.37/8.32 tff(5516,plain,
% 12.37/8.32 (~until2p8(s25)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5515, 5511])).
% 12.37/8.32 tff(5517,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5518,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5519,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5518, 5517])).
% 12.37/8.32 tff(5520,plain,
% 12.37/8.32 (until2p8(s25) | (~xuntil2p9(s24))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5519, 755, 5177])).
% 12.37/8.32 tff(5521,plain,
% 12.37/8.32 (~xuntil2p9(s24)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5520, 5516])).
% 12.37/8.32 tff(5522,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5523,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s24) | xuntil2p9(s24) | (~until2p8(s24)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5524,plain,
% 12.37/8.32 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s24) | xuntil2p9(s24) | (~until2p8(s24))),
% 12.37/8.32 inference(modus_ponens,[status(thm)],[5523, 5522])).
% 12.37/8.32 tff(5525,plain,
% 12.37/8.32 (xuntil2p9(s24) | (~until2p8(s24))),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5524, 5162, 4140])).
% 12.37/8.32 tff(5526,plain,
% 12.37/8.32 (~until2p8(s24)),
% 12.37/8.32 inference(unit_resolution,[status(thm)],[5525, 5521])).
% 12.37/8.32 tff(5527,plain,
% 12.37/8.32 (((~![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)))),
% 12.37/8.32 inference(rewrite,[status(thm)],[])).
% 12.37/8.32 tff(5528,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23)))),
% 12.37/8.32 inference(quant_inst,[status(thm)],[])).
% 12.37/8.32 tff(5529,plain,
% 12.37/8.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5528, 5527])).
% 12.37/8.33 tff(5530,plain,
% 12.37/8.33 (until2p8(s24) | (~xuntil2p9(s23))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5529, 724, 5177])).
% 12.37/8.33 tff(5531,plain,
% 12.37/8.33 (~xuntil2p9(s23)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5530, 5526])).
% 12.37/8.33 tff(5532,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5533,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s23) | xuntil2p9(s23) | (~until2p8(s23)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5534,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s23) | xuntil2p9(s23) | (~until2p8(s23))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5533, 5532])).
% 12.37/8.33 tff(5535,plain,
% 12.37/8.33 (xuntil2p9(s23) | (~until2p8(s23))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5534, 5162, 4148])).
% 12.37/8.33 tff(5536,plain,
% 12.37/8.33 (~until2p8(s23)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5535, 5531])).
% 12.37/8.33 tff(5537,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5538,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5539,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5538, 5537])).
% 12.37/8.33 tff(5540,plain,
% 12.37/8.33 (until2p8(s23) | (~xuntil2p9(s22))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5539, 696, 5177])).
% 12.37/8.33 tff(5541,plain,
% 12.37/8.33 (~xuntil2p9(s22)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5540, 5536])).
% 12.37/8.33 tff(5542,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5543,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s22) | xuntil2p9(s22) | (~until2p8(s22)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5544,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s22) | xuntil2p9(s22) | (~until2p8(s22))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5543, 5542])).
% 12.37/8.33 tff(5545,plain,
% 12.37/8.33 (xuntil2p9(s22) | (~until2p8(s22))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5544, 5162, 4156])).
% 12.37/8.33 tff(5546,plain,
% 12.37/8.33 (~until2p8(s22)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5545, 5541])).
% 12.37/8.33 tff(5547,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5548,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5549,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5548, 5547])).
% 12.37/8.33 tff(5550,plain,
% 12.37/8.33 (until2p8(s22) | (~xuntil2p9(s21))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5549, 665, 5177])).
% 12.37/8.33 tff(5551,plain,
% 12.37/8.33 (~xuntil2p9(s21)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5550, 5546])).
% 12.37/8.33 tff(5552,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5553,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s21) | xuntil2p9(s21) | (~until2p8(s21)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5554,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s21) | xuntil2p9(s21) | (~until2p8(s21))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5553, 5552])).
% 12.37/8.33 tff(5555,plain,
% 12.37/8.33 (xuntil2p9(s21) | (~until2p8(s21))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5554, 5162, 4164])).
% 12.37/8.33 tff(5556,plain,
% 12.37/8.33 (~until2p8(s21)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5555, 5551])).
% 12.37/8.33 tff(5557,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5558,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5559,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5558, 5557])).
% 12.37/8.33 tff(5560,plain,
% 12.37/8.33 (until2p8(s21) | (~xuntil2p9(s20))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5559, 637, 5177])).
% 12.37/8.33 tff(5561,plain,
% 12.37/8.33 (~xuntil2p9(s20)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5560, 5556])).
% 12.37/8.33 tff(5562,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5563,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s20) | xuntil2p9(s20) | (~until2p8(s20)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5564,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s20) | xuntil2p9(s20) | (~until2p8(s20))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5563, 5562])).
% 12.37/8.33 tff(5565,plain,
% 12.37/8.33 (xuntil2p9(s20) | (~until2p8(s20))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5564, 5162, 4172])).
% 12.37/8.33 tff(5566,plain,
% 12.37/8.33 (~until2p8(s20)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5565, 5561])).
% 12.37/8.33 tff(5567,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5568,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5569,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5568, 5567])).
% 12.37/8.33 tff(5570,plain,
% 12.37/8.33 (until2p8(s20) | (~xuntil2p9(s19))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5569, 606, 5177])).
% 12.37/8.33 tff(5571,plain,
% 12.37/8.33 (~xuntil2p9(s19)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5570, 5566])).
% 12.37/8.33 tff(5572,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5573,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s19) | xuntil2p9(s19) | (~until2p8(s19)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5574,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s19) | xuntil2p9(s19) | (~until2p8(s19))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5573, 5572])).
% 12.37/8.33 tff(5575,plain,
% 12.37/8.33 (xuntil2p9(s19) | (~until2p8(s19))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5574, 5162, 4180])).
% 12.37/8.33 tff(5576,plain,
% 12.37/8.33 (~until2p8(s19)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5575, 5571])).
% 12.37/8.33 tff(5577,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5578,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5579,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5578, 5577])).
% 12.37/8.33 tff(5580,plain,
% 12.37/8.33 (until2p8(s19) | (~xuntil2p9(s18))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5579, 578, 5177])).
% 12.37/8.33 tff(5581,plain,
% 12.37/8.33 (~xuntil2p9(s18)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5580, 5576])).
% 12.37/8.33 tff(5582,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5583,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s18) | xuntil2p9(s18) | (~until2p8(s18)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5584,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s18) | xuntil2p9(s18) | (~until2p8(s18))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5583, 5582])).
% 12.37/8.33 tff(5585,plain,
% 12.37/8.33 (xuntil2p9(s18) | (~until2p8(s18))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5584, 5162, 4188])).
% 12.37/8.33 tff(5586,plain,
% 12.37/8.33 (~until2p8(s18)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5585, 5581])).
% 12.37/8.33 tff(5587,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5588,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5589,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5588, 5587])).
% 12.37/8.33 tff(5590,plain,
% 12.37/8.33 (until2p8(s18) | (~xuntil2p9(s17))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5589, 547, 5177])).
% 12.37/8.33 tff(5591,plain,
% 12.37/8.33 (~xuntil2p9(s17)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5590, 5586])).
% 12.37/8.33 tff(5592,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5593,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s17) | xuntil2p9(s17) | (~until2p8(s17)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5594,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s17) | xuntil2p9(s17) | (~until2p8(s17))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5593, 5592])).
% 12.37/8.33 tff(5595,plain,
% 12.37/8.33 (xuntil2p9(s17) | (~until2p8(s17))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5594, 5162, 4196])).
% 12.37/8.33 tff(5596,plain,
% 12.37/8.33 (~until2p8(s17)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5595, 5591])).
% 12.37/8.33 tff(5597,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5598,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5599,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5598, 5597])).
% 12.37/8.33 tff(5600,plain,
% 12.37/8.33 (until2p8(s17) | (~xuntil2p9(s16))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5599, 519, 5177])).
% 12.37/8.33 tff(5601,plain,
% 12.37/8.33 (~xuntil2p9(s16)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5600, 5596])).
% 12.37/8.33 tff(5602,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5603,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s16) | xuntil2p9(s16) | (~until2p8(s16)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5604,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s16) | xuntil2p9(s16) | (~until2p8(s16))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5603, 5602])).
% 12.37/8.33 tff(5605,plain,
% 12.37/8.33 (xuntil2p9(s16) | (~until2p8(s16))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5604, 5162, 4204])).
% 12.37/8.33 tff(5606,plain,
% 12.37/8.33 (~until2p8(s16)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5605, 5601])).
% 12.37/8.33 tff(5607,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5608,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5609,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5608, 5607])).
% 12.37/8.33 tff(5610,plain,
% 12.37/8.33 (until2p8(s16) | (~xuntil2p9(s15))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5609, 490, 5177])).
% 12.37/8.33 tff(5611,plain,
% 12.37/8.33 (~xuntil2p9(s15)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5610, 5606])).
% 12.37/8.33 tff(5612,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5613,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s15) | xuntil2p9(s15) | (~until2p8(s15)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5614,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s15) | xuntil2p9(s15) | (~until2p8(s15))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5613, 5612])).
% 12.37/8.33 tff(5615,plain,
% 12.37/8.33 (xuntil2p9(s15) | (~until2p8(s15))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5614, 5162, 4212])).
% 12.37/8.33 tff(5616,plain,
% 12.37/8.33 (~until2p8(s15)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5615, 5611])).
% 12.37/8.33 tff(5617,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5618,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5619,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5618, 5617])).
% 12.37/8.33 tff(5620,plain,
% 12.37/8.33 (until2p8(s15) | (~xuntil2p9(s14))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5619, 464, 5177])).
% 12.37/8.33 tff(5621,plain,
% 12.37/8.33 (~xuntil2p9(s14)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5620, 5616])).
% 12.37/8.33 tff(5622,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5623,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s14) | xuntil2p9(s14) | (~until2p8(s14)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5624,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s14) | xuntil2p9(s14) | (~until2p8(s14))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5623, 5622])).
% 12.37/8.33 tff(5625,plain,
% 12.37/8.33 (xuntil2p9(s14) | (~until2p8(s14))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5624, 5162, 4220])).
% 12.37/8.33 tff(5626,plain,
% 12.37/8.33 (~until2p8(s14)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5625, 5621])).
% 12.37/8.33 tff(5627,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5628,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5629,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5628, 5627])).
% 12.37/8.33 tff(5630,plain,
% 12.37/8.33 (until2p8(s14) | (~xuntil2p9(s13))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5629, 435, 5177])).
% 12.37/8.33 tff(5631,plain,
% 12.37/8.33 (~xuntil2p9(s13)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5630, 5626])).
% 12.37/8.33 tff(5632,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5633,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s13) | xuntil2p9(s13) | (~until2p8(s13)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5634,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s13) | xuntil2p9(s13) | (~until2p8(s13))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5633, 5632])).
% 12.37/8.33 tff(5635,plain,
% 12.37/8.33 (xuntil2p9(s13) | (~until2p8(s13))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5634, 5162, 4228])).
% 12.37/8.33 tff(5636,plain,
% 12.37/8.33 (~until2p8(s13)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5635, 5631])).
% 12.37/8.33 tff(5637,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5638,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5639,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5638, 5637])).
% 12.37/8.33 tff(5640,plain,
% 12.37/8.33 (until2p8(s13) | (~xuntil2p9(s12))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5639, 10, 5177])).
% 12.37/8.33 tff(5641,plain,
% 12.37/8.33 (~xuntil2p9(s12)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5640, 5636])).
% 12.37/8.33 tff(5642,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5643,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s12) | xuntil2p9(s12) | (~until2p8(s12)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5644,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s12) | xuntil2p9(s12) | (~until2p8(s12))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5643, 5642])).
% 12.37/8.33 tff(5645,plain,
% 12.37/8.33 (xuntil2p9(s12) | (~until2p8(s12))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5644, 5162, 4236])).
% 12.37/8.33 tff(5646,plain,
% 12.37/8.33 (~until2p8(s12)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5645, 5641])).
% 12.37/8.33 tff(5647,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5648,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5649,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5648, 5647])).
% 12.37/8.33 tff(5650,plain,
% 12.37/8.33 (until2p8(s12) | (~xuntil2p9(s11))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5649, 392, 5177])).
% 12.37/8.33 tff(5651,plain,
% 12.37/8.33 (~xuntil2p9(s11)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5650, 5646])).
% 12.37/8.33 tff(5652,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5653,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s11) | xuntil2p9(s11) | (~until2p8(s11)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5654,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s11) | xuntil2p9(s11) | (~until2p8(s11))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5653, 5652])).
% 12.37/8.33 tff(5655,plain,
% 12.37/8.33 (xuntil2p9(s11) | (~until2p8(s11))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5654, 5162, 4244])).
% 12.37/8.33 tff(5656,plain,
% 12.37/8.33 (~until2p8(s11)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5655, 5651])).
% 12.37/8.33 tff(5657,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5658,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5659,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5658, 5657])).
% 12.37/8.33 tff(5660,plain,
% 12.37/8.33 (until2p8(s11) | (~xuntil2p9(s10))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5659, 366, 5177])).
% 12.37/8.33 tff(5661,plain,
% 12.37/8.33 (~xuntil2p9(s10)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5660, 5656])).
% 12.37/8.33 tff(5662,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5663,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s10) | xuntil2p9(s10) | (~until2p8(s10)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5664,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s10) | xuntil2p9(s10) | (~until2p8(s10))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5663, 5662])).
% 12.37/8.33 tff(5665,plain,
% 12.37/8.33 (xuntil2p9(s10) | (~until2p8(s10))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5664, 5162, 4252])).
% 12.37/8.33 tff(5666,plain,
% 12.37/8.33 (~until2p8(s10)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5665, 5661])).
% 12.37/8.33 tff(5667,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5668,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5669,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5668, 5667])).
% 12.37/8.33 tff(5670,plain,
% 12.37/8.33 (until2p8(s10) | (~xuntil2p9(s9))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5669, 337, 5177])).
% 12.37/8.33 tff(5671,plain,
% 12.37/8.33 (~xuntil2p9(s9)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5670, 5666])).
% 12.37/8.33 tff(5672,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5673,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s9) | xuntil2p9(s9) | (~until2p8(s9)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5674,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s9) | xuntil2p9(s9) | (~until2p8(s9))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5673, 5672])).
% 12.37/8.33 tff(5675,plain,
% 12.37/8.33 (xuntil2p9(s9) | (~until2p8(s9))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5674, 5162, 4260])).
% 12.37/8.33 tff(5676,plain,
% 12.37/8.33 (~until2p8(s9)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5675, 5671])).
% 12.37/8.33 tff(5677,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5678,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5679,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5678, 5677])).
% 12.37/8.33 tff(5680,plain,
% 12.37/8.33 (until2p8(s9) | (~xuntil2p9(s8))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5679, 311, 5177])).
% 12.37/8.33 tff(5681,plain,
% 12.37/8.33 (~xuntil2p9(s8)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5680, 5676])).
% 12.37/8.33 tff(5682,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5683,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s8) | xuntil2p9(s8) | (~until2p8(s8)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5684,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s8) | xuntil2p9(s8) | (~until2p8(s8))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5683, 5682])).
% 12.37/8.33 tff(5685,plain,
% 12.37/8.33 (xuntil2p9(s8) | (~until2p8(s8))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5684, 5162, 4268])).
% 12.37/8.33 tff(5686,plain,
% 12.37/8.33 (~until2p8(s8)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5685, 5681])).
% 12.37/8.33 tff(5687,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5688,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5689,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5688, 5687])).
% 12.37/8.33 tff(5690,plain,
% 12.37/8.33 (until2p8(s8) | (~xuntil2p9(s7))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5689, 28, 5177])).
% 12.37/8.33 tff(5691,plain,
% 12.37/8.33 (~xuntil2p9(s7)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5690, 5686])).
% 12.37/8.33 tff(5692,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5693,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s7) | xuntil2p9(s7) | (~until2p8(s7)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5694,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s7) | xuntil2p9(s7) | (~until2p8(s7))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5693, 5692])).
% 12.37/8.33 tff(5695,plain,
% 12.37/8.33 (xuntil2p9(s7) | (~until2p8(s7))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5694, 5162, 4276])).
% 12.37/8.33 tff(5696,plain,
% 12.37/8.33 (~until2p8(s7)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5695, 5691])).
% 12.37/8.33 tff(5697,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5698,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5699,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5698, 5697])).
% 12.37/8.33 tff(5700,plain,
% 12.37/8.33 (until2p8(s7) | (~xuntil2p9(s6))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5699, 268, 5177])).
% 12.37/8.33 tff(5701,plain,
% 12.37/8.33 (~xuntil2p9(s6)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5700, 5696])).
% 12.37/8.33 tff(5702,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5703,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s6) | xuntil2p9(s6) | (~until2p8(s6)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5704,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s6) | xuntil2p9(s6) | (~until2p8(s6))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5703, 5702])).
% 12.37/8.33 tff(5705,plain,
% 12.37/8.33 (xuntil2p9(s6) | (~until2p8(s6))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5704, 5162, 4284])).
% 12.37/8.33 tff(5706,plain,
% 12.37/8.33 (~until2p8(s6)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5705, 5701])).
% 12.37/8.33 tff(5707,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5708,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5709,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5708, 5707])).
% 12.37/8.33 tff(5710,plain,
% 12.37/8.33 (until2p8(s6) | (~xuntil2p9(s5))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5709, 242, 5177])).
% 12.37/8.33 tff(5711,plain,
% 12.37/8.33 (~xuntil2p9(s5)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5710, 5706])).
% 12.37/8.33 tff(5712,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5713,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s5) | xuntil2p9(s5) | (~until2p8(s5)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5714,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s5) | xuntil2p9(s5) | (~until2p8(s5))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5713, 5712])).
% 12.37/8.33 tff(5715,plain,
% 12.37/8.33 (xuntil2p9(s5) | (~until2p8(s5))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5714, 5162, 4292])).
% 12.37/8.33 tff(5716,plain,
% 12.37/8.33 (~until2p8(s5)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5715, 5711])).
% 12.37/8.33 tff(5717,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5718,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5719,plain,
% 12.37/8.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5718, 5717])).
% 12.37/8.33 tff(5720,plain,
% 12.37/8.33 (until2p8(s5) | (~xuntil2p9(s4))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5719, 216, 5177])).
% 12.37/8.33 tff(5721,plain,
% 12.37/8.33 (~xuntil2p9(s4)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5720, 5716])).
% 12.37/8.33 tff(5722,plain,
% 12.37/8.33 (((~![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)))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5723,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s4) | xuntil2p9(s4) | (~until2p8(s4)))),
% 12.37/8.33 inference(quant_inst,[status(thm)],[])).
% 12.37/8.33 tff(5724,plain,
% 12.37/8.33 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s4) | xuntil2p9(s4) | (~until2p8(s4))),
% 12.37/8.33 inference(modus_ponens,[status(thm)],[5723, 5722])).
% 12.37/8.33 tff(5725,plain,
% 12.37/8.33 (xuntil2p9(s4) | (~until2p8(s4))),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5724, 5162, 4300])).
% 12.37/8.33 tff(5726,plain,
% 12.37/8.33 (~until2p8(s4)),
% 12.37/8.33 inference(unit_resolution,[status(thm)],[5725, 5721])).
% 12.37/8.33 tff(5727,plain,
% 12.37/8.33 (^[Y: $i, X: $i] : refl(((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)) <=> ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)))),
% 12.37/8.33 inference(bind,[status(th)],[])).
% 12.37/8.33 tff(5728,plain,
% 12.37/8.33 (![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))),
% 12.37/8.33 inference(quant_intro,[status(thm)],[5727])).
% 12.37/8.33 tff(5729,plain,
% 12.37/8.33 (![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))),
% 12.37/8.33 inference(rewrite,[status(thm)],[])).
% 12.37/8.33 tff(5730,plain,
% 12.37/8.33 (^[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))))),
% 12.37/8.34 inference(bind,[status(th)],[])).
% 12.37/8.34 tff(5731,plain,
% 12.37/8.34 (![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))),
% 12.37/8.34 inference(quant_intro,[status(thm)],[5730])).
% 12.37/8.34 tff(5732,axiom,(![Y: $i, X: $i] : (((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty7')).
% 12.37/8.34 tff(5733,plain,
% 12.37/8.34 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5732, 5731])).
% 12.37/8.34 tff(5734,plain,
% 12.37/8.34 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5733, 5729])).
% 12.37/8.34 tff(5735,plain,(
% 12.37/8.34 ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 12.37/8.34 inference(skolemize,[status(sab)],[5734])).
% 12.37/8.34 tff(5736,plain,
% 12.37/8.34 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5735, 5728])).
% 12.37/8.34 tff(5737,assumption,(xuntil7(s59)), introduced(assumption)).
% 12.37/8.34 tff(5738,assumption,(~until2p8(s37)), introduced(assumption)).
% 12.37/8.34 tff(5739,assumption,(trans(s59, s37)), introduced(assumption)).
% 12.37/8.34 tff(5740,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5741,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s37)) | (~xuntil7(s59)) | until2p8(s37)) <=> (until2p8(s37) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s37)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5742,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5741])).
% 12.37/8.34 tff(5743,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5742, 5740])).
% 12.37/8.34 tff(5744,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s37)) | (~xuntil7(s59)) | until2p8(s37))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5745,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s37))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5744, 5743])).
% 12.37/8.34 tff(5746,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5745, 5148, 5739, 5736, 5738, 5737])).
% 12.37/8.34 tff(5747,plain,((~trans(s59, s37)) | until2p8(s37) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5748,plain,
% 12.37/8.34 (~trans(s59, s37)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5747, 5396, 5138])).
% 12.37/8.34 tff(5749,assumption,(~until2p8(s25)), introduced(assumption)).
% 12.37/8.34 tff(5750,assumption,(trans(s59, s25)), introduced(assumption)).
% 12.37/8.34 tff(5751,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5752,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s25)) | (~xuntil7(s59)) | until2p8(s25)) <=> (until2p8(s25) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s25)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5753,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5752])).
% 12.37/8.34 tff(5754,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5753, 5751])).
% 12.37/8.34 tff(5755,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s25)) | (~xuntil7(s59)) | until2p8(s25))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5756,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s25))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5755, 5754])).
% 12.37/8.34 tff(5757,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5756, 5148, 5750, 5736, 5749, 5737])).
% 12.37/8.34 tff(5758,plain,((~trans(s59, s25)) | until2p8(s25) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5759,plain,
% 12.37/8.34 (~trans(s59, s25)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5758, 5516, 5138])).
% 12.37/8.34 tff(5760,assumption,(~until2p8(s55)), introduced(assumption)).
% 12.37/8.34 tff(5761,assumption,(trans(s59, s55)), introduced(assumption)).
% 12.37/8.34 tff(5762,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5763,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s55)) | (~xuntil7(s59)) | until2p8(s55)) <=> (until2p8(s55) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s55)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5764,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5763])).
% 12.37/8.34 tff(5765,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5764, 5762])).
% 12.37/8.34 tff(5766,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s55)) | (~xuntil7(s59)) | until2p8(s55))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5767,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s55))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5766, 5765])).
% 12.37/8.34 tff(5768,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5767, 5148, 5761, 5736, 5760, 5737])).
% 12.37/8.34 tff(5769,plain,((~trans(s59, s55)) | until2p8(s55) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5770,plain,
% 12.37/8.34 (~trans(s59, s55)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5769, 5216, 5138])).
% 12.37/8.34 tff(5771,assumption,(~until2p8(s51)), introduced(assumption)).
% 12.37/8.34 tff(5772,assumption,(trans(s59, s51)), introduced(assumption)).
% 12.37/8.34 tff(5773,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5774,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s51)) | (~xuntil7(s59)) | until2p8(s51)) <=> (until2p8(s51) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s51)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5775,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5774])).
% 12.37/8.34 tff(5776,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5775, 5773])).
% 12.37/8.34 tff(5777,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s51)) | (~xuntil7(s59)) | until2p8(s51))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5778,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s51))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5777, 5776])).
% 12.37/8.34 tff(5779,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5778, 5148, 5772, 5736, 5771, 5737])).
% 12.37/8.34 tff(5780,plain,((~trans(s59, s51)) | until2p8(s51) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5781,plain,
% 12.37/8.34 (~trans(s59, s51)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5780, 5256, 5138])).
% 12.37/8.34 tff(5782,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5783,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3)))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5784,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5783, 5782])).
% 12.37/8.34 tff(5785,plain,
% 12.37/8.34 (until2p8(s4) | (~xuntil2p9(s3))),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5784, 187, 5177])).
% 12.37/8.34 tff(5786,plain,
% 12.37/8.34 (~xuntil2p9(s3)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5785, 5726])).
% 12.37/8.34 tff(5787,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5788,plain,
% 12.37/8.34 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s3) | xuntil2p9(s3) | (~until2p8(s3)))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5789,plain,
% 12.37/8.34 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s3) | xuntil2p9(s3) | (~until2p8(s3))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5788, 5787])).
% 12.37/8.34 tff(5790,plain,
% 12.37/8.34 (xuntil2p9(s3) | (~until2p8(s3))),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5789, 5162, 4308])).
% 12.37/8.34 tff(5791,plain,
% 12.37/8.34 (~until2p8(s3)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5790, 5786])).
% 12.37/8.34 tff(5792,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5793,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2)))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5794,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5793, 5792])).
% 12.37/8.34 tff(5795,plain,
% 12.37/8.34 (until2p8(s3) | (~xuntil2p9(s2))),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5794, 161, 5177])).
% 12.37/8.34 tff(5796,plain,
% 12.37/8.34 (~xuntil2p9(s2)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5795, 5791])).
% 12.37/8.34 tff(5797,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5798,plain,
% 12.37/8.34 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s2) | xuntil2p9(s2) | (~until2p8(s2)))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5799,plain,
% 12.37/8.34 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s2) | xuntil2p9(s2) | (~until2p8(s2))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5798, 5797])).
% 12.37/8.34 tff(5800,plain,
% 12.37/8.34 (xuntil2p9(s2) | (~until2p8(s2))),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5799, 5162, 4316])).
% 12.37/8.34 tff(5801,plain,
% 12.37/8.34 (~until2p8(s2)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5800, 5796])).
% 12.37/8.34 tff(5802,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5803,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1)))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5804,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5803, 5802])).
% 12.37/8.34 tff(5805,plain,
% 12.37/8.34 (until2p8(s2) | (~xuntil2p9(s1))),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5804, 39, 5177])).
% 12.37/8.34 tff(5806,plain,
% 12.37/8.34 (~xuntil2p9(s1)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5805, 5801])).
% 12.37/8.34 tff(5807,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5808,plain,
% 12.37/8.34 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s1) | xuntil2p9(s1) | (~until2p8(s1)))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5809,plain,
% 12.37/8.34 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s1) | xuntil2p9(s1) | (~until2p8(s1))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5808, 5807])).
% 12.37/8.34 tff(5810,plain,
% 12.37/8.34 (xuntil2p9(s1) | (~until2p8(s1))),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5809, 5162, 4324])).
% 12.37/8.34 tff(5811,plain,
% 12.37/8.34 (~until2p8(s1)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5810, 5806])).
% 12.37/8.34 tff(5812,assumption,(~until2p8(s1)), introduced(assumption)).
% 12.37/8.34 tff(5813,assumption,(trans(s59, s1)), introduced(assumption)).
% 12.37/8.34 tff(5814,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5815,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s1)) | (~xuntil7(s59)) | until2p8(s1)) <=> (until2p8(s1) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s1)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5816,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5815])).
% 12.37/8.34 tff(5817,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5816, 5814])).
% 12.37/8.34 tff(5818,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s1)) | (~xuntil7(s59)) | until2p8(s1))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5819,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s1))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5818, 5817])).
% 12.37/8.34 tff(5820,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5819, 5148, 5813, 5736, 5812, 5737])).
% 12.37/8.34 tff(5821,plain,((~trans(s59, s1)) | until2p8(s1) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5822,plain,
% 12.37/8.34 (~trans(s59, s1)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5821, 5811, 5138])).
% 12.37/8.34 tff(5823,assumption,(~until2p8(s9)), introduced(assumption)).
% 12.37/8.34 tff(5824,assumption,(trans(s59, s9)), introduced(assumption)).
% 12.37/8.34 tff(5825,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5826,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s9)) | (~xuntil7(s59)) | until2p8(s9)) <=> (until2p8(s9) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s9)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5827,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5826])).
% 12.37/8.34 tff(5828,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5827, 5825])).
% 12.37/8.34 tff(5829,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s9)) | (~xuntil7(s59)) | until2p8(s9))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5830,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s9))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5829, 5828])).
% 12.37/8.34 tff(5831,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5830, 5148, 5824, 5736, 5823, 5737])).
% 12.37/8.34 tff(5832,plain,((~trans(s59, s9)) | until2p8(s9) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5833,plain,
% 12.37/8.34 (~trans(s59, s9)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5832, 5676, 5138])).
% 12.37/8.34 tff(5834,assumption,(~until2p8(s26)), introduced(assumption)).
% 12.37/8.34 tff(5835,assumption,(trans(s59, s26)), introduced(assumption)).
% 12.37/8.34 tff(5836,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5837,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s26)) | (~xuntil7(s59)) | until2p8(s26)) <=> (until2p8(s26) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s26)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5838,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5837])).
% 12.37/8.34 tff(5839,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5838, 5836])).
% 12.37/8.34 tff(5840,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s26)) | (~xuntil7(s59)) | until2p8(s26))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5841,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s26))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5840, 5839])).
% 12.37/8.34 tff(5842,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5841, 5148, 5835, 5736, 5834, 5737])).
% 12.37/8.34 tff(5843,plain,((~trans(s59, s26)) | until2p8(s26) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5844,plain,
% 12.37/8.34 (~trans(s59, s26)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5843, 5506, 5138])).
% 12.37/8.34 tff(5845,assumption,(~until2p8(s56)), introduced(assumption)).
% 12.37/8.34 tff(5846,assumption,(trans(s59, s56)), introduced(assumption)).
% 12.37/8.34 tff(5847,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5848,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s56)) | (~xuntil7(s59)) | until2p8(s56)) <=> (until2p8(s56) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s56)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5849,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5848])).
% 12.37/8.34 tff(5850,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5849, 5847])).
% 12.37/8.34 tff(5851,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s56)) | (~xuntil7(s59)) | until2p8(s56))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5852,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s56))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5851, 5850])).
% 12.37/8.34 tff(5853,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5852, 5148, 5846, 5736, 5845, 5737])).
% 12.37/8.34 tff(5854,plain,((~trans(s59, s56)) | until2p8(s56) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5855,plain,
% 12.37/8.34 (~trans(s59, s56)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5854, 5206, 5138])).
% 12.37/8.34 tff(5856,assumption,(~until2p8(s48)), introduced(assumption)).
% 12.37/8.34 tff(5857,assumption,(trans(s59, s48)), introduced(assumption)).
% 12.37/8.34 tff(5858,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5859,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s48)) | (~xuntil7(s59)) | until2p8(s48)) <=> (until2p8(s48) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s48)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5860,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5859])).
% 12.37/8.34 tff(5861,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5860, 5858])).
% 12.37/8.34 tff(5862,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s48)) | (~xuntil7(s59)) | until2p8(s48))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5863,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s48))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5862, 5861])).
% 12.37/8.34 tff(5864,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5863, 5148, 5857, 5736, 5856, 5737])).
% 12.37/8.34 tff(5865,plain,((~trans(s59, s48)) | until2p8(s48) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5866,plain,
% 12.37/8.34 (~trans(s59, s48)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5865, 5286, 5138])).
% 12.37/8.34 tff(5867,assumption,(~until2p8(s10)), introduced(assumption)).
% 12.37/8.34 tff(5868,assumption,(trans(s59, s10)), introduced(assumption)).
% 12.37/8.34 tff(5869,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5870,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s10)) | (~xuntil7(s59)) | until2p8(s10)) <=> (until2p8(s10) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s10)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5871,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5870])).
% 12.37/8.34 tff(5872,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(transitivity,[status(thm)],[5871, 5869])).
% 12.37/8.34 tff(5873,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s10)) | (~xuntil7(s59)) | until2p8(s10))),
% 12.37/8.34 inference(quant_inst,[status(thm)],[])).
% 12.37/8.34 tff(5874,plain,
% 12.37/8.34 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s10))),
% 12.37/8.34 inference(modus_ponens,[status(thm)],[5873, 5872])).
% 12.37/8.34 tff(5875,plain,
% 12.37/8.34 ($false),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5874, 5148, 5868, 5736, 5867, 5737])).
% 12.37/8.34 tff(5876,plain,((~trans(s59, s10)) | until2p8(s10) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.34 tff(5877,plain,
% 12.37/8.34 (~trans(s59, s10)),
% 12.37/8.34 inference(unit_resolution,[status(thm)],[5876, 5666, 5138])).
% 12.37/8.34 tff(5878,assumption,(~until2p8(s32)), introduced(assumption)).
% 12.37/8.34 tff(5879,assumption,(trans(s59, s32)), introduced(assumption)).
% 12.37/8.34 tff(5880,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5881,plain,
% 12.37/8.34 (((~last(s59)) | (~trans(s59, s32)) | (~xuntil7(s59)) | until2p8(s32)) <=> (until2p8(s32) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s32)))),
% 12.37/8.34 inference(rewrite,[status(thm)],[])).
% 12.37/8.34 tff(5882,plain,
% 12.37/8.34 (((~![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))))),
% 12.37/8.34 inference(monotonicity,[status(thm)],[5881])).
% 12.37/8.34 tff(5883,plain,
% 12.37/8.34 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5882, 5880])).
% 12.37/8.35 tff(5884,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s32)) | (~xuntil7(s59)) | until2p8(s32))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5885,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s32))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5884, 5883])).
% 12.37/8.35 tff(5886,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5885, 5148, 5879, 5736, 5878, 5737])).
% 12.37/8.35 tff(5887,plain,((~trans(s59, s32)) | until2p8(s32) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5888,plain,
% 12.37/8.35 (~trans(s59, s32)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5887, 5446, 5138])).
% 12.37/8.35 tff(5889,assumption,(~until2p8(s29)), introduced(assumption)).
% 12.37/8.35 tff(5890,assumption,(trans(s59, s29)), introduced(assumption)).
% 12.37/8.35 tff(5891,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5892,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s29)) | (~xuntil7(s59)) | until2p8(s29)) <=> (until2p8(s29) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s29)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5893,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5892])).
% 12.37/8.35 tff(5894,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5893, 5891])).
% 12.37/8.35 tff(5895,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s29)) | (~xuntil7(s59)) | until2p8(s29))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5896,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s29))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5895, 5894])).
% 12.37/8.35 tff(5897,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5896, 5148, 5890, 5736, 5889, 5737])).
% 12.37/8.35 tff(5898,plain,((~trans(s59, s29)) | until2p8(s29) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5899,plain,
% 12.37/8.35 (~trans(s59, s29)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5898, 5476, 5138])).
% 12.37/8.35 tff(5900,assumption,(~until2p8(s38)), introduced(assumption)).
% 12.37/8.35 tff(5901,assumption,(trans(s59, s38)), introduced(assumption)).
% 12.37/8.35 tff(5902,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5903,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s38)) | (~xuntil7(s59)) | until2p8(s38)) <=> (until2p8(s38) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s38)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5904,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5903])).
% 12.37/8.35 tff(5905,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5904, 5902])).
% 12.37/8.35 tff(5906,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s38)) | (~xuntil7(s59)) | until2p8(s38))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5907,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s38))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5906, 5905])).
% 12.37/8.35 tff(5908,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5907, 5148, 5901, 5736, 5900, 5737])).
% 12.37/8.35 tff(5909,plain,((~trans(s59, s38)) | until2p8(s38) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5910,plain,
% 12.37/8.35 (~trans(s59, s38)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5909, 5386, 5138])).
% 12.37/8.35 tff(5911,assumption,(~until2p8(s41)), introduced(assumption)).
% 12.37/8.35 tff(5912,assumption,(trans(s59, s41)), introduced(assumption)).
% 12.37/8.35 tff(5913,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5914,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s41)) | (~xuntil7(s59)) | until2p8(s41)) <=> (until2p8(s41) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s41)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5915,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5914])).
% 12.37/8.35 tff(5916,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5915, 5913])).
% 12.37/8.35 tff(5917,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s41)) | (~xuntil7(s59)) | until2p8(s41))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5918,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s41))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5917, 5916])).
% 12.37/8.35 tff(5919,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5918, 5148, 5912, 5736, 5911, 5737])).
% 12.37/8.35 tff(5920,plain,((~trans(s59, s41)) | until2p8(s41) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5921,plain,
% 12.37/8.35 (~trans(s59, s41)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5920, 5356, 5138])).
% 12.37/8.35 tff(5922,assumption,(~until2p8(s34)), introduced(assumption)).
% 12.37/8.35 tff(5923,assumption,(trans(s59, s34)), introduced(assumption)).
% 12.37/8.35 tff(5924,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5925,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s34)) | (~xuntil7(s59)) | until2p8(s34)) <=> (until2p8(s34) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s34)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5926,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5925])).
% 12.37/8.35 tff(5927,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5926, 5924])).
% 12.37/8.35 tff(5928,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s34)) | (~xuntil7(s59)) | until2p8(s34))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5929,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s34))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5928, 5927])).
% 12.37/8.35 tff(5930,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5929, 5148, 5923, 5736, 5922, 5737])).
% 12.37/8.35 tff(5931,plain,((~trans(s59, s34)) | until2p8(s34) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5932,plain,
% 12.37/8.35 (~trans(s59, s34)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5931, 5426, 5138])).
% 12.37/8.35 tff(5933,assumption,(~until2p8(s43)), introduced(assumption)).
% 12.37/8.35 tff(5934,assumption,(trans(s59, s43)), introduced(assumption)).
% 12.37/8.35 tff(5935,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5936,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s43)) | (~xuntil7(s59)) | until2p8(s43)) <=> (until2p8(s43) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s43)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5937,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5936])).
% 12.37/8.35 tff(5938,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5937, 5935])).
% 12.37/8.35 tff(5939,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s43)) | (~xuntil7(s59)) | until2p8(s43))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5940,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s43))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5939, 5938])).
% 12.37/8.35 tff(5941,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5940, 5148, 5934, 5736, 5933, 5737])).
% 12.37/8.35 tff(5942,plain,((~trans(s59, s43)) | until2p8(s43) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5943,plain,
% 12.37/8.35 (~trans(s59, s43)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5942, 5336, 5138])).
% 12.37/8.35 tff(5944,assumption,(~until2p8(s12)), introduced(assumption)).
% 12.37/8.35 tff(5945,assumption,(trans(s59, s12)), introduced(assumption)).
% 12.37/8.35 tff(5946,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5947,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s12)) | (~xuntil7(s59)) | until2p8(s12)) <=> (until2p8(s12) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s12)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5948,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5947])).
% 12.37/8.35 tff(5949,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5948, 5946])).
% 12.37/8.35 tff(5950,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s12)) | (~xuntil7(s59)) | until2p8(s12))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5951,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s12))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5950, 5949])).
% 12.37/8.35 tff(5952,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5951, 5148, 5945, 5736, 5944, 5737])).
% 12.37/8.35 tff(5953,plain,((~trans(s59, s12)) | until2p8(s12) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5954,plain,
% 12.37/8.35 (~trans(s59, s12)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5953, 5646, 5138])).
% 12.37/8.35 tff(5955,assumption,(~until2p8(s2)), introduced(assumption)).
% 12.37/8.35 tff(5956,assumption,(trans(s59, s2)), introduced(assumption)).
% 12.37/8.35 tff(5957,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5958,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s2)) | (~xuntil7(s59)) | until2p8(s2)) <=> (until2p8(s2) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s2)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5959,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5958])).
% 12.37/8.35 tff(5960,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5959, 5957])).
% 12.37/8.35 tff(5961,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s2)) | (~xuntil7(s59)) | until2p8(s2))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5962,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s2))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5961, 5960])).
% 12.37/8.35 tff(5963,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5962, 5148, 5956, 5736, 5955, 5737])).
% 12.37/8.35 tff(5964,plain,((~trans(s59, s2)) | until2p8(s2) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5965,plain,
% 12.37/8.35 (~trans(s59, s2)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5964, 5801, 5138])).
% 12.37/8.35 tff(5966,assumption,(~until2p8(s36)), introduced(assumption)).
% 12.37/8.35 tff(5967,assumption,(trans(s59, s36)), introduced(assumption)).
% 12.37/8.35 tff(5968,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5969,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s36)) | (~xuntil7(s59)) | until2p8(s36)) <=> (until2p8(s36) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s36)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5970,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5969])).
% 12.37/8.35 tff(5971,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5970, 5968])).
% 12.37/8.35 tff(5972,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s36)) | (~xuntil7(s59)) | until2p8(s36))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5973,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s36))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5972, 5971])).
% 12.37/8.35 tff(5974,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5973, 5148, 5967, 5736, 5966, 5737])).
% 12.37/8.35 tff(5975,plain,((~trans(s59, s36)) | until2p8(s36) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5976,plain,
% 12.37/8.35 (~trans(s59, s36)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5975, 5406, 5138])).
% 12.37/8.35 tff(5977,assumption,(~until2p8(s44)), introduced(assumption)).
% 12.37/8.35 tff(5978,assumption,(trans(s59, s44)), introduced(assumption)).
% 12.37/8.35 tff(5979,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5980,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s44)) | (~xuntil7(s59)) | until2p8(s44)) <=> (until2p8(s44) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s44)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5981,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5980])).
% 12.37/8.35 tff(5982,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5981, 5979])).
% 12.37/8.35 tff(5983,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s44)) | (~xuntil7(s59)) | until2p8(s44))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5984,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s44))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5983, 5982])).
% 12.37/8.35 tff(5985,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5984, 5148, 5978, 5736, 5977, 5737])).
% 12.37/8.35 tff(5986,plain,((~trans(s59, s44)) | until2p8(s44) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5987,plain,
% 12.37/8.35 (~trans(s59, s44)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5986, 5326, 5138])).
% 12.37/8.35 tff(5988,assumption,(~until2p8(s20)), introduced(assumption)).
% 12.37/8.35 tff(5989,assumption,(trans(s59, s20)), introduced(assumption)).
% 12.37/8.35 tff(5990,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5991,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s20)) | (~xuntil7(s59)) | until2p8(s20)) <=> (until2p8(s20) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s20)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(5992,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[5991])).
% 12.37/8.35 tff(5993,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[5992, 5990])).
% 12.37/8.35 tff(5994,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s20)) | (~xuntil7(s59)) | until2p8(s20))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(5995,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s20))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[5994, 5993])).
% 12.37/8.35 tff(5996,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5995, 5148, 5989, 5736, 5988, 5737])).
% 12.37/8.35 tff(5997,plain,((~trans(s59, s20)) | until2p8(s20) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(5998,plain,
% 12.37/8.35 (~trans(s59, s20)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[5997, 5566, 5138])).
% 12.37/8.35 tff(5999,assumption,(~until2p8(s22)), introduced(assumption)).
% 12.37/8.35 tff(6000,assumption,(trans(s59, s22)), introduced(assumption)).
% 12.37/8.35 tff(6001,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(6002,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s22)) | (~xuntil7(s59)) | until2p8(s22)) <=> (until2p8(s22) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s22)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(6003,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[6002])).
% 12.37/8.35 tff(6004,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[6003, 6001])).
% 12.37/8.35 tff(6005,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s22)) | (~xuntil7(s59)) | until2p8(s22))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(6006,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s22))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[6005, 6004])).
% 12.37/8.35 tff(6007,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[6006, 5148, 6000, 5736, 5999, 5737])).
% 12.37/8.35 tff(6008,plain,((~trans(s59, s22)) | until2p8(s22) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(6009,plain,
% 12.37/8.35 (~trans(s59, s22)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[6008, 5546, 5138])).
% 12.37/8.35 tff(6010,assumption,(~until2p8(s53)), introduced(assumption)).
% 12.37/8.35 tff(6011,assumption,(trans(s59, s53)), introduced(assumption)).
% 12.37/8.35 tff(6012,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(6013,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s53)) | (~xuntil7(s59)) | until2p8(s53)) <=> (until2p8(s53) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s53)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(6014,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[6013])).
% 12.37/8.35 tff(6015,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[6014, 6012])).
% 12.37/8.35 tff(6016,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s53)) | (~xuntil7(s59)) | until2p8(s53))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(6017,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s53))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[6016, 6015])).
% 12.37/8.35 tff(6018,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[6017, 5148, 6011, 5736, 6010, 5737])).
% 12.37/8.35 tff(6019,plain,((~trans(s59, s53)) | until2p8(s53) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(6020,plain,
% 12.37/8.35 (~trans(s59, s53)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[6019, 5236, 5138])).
% 12.37/8.35 tff(6021,assumption,(~until2p8(s30)), introduced(assumption)).
% 12.37/8.35 tff(6022,assumption,(trans(s59, s30)), introduced(assumption)).
% 12.37/8.35 tff(6023,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(6024,plain,
% 12.37/8.35 (((~last(s59)) | (~trans(s59, s30)) | (~xuntil7(s59)) | until2p8(s30)) <=> (until2p8(s30) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s30)))),
% 12.37/8.35 inference(rewrite,[status(thm)],[])).
% 12.37/8.35 tff(6025,plain,
% 12.37/8.35 (((~![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))))),
% 12.37/8.35 inference(monotonicity,[status(thm)],[6024])).
% 12.37/8.35 tff(6026,plain,
% 12.37/8.35 (((~![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)))),
% 12.37/8.35 inference(transitivity,[status(thm)],[6025, 6023])).
% 12.37/8.35 tff(6027,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s30)) | (~xuntil7(s59)) | until2p8(s30))),
% 12.37/8.35 inference(quant_inst,[status(thm)],[])).
% 12.37/8.35 tff(6028,plain,
% 12.37/8.35 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s30))),
% 12.37/8.35 inference(modus_ponens,[status(thm)],[6027, 6026])).
% 12.37/8.35 tff(6029,plain,
% 12.37/8.35 ($false),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[6028, 5148, 6022, 5736, 6021, 5737])).
% 12.37/8.35 tff(6030,plain,((~trans(s59, s30)) | until2p8(s30) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.35 tff(6031,plain,
% 12.37/8.35 (~trans(s59, s30)),
% 12.37/8.35 inference(unit_resolution,[status(thm)],[6030, 5466, 5138])).
% 12.37/8.35 tff(6032,assumption,(~until2p8(s18)), introduced(assumption)).
% 12.37/8.35 tff(6033,assumption,(trans(s59, s18)), introduced(assumption)).
% 12.37/8.35 tff(6034,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6035,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s18)) | (~xuntil7(s59)) | until2p8(s18)) <=> (until2p8(s18) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s18)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6036,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6035])).
% 12.37/8.36 tff(6037,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6036, 6034])).
% 12.37/8.36 tff(6038,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s18)) | (~xuntil7(s59)) | until2p8(s18))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6039,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s18))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6038, 6037])).
% 12.37/8.36 tff(6040,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6039, 5148, 6033, 5736, 6032, 5737])).
% 12.37/8.36 tff(6041,plain,((~trans(s59, s18)) | until2p8(s18) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6042,plain,
% 12.37/8.36 (~trans(s59, s18)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6041, 5586, 5138])).
% 12.37/8.36 tff(6043,assumption,(~until2p8(s28)), introduced(assumption)).
% 12.37/8.36 tff(6044,assumption,(trans(s59, s28)), introduced(assumption)).
% 12.37/8.36 tff(6045,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6046,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s28)) | (~xuntil7(s59)) | until2p8(s28)) <=> (until2p8(s28) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s28)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6047,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6046])).
% 12.37/8.36 tff(6048,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6047, 6045])).
% 12.37/8.36 tff(6049,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s28)) | (~xuntil7(s59)) | until2p8(s28))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6050,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s28))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6049, 6048])).
% 12.37/8.36 tff(6051,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6050, 5148, 6044, 5736, 6043, 5737])).
% 12.37/8.36 tff(6052,plain,((~trans(s59, s28)) | until2p8(s28) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6053,plain,
% 12.37/8.36 (~trans(s59, s28)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6052, 5486, 5138])).
% 12.37/8.36 tff(6054,assumption,(~until2p8(s14)), introduced(assumption)).
% 12.37/8.36 tff(6055,assumption,(trans(s59, s14)), introduced(assumption)).
% 12.37/8.36 tff(6056,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6057,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s14)) | (~xuntil7(s59)) | until2p8(s14)) <=> (until2p8(s14) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s14)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6058,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6057])).
% 12.37/8.36 tff(6059,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6058, 6056])).
% 12.37/8.36 tff(6060,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s14)) | (~xuntil7(s59)) | until2p8(s14))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6061,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s14))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6060, 6059])).
% 12.37/8.36 tff(6062,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6061, 5148, 6055, 5736, 6054, 5737])).
% 12.37/8.36 tff(6063,plain,((~trans(s59, s14)) | until2p8(s14) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6064,plain,
% 12.37/8.36 (~trans(s59, s14)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6063, 5626, 5138])).
% 12.37/8.36 tff(6065,assumption,(~until2p8(s7)), introduced(assumption)).
% 12.37/8.36 tff(6066,assumption,(trans(s59, s7)), introduced(assumption)).
% 12.37/8.36 tff(6067,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6068,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s7)) | (~xuntil7(s59)) | until2p8(s7)) <=> (until2p8(s7) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s7)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6069,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6068])).
% 12.37/8.36 tff(6070,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6069, 6067])).
% 12.37/8.36 tff(6071,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s7)) | (~xuntil7(s59)) | until2p8(s7))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6072,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s7))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6071, 6070])).
% 12.37/8.36 tff(6073,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6072, 5148, 6066, 5736, 6065, 5737])).
% 12.37/8.36 tff(6074,plain,((~trans(s59, s7)) | until2p8(s7) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6075,plain,
% 12.37/8.36 (~trans(s59, s7)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6074, 5696, 5138])).
% 12.37/8.36 tff(6076,assumption,(~until2p8(s15)), introduced(assumption)).
% 12.37/8.36 tff(6077,assumption,(trans(s59, s15)), introduced(assumption)).
% 12.37/8.36 tff(6078,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6079,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s15)) | (~xuntil7(s59)) | until2p8(s15)) <=> (until2p8(s15) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s15)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6080,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6079])).
% 12.37/8.36 tff(6081,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6080, 6078])).
% 12.37/8.36 tff(6082,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s15)) | (~xuntil7(s59)) | until2p8(s15))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6083,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s15))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6082, 6081])).
% 12.37/8.36 tff(6084,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6083, 5148, 6077, 5736, 6076, 5737])).
% 12.37/8.36 tff(6085,plain,((~trans(s59, s15)) | until2p8(s15) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6086,plain,
% 12.37/8.36 (~trans(s59, s15)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6085, 5616, 5138])).
% 12.37/8.36 tff(6087,assumption,(~until2p8(s33)), introduced(assumption)).
% 12.37/8.36 tff(6088,assumption,(trans(s59, s33)), introduced(assumption)).
% 12.37/8.36 tff(6089,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6090,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s33)) | (~xuntil7(s59)) | until2p8(s33)) <=> (until2p8(s33) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s33)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6091,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6090])).
% 12.37/8.36 tff(6092,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6091, 6089])).
% 12.37/8.36 tff(6093,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s33)) | (~xuntil7(s59)) | until2p8(s33))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6094,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s33))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6093, 6092])).
% 12.37/8.36 tff(6095,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6094, 5148, 6088, 5736, 6087, 5737])).
% 12.37/8.36 tff(6096,plain,((~trans(s59, s33)) | until2p8(s33) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6097,plain,
% 12.37/8.36 (~trans(s59, s33)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6096, 5436, 5138])).
% 12.37/8.36 tff(6098,assumption,(~until2p8(s35)), introduced(assumption)).
% 12.37/8.36 tff(6099,assumption,(trans(s59, s35)), introduced(assumption)).
% 12.37/8.36 tff(6100,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6101,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s35)) | (~xuntil7(s59)) | until2p8(s35)) <=> (until2p8(s35) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s35)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6102,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6101])).
% 12.37/8.36 tff(6103,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6102, 6100])).
% 12.37/8.36 tff(6104,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s35)) | (~xuntil7(s59)) | until2p8(s35))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6105,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s35))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6104, 6103])).
% 12.37/8.36 tff(6106,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6105, 5148, 6099, 5736, 6098, 5737])).
% 12.37/8.36 tff(6107,plain,((~trans(s59, s35)) | until2p8(s35) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6108,plain,
% 12.37/8.36 (~trans(s59, s35)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6107, 5416, 5138])).
% 12.37/8.36 tff(6109,assumption,(~until2p8(s24)), introduced(assumption)).
% 12.37/8.36 tff(6110,assumption,(trans(s59, s24)), introduced(assumption)).
% 12.37/8.36 tff(6111,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6112,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s24)) | (~xuntil7(s59)) | until2p8(s24)) <=> (until2p8(s24) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s24)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6113,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6112])).
% 12.37/8.36 tff(6114,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6113, 6111])).
% 12.37/8.36 tff(6115,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s24)) | (~xuntil7(s59)) | until2p8(s24))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6116,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s24))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6115, 6114])).
% 12.37/8.36 tff(6117,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6116, 5148, 6110, 5736, 6109, 5737])).
% 12.37/8.36 tff(6118,plain,((~trans(s59, s24)) | until2p8(s24) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6119,plain,
% 12.37/8.36 (~trans(s59, s24)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6118, 5526, 5138])).
% 12.37/8.36 tff(6120,assumption,(~until2p8(s47)), introduced(assumption)).
% 12.37/8.36 tff(6121,assumption,(trans(s59, s47)), introduced(assumption)).
% 12.37/8.36 tff(6122,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6123,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s47)) | (~xuntil7(s59)) | until2p8(s47)) <=> (until2p8(s47) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s47)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6124,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6123])).
% 12.37/8.36 tff(6125,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6124, 6122])).
% 12.37/8.36 tff(6126,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s47)) | (~xuntil7(s59)) | until2p8(s47))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6127,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s47))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6126, 6125])).
% 12.37/8.36 tff(6128,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6127, 5148, 6121, 5736, 6120, 5737])).
% 12.37/8.36 tff(6129,plain,((~trans(s59, s47)) | until2p8(s47) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6130,plain,
% 12.37/8.36 (~trans(s59, s47)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6129, 5296, 5138])).
% 12.37/8.36 tff(6131,assumption,(~until2p8(s6)), introduced(assumption)).
% 12.37/8.36 tff(6132,assumption,(trans(s59, s6)), introduced(assumption)).
% 12.37/8.36 tff(6133,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6134,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s6)) | (~xuntil7(s59)) | until2p8(s6)) <=> (until2p8(s6) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s6)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6135,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6134])).
% 12.37/8.36 tff(6136,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6135, 6133])).
% 12.37/8.36 tff(6137,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s6)) | (~xuntil7(s59)) | until2p8(s6))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6138,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s6))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6137, 6136])).
% 12.37/8.36 tff(6139,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6138, 5148, 6132, 5736, 6131, 5737])).
% 12.37/8.36 tff(6140,plain,((~trans(s59, s6)) | until2p8(s6) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6141,plain,
% 12.37/8.36 (~trans(s59, s6)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6140, 5706, 5138])).
% 12.37/8.36 tff(6142,assumption,(~until2p8(s13)), introduced(assumption)).
% 12.37/8.36 tff(6143,assumption,(trans(s59, s13)), introduced(assumption)).
% 12.37/8.36 tff(6144,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6145,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s13)) | (~xuntil7(s59)) | until2p8(s13)) <=> (until2p8(s13) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s13)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6146,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6145])).
% 12.37/8.36 tff(6147,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6146, 6144])).
% 12.37/8.36 tff(6148,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s13)) | (~xuntil7(s59)) | until2p8(s13))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6149,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s13))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6148, 6147])).
% 12.37/8.36 tff(6150,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6149, 5148, 6143, 5736, 6142, 5737])).
% 12.37/8.36 tff(6151,plain,((~trans(s59, s13)) | until2p8(s13) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6152,plain,
% 12.37/8.36 (~trans(s59, s13)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6151, 5636, 5138])).
% 12.37/8.36 tff(6153,assumption,(~until2p8(s17)), introduced(assumption)).
% 12.37/8.36 tff(6154,assumption,(trans(s59, s17)), introduced(assumption)).
% 12.37/8.36 tff(6155,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6156,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s17)) | (~xuntil7(s59)) | until2p8(s17)) <=> (until2p8(s17) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s17)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6157,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6156])).
% 12.37/8.36 tff(6158,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6157, 6155])).
% 12.37/8.36 tff(6159,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s17)) | (~xuntil7(s59)) | until2p8(s17))),
% 12.37/8.36 inference(quant_inst,[status(thm)],[])).
% 12.37/8.36 tff(6160,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s17))),
% 12.37/8.36 inference(modus_ponens,[status(thm)],[6159, 6158])).
% 12.37/8.36 tff(6161,plain,
% 12.37/8.36 ($false),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6160, 5148, 6154, 5736, 6153, 5737])).
% 12.37/8.36 tff(6162,plain,((~trans(s59, s17)) | until2p8(s17) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.36 tff(6163,plain,
% 12.37/8.36 (~trans(s59, s17)),
% 12.37/8.36 inference(unit_resolution,[status(thm)],[6162, 5596, 5138])).
% 12.37/8.36 tff(6164,assumption,(~until2p8(s45)), introduced(assumption)).
% 12.37/8.36 tff(6165,assumption,(trans(s59, s45)), introduced(assumption)).
% 12.37/8.36 tff(6166,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6167,plain,
% 12.37/8.36 (((~last(s59)) | (~trans(s59, s45)) | (~xuntil7(s59)) | until2p8(s45)) <=> (until2p8(s45) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s45)))),
% 12.37/8.36 inference(rewrite,[status(thm)],[])).
% 12.37/8.36 tff(6168,plain,
% 12.37/8.36 (((~![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))))),
% 12.37/8.36 inference(monotonicity,[status(thm)],[6167])).
% 12.37/8.36 tff(6169,plain,
% 12.37/8.36 (((~![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)))),
% 12.37/8.36 inference(transitivity,[status(thm)],[6168, 6166])).
% 12.37/8.36 tff(6170,plain,
% 12.37/8.36 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s45)) | (~xuntil7(s59)) | until2p8(s45))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6171,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s45))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6170, 6169])).
% 12.37/8.37 tff(6172,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6171, 5148, 6165, 5736, 6164, 5737])).
% 12.37/8.37 tff(6173,plain,((~trans(s59, s45)) | until2p8(s45) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6174,plain,
% 12.37/8.37 (~trans(s59, s45)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6173, 5316, 5138])).
% 12.37/8.37 tff(6175,assumption,(~until2p8(s40)), introduced(assumption)).
% 12.37/8.37 tff(6176,assumption,(trans(s59, s40)), introduced(assumption)).
% 12.37/8.37 tff(6177,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6178,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s40)) | (~xuntil7(s59)) | until2p8(s40)) <=> (until2p8(s40) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s40)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6179,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6178])).
% 12.37/8.37 tff(6180,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6179, 6177])).
% 12.37/8.37 tff(6181,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s40)) | (~xuntil7(s59)) | until2p8(s40))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6182,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s40))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 12.37/8.37 tff(6183,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6182, 5148, 6176, 5736, 6175, 5737])).
% 12.37/8.37 tff(6184,plain,((~trans(s59, s40)) | until2p8(s40) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6185,plain,
% 12.37/8.37 (~trans(s59, s40)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6184, 5366, 5138])).
% 12.37/8.37 tff(6186,assumption,(~until2p8(s27)), introduced(assumption)).
% 12.37/8.37 tff(6187,assumption,(trans(s59, s27)), introduced(assumption)).
% 12.37/8.37 tff(6188,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6189,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s27)) | (~xuntil7(s59)) | until2p8(s27)) <=> (until2p8(s27) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s27)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6190,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6189])).
% 12.37/8.37 tff(6191,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6190, 6188])).
% 12.37/8.37 tff(6192,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s27)) | (~xuntil7(s59)) | until2p8(s27))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6193,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s27))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6192, 6191])).
% 12.37/8.37 tff(6194,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6193, 5148, 6187, 5736, 6186, 5737])).
% 12.37/8.37 tff(6195,plain,((~trans(s59, s27)) | until2p8(s27) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6196,plain,
% 12.37/8.37 (~trans(s59, s27)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6195, 5496, 5138])).
% 12.37/8.37 tff(6197,assumption,(~until2p8(s3)), introduced(assumption)).
% 12.37/8.37 tff(6198,assumption,(trans(s59, s3)), introduced(assumption)).
% 12.37/8.37 tff(6199,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6200,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s3)) | (~xuntil7(s59)) | until2p8(s3)) <=> (until2p8(s3) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s3)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6201,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6200])).
% 12.37/8.37 tff(6202,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6201, 6199])).
% 12.37/8.37 tff(6203,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s3)) | (~xuntil7(s59)) | until2p8(s3))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6204,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s3))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6203, 6202])).
% 12.37/8.37 tff(6205,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6204, 5148, 6198, 5736, 6197, 5737])).
% 12.37/8.37 tff(6206,plain,((~trans(s59, s3)) | until2p8(s3) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6207,plain,
% 12.37/8.37 (~trans(s59, s3)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6206, 5791, 5138])).
% 12.37/8.37 tff(6208,assumption,(~until2p8(s50)), introduced(assumption)).
% 12.37/8.37 tff(6209,assumption,(trans(s59, s50)), introduced(assumption)).
% 12.37/8.37 tff(6210,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6211,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s50)) | (~xuntil7(s59)) | until2p8(s50)) <=> (until2p8(s50) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s50)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6212,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6211])).
% 12.37/8.37 tff(6213,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6212, 6210])).
% 12.37/8.37 tff(6214,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s50)) | (~xuntil7(s59)) | until2p8(s50))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6215,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s50))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6214, 6213])).
% 12.37/8.37 tff(6216,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6215, 5148, 6209, 5736, 6208, 5737])).
% 12.37/8.37 tff(6217,plain,((~trans(s59, s50)) | until2p8(s50) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6218,plain,
% 12.37/8.37 (~trans(s59, s50)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6217, 5266, 5138])).
% 12.37/8.37 tff(6219,assumption,(~until2p8(s59)), introduced(assumption)).
% 12.37/8.37 tff(6220,assumption,(trans(s59, s59)), introduced(assumption)).
% 12.37/8.37 tff(6221,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6222,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s59)) | (~xuntil7(s59)) | until2p8(s59)) <=> (until2p8(s59) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s59)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6223,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6222])).
% 12.37/8.37 tff(6224,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6223, 6221])).
% 12.37/8.37 tff(6225,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s59)) | (~xuntil7(s59)) | until2p8(s59))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6226,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s59))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6225, 6224])).
% 12.37/8.37 tff(6227,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6226, 5148, 6220, 5736, 6219, 5737])).
% 12.37/8.37 tff(6228,plain,((~trans(s59, s59)) | until2p8(s59) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6229,plain,
% 12.37/8.37 (~trans(s59, s59)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6228, 5167, 5138])).
% 12.37/8.37 tff(6230,assumption,(~until2p8(s8)), introduced(assumption)).
% 12.37/8.37 tff(6231,assumption,(trans(s59, s8)), introduced(assumption)).
% 12.37/8.37 tff(6232,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6233,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s8)) | (~xuntil7(s59)) | until2p8(s8)) <=> (until2p8(s8) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s8)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6234,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6233])).
% 12.37/8.37 tff(6235,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6234, 6232])).
% 12.37/8.37 tff(6236,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s8)) | (~xuntil7(s59)) | until2p8(s8))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6237,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s8))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6236, 6235])).
% 12.37/8.37 tff(6238,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6237, 5148, 6231, 5736, 6230, 5737])).
% 12.37/8.37 tff(6239,plain,((~trans(s59, s8)) | until2p8(s8) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6240,plain,
% 12.37/8.37 (~trans(s59, s8)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6239, 5686, 5138])).
% 12.37/8.37 tff(6241,assumption,(~until2p8(s31)), introduced(assumption)).
% 12.37/8.37 tff(6242,assumption,(trans(s59, s31)), introduced(assumption)).
% 12.37/8.37 tff(6243,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6244,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s31)) | (~xuntil7(s59)) | until2p8(s31)) <=> (until2p8(s31) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s31)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6245,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6244])).
% 12.37/8.37 tff(6246,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6245, 6243])).
% 12.37/8.37 tff(6247,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s31)) | (~xuntil7(s59)) | until2p8(s31))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6248,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s31))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6247, 6246])).
% 12.37/8.37 tff(6249,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6248, 5148, 6242, 5736, 6241, 5737])).
% 12.37/8.37 tff(6250,plain,((~trans(s59, s31)) | until2p8(s31) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6251,plain,
% 12.37/8.37 (~trans(s59, s31)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6250, 5456, 5138])).
% 12.37/8.37 tff(6252,assumption,(~until2p8(s39)), introduced(assumption)).
% 12.37/8.37 tff(6253,assumption,(trans(s59, s39)), introduced(assumption)).
% 12.37/8.37 tff(6254,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6255,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s39)) | (~xuntil7(s59)) | until2p8(s39)) <=> (until2p8(s39) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s39)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6256,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6255])).
% 12.37/8.37 tff(6257,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6256, 6254])).
% 12.37/8.37 tff(6258,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s39)) | (~xuntil7(s59)) | until2p8(s39))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6259,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s39))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 12.37/8.37 tff(6260,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6259, 5148, 6253, 5736, 6252, 5737])).
% 12.37/8.37 tff(6261,plain,((~trans(s59, s39)) | until2p8(s39) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6262,plain,
% 12.37/8.37 (~trans(s59, s39)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6261, 5376, 5138])).
% 12.37/8.37 tff(6263,assumption,(~until2p8(s52)), introduced(assumption)).
% 12.37/8.37 tff(6264,assumption,(trans(s59, s52)), introduced(assumption)).
% 12.37/8.37 tff(6265,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6266,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s52)) | (~xuntil7(s59)) | until2p8(s52)) <=> (until2p8(s52) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s52)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6267,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6266])).
% 12.37/8.37 tff(6268,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6267, 6265])).
% 12.37/8.37 tff(6269,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s52)) | (~xuntil7(s59)) | until2p8(s52))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6270,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s52))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6269, 6268])).
% 12.37/8.37 tff(6271,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6270, 5148, 6264, 5736, 6263, 5737])).
% 12.37/8.37 tff(6272,plain,((~trans(s59, s52)) | until2p8(s52) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6273,plain,
% 12.37/8.37 (~trans(s59, s52)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6272, 5246, 5138])).
% 12.37/8.37 tff(6274,assumption,(~until2p8(s46)), introduced(assumption)).
% 12.37/8.37 tff(6275,assumption,(trans(s59, s46)), introduced(assumption)).
% 12.37/8.37 tff(6276,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6277,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s46)) | (~xuntil7(s59)) | until2p8(s46)) <=> (until2p8(s46) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s46)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6278,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6277])).
% 12.37/8.37 tff(6279,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6278, 6276])).
% 12.37/8.37 tff(6280,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s46)) | (~xuntil7(s59)) | until2p8(s46))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6281,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s46))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6280, 6279])).
% 12.37/8.37 tff(6282,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6281, 5148, 6275, 5736, 6274, 5737])).
% 12.37/8.37 tff(6283,plain,((~trans(s59, s46)) | until2p8(s46) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6284,plain,
% 12.37/8.37 (~trans(s59, s46)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6283, 5306, 5138])).
% 12.37/8.37 tff(6285,assumption,(~until2p8(s49)), introduced(assumption)).
% 12.37/8.37 tff(6286,assumption,(trans(s59, s49)), introduced(assumption)).
% 12.37/8.37 tff(6287,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6288,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s49)) | (~xuntil7(s59)) | until2p8(s49)) <=> (until2p8(s49) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s49)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6289,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6288])).
% 12.37/8.37 tff(6290,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6289, 6287])).
% 12.37/8.37 tff(6291,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s49)) | (~xuntil7(s59)) | until2p8(s49))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6292,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s49))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6291, 6290])).
% 12.37/8.37 tff(6293,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6292, 5148, 6286, 5736, 6285, 5737])).
% 12.37/8.37 tff(6294,plain,((~trans(s59, s49)) | until2p8(s49) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6295,plain,
% 12.37/8.37 (~trans(s59, s49)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6294, 5276, 5138])).
% 12.37/8.37 tff(6296,assumption,(~until2p8(s19)), introduced(assumption)).
% 12.37/8.37 tff(6297,assumption,(trans(s59, s19)), introduced(assumption)).
% 12.37/8.37 tff(6298,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6299,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s19)) | (~xuntil7(s59)) | until2p8(s19)) <=> (until2p8(s19) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s19)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6300,plain,
% 12.37/8.37 (((~![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))))),
% 12.37/8.37 inference(monotonicity,[status(thm)],[6299])).
% 12.37/8.37 tff(6301,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(transitivity,[status(thm)],[6300, 6298])).
% 12.37/8.37 tff(6302,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s19)) | (~xuntil7(s59)) | until2p8(s19))),
% 12.37/8.37 inference(quant_inst,[status(thm)],[])).
% 12.37/8.37 tff(6303,plain,
% 12.37/8.37 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s19))),
% 12.37/8.37 inference(modus_ponens,[status(thm)],[6302, 6301])).
% 12.37/8.37 tff(6304,plain,
% 12.37/8.37 ($false),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6303, 5148, 6297, 5736, 6296, 5737])).
% 12.37/8.37 tff(6305,plain,((~trans(s59, s19)) | until2p8(s19) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.37 tff(6306,plain,
% 12.37/8.37 (~trans(s59, s19)),
% 12.37/8.37 inference(unit_resolution,[status(thm)],[6305, 5576, 5138])).
% 12.37/8.37 tff(6307,assumption,(~until2p8(s58)), introduced(assumption)).
% 12.37/8.37 tff(6308,assumption,(trans(s59, s58)), introduced(assumption)).
% 12.37/8.37 tff(6309,plain,
% 12.37/8.37 (((~![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)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.37 tff(6310,plain,
% 12.37/8.37 (((~last(s59)) | (~trans(s59, s58)) | (~xuntil7(s59)) | until2p8(s58)) <=> (until2p8(s58) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s58)))),
% 12.37/8.37 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6311,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6310])).
% 12.37/8.38 tff(6312,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6311, 6309])).
% 12.37/8.38 tff(6313,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s58)) | (~xuntil7(s59)) | until2p8(s58))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6314,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s58))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6313, 6312])).
% 12.37/8.38 tff(6315,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6314, 5148, 6308, 5736, 6307, 5737])).
% 12.37/8.38 tff(6316,plain,((~trans(s59, s58)) | until2p8(s58) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6317,plain,
% 12.37/8.38 (~trans(s59, s58)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6316, 5186, 5138])).
% 12.37/8.38 tff(6318,assumption,(~until2p8(s21)), introduced(assumption)).
% 12.37/8.38 tff(6319,assumption,(trans(s59, s21)), introduced(assumption)).
% 12.37/8.38 tff(6320,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6321,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s21)) | (~xuntil7(s59)) | until2p8(s21)) <=> (until2p8(s21) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s21)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6322,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6321])).
% 12.37/8.38 tff(6323,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6322, 6320])).
% 12.37/8.38 tff(6324,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s21)) | (~xuntil7(s59)) | until2p8(s21))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6325,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s21))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6324, 6323])).
% 12.37/8.38 tff(6326,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6325, 5148, 6319, 5736, 6318, 5737])).
% 12.37/8.38 tff(6327,plain,((~trans(s59, s21)) | until2p8(s21) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6328,plain,
% 12.37/8.38 (~trans(s59, s21)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6327, 5556, 5138])).
% 12.37/8.38 tff(6329,assumption,(~until2p8(s23)), introduced(assumption)).
% 12.37/8.38 tff(6330,assumption,(trans(s59, s23)), introduced(assumption)).
% 12.37/8.38 tff(6331,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6332,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s23)) | (~xuntil7(s59)) | until2p8(s23)) <=> (until2p8(s23) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s23)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6333,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6332])).
% 12.37/8.38 tff(6334,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6333, 6331])).
% 12.37/8.38 tff(6335,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s23)) | (~xuntil7(s59)) | until2p8(s23))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6336,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s23))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6335, 6334])).
% 12.37/8.38 tff(6337,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6336, 5148, 6330, 5736, 6329, 5737])).
% 12.37/8.38 tff(6338,plain,((~trans(s59, s23)) | until2p8(s23) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6339,plain,
% 12.37/8.38 (~trans(s59, s23)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6338, 5536, 5138])).
% 12.37/8.38 tff(6340,assumption,(~until2p8(s16)), introduced(assumption)).
% 12.37/8.38 tff(6341,assumption,(trans(s59, s16)), introduced(assumption)).
% 12.37/8.38 tff(6342,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6343,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s16)) | (~xuntil7(s59)) | until2p8(s16)) <=> (until2p8(s16) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s16)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6344,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6343])).
% 12.37/8.38 tff(6345,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6344, 6342])).
% 12.37/8.38 tff(6346,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s16)) | (~xuntil7(s59)) | until2p8(s16))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6347,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s16))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6346, 6345])).
% 12.37/8.38 tff(6348,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6347, 5148, 6341, 5736, 6340, 5737])).
% 12.37/8.38 tff(6349,plain,((~trans(s59, s16)) | until2p8(s16) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6350,plain,
% 12.37/8.38 (~trans(s59, s16)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6349, 5606, 5138])).
% 12.37/8.38 tff(6351,assumption,(~until2p8(s42)), introduced(assumption)).
% 12.37/8.38 tff(6352,assumption,(trans(s59, s42)), introduced(assumption)).
% 12.37/8.38 tff(6353,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6354,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s42)) | (~xuntil7(s59)) | until2p8(s42)) <=> (until2p8(s42) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s42)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6355,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6354])).
% 12.37/8.38 tff(6356,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6355, 6353])).
% 12.37/8.38 tff(6357,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s42)) | (~xuntil7(s59)) | until2p8(s42))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6358,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s42))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6357, 6356])).
% 12.37/8.38 tff(6359,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6358, 5148, 6352, 5736, 6351, 5737])).
% 12.37/8.38 tff(6360,plain,((~trans(s59, s42)) | until2p8(s42) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6361,plain,
% 12.37/8.38 (~trans(s59, s42)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6360, 5346, 5138])).
% 12.37/8.38 tff(6362,assumption,(~until2p8(s11)), introduced(assumption)).
% 12.37/8.38 tff(6363,assumption,(trans(s59, s11)), introduced(assumption)).
% 12.37/8.38 tff(6364,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6365,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s11)) | (~xuntil7(s59)) | until2p8(s11)) <=> (until2p8(s11) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s11)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6366,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6365])).
% 12.37/8.38 tff(6367,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6366, 6364])).
% 12.37/8.38 tff(6368,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s11)) | (~xuntil7(s59)) | until2p8(s11))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6369,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s11))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6368, 6367])).
% 12.37/8.38 tff(6370,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6369, 5148, 6363, 5736, 6362, 5737])).
% 12.37/8.38 tff(6371,plain,((~trans(s59, s11)) | until2p8(s11) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6372,plain,
% 12.37/8.38 (~trans(s59, s11)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6371, 5656, 5138])).
% 12.37/8.38 tff(6373,assumption,(~until2p8(s54)), introduced(assumption)).
% 12.37/8.38 tff(6374,assumption,(trans(s59, s54)), introduced(assumption)).
% 12.37/8.38 tff(6375,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6376,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s54)) | (~xuntil7(s59)) | until2p8(s54)) <=> (until2p8(s54) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s54)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6377,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6376])).
% 12.37/8.38 tff(6378,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6377, 6375])).
% 12.37/8.38 tff(6379,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s54)) | (~xuntil7(s59)) | until2p8(s54))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6380,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s54))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6379, 6378])).
% 12.37/8.38 tff(6381,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6380, 5148, 6374, 5736, 6373, 5737])).
% 12.37/8.38 tff(6382,plain,((~trans(s59, s54)) | until2p8(s54) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6383,plain,
% 12.37/8.38 (~trans(s59, s54)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6382, 5226, 5138])).
% 12.37/8.38 tff(6384,assumption,(~until2p8(s57)), introduced(assumption)).
% 12.37/8.38 tff(6385,assumption,(trans(s59, s57)), introduced(assumption)).
% 12.37/8.38 tff(6386,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6387,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s57)) | (~xuntil7(s59)) | until2p8(s57)) <=> (until2p8(s57) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s57)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6388,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6387])).
% 12.37/8.38 tff(6389,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6388, 6386])).
% 12.37/8.38 tff(6390,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s57)) | (~xuntil7(s59)) | until2p8(s57))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6391,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s57))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6390, 6389])).
% 12.37/8.38 tff(6392,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6391, 5148, 6385, 5736, 6384, 5737])).
% 12.37/8.38 tff(6393,plain,((~trans(s59, s57)) | until2p8(s57) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6394,plain,
% 12.37/8.38 (~trans(s59, s57)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6393, 5196, 5138])).
% 12.37/8.38 tff(6395,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6396,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0)))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6397,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6396, 6395])).
% 12.37/8.38 tff(6398,plain,
% 12.37/8.38 (until2p8(s1) | (~xuntil2p9(s0))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6397, 88, 5177])).
% 12.37/8.38 tff(6399,plain,
% 12.37/8.38 (~xuntil2p9(s0)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6398, 5811])).
% 12.37/8.38 tff(6400,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6401,plain,
% 12.37/8.38 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s0) | xuntil2p9(s0) | (~until2p8(s0)))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6402,plain,
% 12.37/8.38 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s0) | xuntil2p9(s0) | (~until2p8(s0))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6401, 6400])).
% 12.37/8.38 tff(6403,plain,
% 12.37/8.38 (xuntil2p9(s0) | (~until2p8(s0))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6402, 5162, 4332])).
% 12.37/8.38 tff(6404,plain,
% 12.37/8.38 (~until2p8(s0)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6403, 6399])).
% 12.37/8.38 tff(6405,assumption,(~until2p8(s0)), introduced(assumption)).
% 12.37/8.38 tff(6406,assumption,(trans(s59, s0)), introduced(assumption)).
% 12.37/8.38 tff(6407,plain,
% 12.37/8.38 (((~![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))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6408,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s0)) | (~xuntil7(s59)) | until2p8(s0)) <=> ((~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s0)) | until2p8(s0))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6409,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6408])).
% 12.37/8.38 tff(6410,plain,
% 12.37/8.38 (((~![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))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6409, 6407])).
% 12.37/8.38 tff(6411,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s0)) | (~xuntil7(s59)) | until2p8(s0))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6412,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s0)) | until2p8(s0)),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6411, 6410])).
% 12.37/8.38 tff(6413,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6412, 5148, 6406, 5736, 5737, 6405])).
% 12.37/8.38 tff(6414,plain,((~trans(s59, s0)) | (~xuntil7(s59)) | until2p8(s0)), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6415,plain,
% 12.37/8.38 (~trans(s59, s0)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6414, 5138, 6404])).
% 12.37/8.38 tff(6416,assumption,(~until2p8(s5)), introduced(assumption)).
% 12.37/8.38 tff(6417,assumption,(trans(s59, s5)), introduced(assumption)).
% 12.37/8.38 tff(6418,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6419,plain,
% 12.37/8.38 (((~last(s59)) | (~trans(s59, s5)) | (~xuntil7(s59)) | until2p8(s5)) <=> (until2p8(s5) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s5)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6420,plain,
% 12.37/8.38 (((~![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))))),
% 12.37/8.38 inference(monotonicity,[status(thm)],[6419])).
% 12.37/8.38 tff(6421,plain,
% 12.37/8.38 (((~![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)))),
% 12.37/8.38 inference(transitivity,[status(thm)],[6420, 6418])).
% 12.37/8.38 tff(6422,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s5)) | (~xuntil7(s59)) | until2p8(s5))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6423,plain,
% 12.37/8.38 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s5))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6422, 6421])).
% 12.37/8.38 tff(6424,plain,
% 12.37/8.38 ($false),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6423, 5148, 6417, 5736, 6416, 5737])).
% 12.37/8.38 tff(6425,plain,((~trans(s59, s5)) | until2p8(s5) | (~xuntil7(s59))), inference(lemma,lemma(discharge,[]))).
% 12.37/8.38 tff(6426,plain,
% 12.37/8.38 (~trans(s59, s5)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6425, 5716, 5138])).
% 12.37/8.38 tff(6427,assumption,(~loop), introduced(assumption)).
% 12.37/8.38 tff(6428,plain,
% 12.37/8.38 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil7(X))) <=> (loop | (~last(X)) | (~xuntil7(X))))),
% 12.37/8.38 inference(bind,[status(th)],[])).
% 12.37/8.38 tff(6429,plain,
% 12.37/8.38 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 12.37/8.38 inference(quant_intro,[status(thm)],[6428])).
% 12.37/8.38 tff(6430,plain,
% 12.37/8.38 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6431,plain,
% 12.37/8.38 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil7(X))) <=> (loop | (~last(X)) | (~xuntil7(X))))),
% 12.37/8.38 inference(bind,[status(th)],[])).
% 12.37/8.38 tff(6432,plain,
% 12.37/8.38 (![X: $i] : ((loop | (~last(X))) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 12.37/8.38 inference(quant_intro,[status(thm)],[6431])).
% 12.37/8.38 tff(6433,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty6')).
% 12.37/8.38 tff(6434,plain,
% 12.37/8.38 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6433, 6432])).
% 12.37/8.38 tff(6435,plain,
% 12.37/8.38 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6434, 6430])).
% 12.37/8.38 tff(6436,plain,(
% 12.37/8.38 ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 12.37/8.38 inference(skolemize,[status(sab)],[6435])).
% 12.37/8.38 tff(6437,plain,
% 12.37/8.38 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6436, 6429])).
% 12.37/8.38 tff(6438,plain,
% 12.37/8.38 (((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | (loop | (~last(s59)) | (~xuntil7(s59)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | loop | (~last(s59)) | (~xuntil7(s59)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6439,plain,
% 12.37/8.38 ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | (loop | (~last(s59)) | (~xuntil7(s59)))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6440,plain,
% 12.37/8.38 ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | loop | (~last(s59)) | (~xuntil7(s59))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6439, 6438])).
% 12.37/8.38 tff(6441,plain,
% 12.37/8.38 (loop | (~xuntil7(s59))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6440, 5148, 6437])).
% 12.37/8.38 tff(6442,plain,
% 12.37/8.38 (~xuntil7(s59)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6441, 6427])).
% 12.37/8.38 tff(6443,plain,
% 12.37/8.38 (^[X: $i] : refl((loop | (~always5(X)) | (~last(X))) <=> (loop | (~always5(X)) | (~last(X))))),
% 12.37/8.38 inference(bind,[status(th)],[])).
% 12.37/8.38 tff(6444,plain,
% 12.37/8.38 (![X: $i] : (loop | (~always5(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 12.37/8.38 inference(quant_intro,[status(thm)],[6443])).
% 12.37/8.38 tff(6445,plain,
% 12.37/8.38 (![X: $i] : (loop | (~always5(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6446,plain,
% 12.37/8.38 (^[X: $i] : rewrite(((loop | (~always5(X))) | (~last(X))) <=> (loop | (~always5(X)) | (~last(X))))),
% 12.37/8.38 inference(bind,[status(th)],[])).
% 12.37/8.38 tff(6447,plain,
% 12.37/8.38 (![X: $i] : ((loop | (~always5(X))) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 12.37/8.38 inference(quant_intro,[status(thm)],[6446])).
% 12.37/8.38 tff(6448,axiom,(![X: $i] : ((loop | (~always5(X))) | (~last(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty3')).
% 12.37/8.38 tff(6449,plain,
% 12.37/8.38 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6448, 6447])).
% 12.37/8.38 tff(6450,plain,
% 12.37/8.38 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6449, 6445])).
% 12.37/8.38 tff(6451,plain,(
% 12.37/8.38 ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 12.37/8.38 inference(skolemize,[status(sab)],[6450])).
% 12.37/8.38 tff(6452,plain,
% 12.37/8.38 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6451, 6444])).
% 12.37/8.38 tff(6453,plain,
% 12.37/8.38 (((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | (loop | (~always5(s59)) | (~last(s59)))) <=> ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | loop | (~always5(s59)) | (~last(s59)))),
% 12.37/8.38 inference(rewrite,[status(thm)],[])).
% 12.37/8.38 tff(6454,plain,
% 12.37/8.38 ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | (loop | (~always5(s59)) | (~last(s59)))),
% 12.37/8.38 inference(quant_inst,[status(thm)],[])).
% 12.37/8.38 tff(6455,plain,
% 12.37/8.38 ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | loop | (~always5(s59)) | (~last(s59))),
% 12.37/8.38 inference(modus_ponens,[status(thm)],[6454, 6453])).
% 12.37/8.38 tff(6456,plain,
% 12.37/8.38 (loop | (~always5(s59))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6455, 5148, 6452])).
% 12.37/8.38 tff(6457,plain,
% 12.37/8.38 (~always5(s59)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6456, 6427])).
% 12.37/8.38 tff(6458,plain,
% 12.37/8.38 (~until6(s59)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5137, 4345, 6457, 6442])).
% 12.37/8.38 tff(6459,plain,
% 12.37/8.38 (~xuntil7(s58)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5130, 6458])).
% 12.37/8.38 tff(6460,plain,
% 12.37/8.38 (~always5(s58)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3867, 6457])).
% 12.37/8.38 tff(6461,plain,
% 12.37/8.38 (xuntil7(s58) | (~until6(s58))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5124, 4345, 6460])).
% 12.37/8.38 tff(6462,plain,
% 12.37/8.38 (~until6(s58)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6461, 6459])).
% 12.37/8.38 tff(6463,plain,
% 12.37/8.38 (~xuntil7(s57)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5117, 6462])).
% 12.37/8.38 tff(6464,plain,
% 12.37/8.38 (~always5(s57)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3875, 6460])).
% 12.37/8.38 tff(6465,plain,
% 12.37/8.38 (xuntil7(s57) | (~until6(s57))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5111, 4345, 6464])).
% 12.37/8.38 tff(6466,plain,
% 12.37/8.38 (~until6(s57)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6465, 6463])).
% 12.37/8.38 tff(6467,plain,
% 12.37/8.38 (~xuntil7(s56)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5104, 6466])).
% 12.37/8.38 tff(6468,plain,
% 12.37/8.38 (~always5(s56)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3883, 6464])).
% 12.37/8.38 tff(6469,plain,
% 12.37/8.38 (xuntil7(s56) | (~until6(s56))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5098, 4345, 6468])).
% 12.37/8.38 tff(6470,plain,
% 12.37/8.38 (~until6(s56)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6469, 6467])).
% 12.37/8.38 tff(6471,plain,
% 12.37/8.38 (~xuntil7(s55)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5091, 6470])).
% 12.37/8.38 tff(6472,plain,
% 12.37/8.38 (~always5(s55)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3891, 6468])).
% 12.37/8.38 tff(6473,plain,
% 12.37/8.38 (xuntil7(s55) | (~until6(s55))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5085, 4345, 6472])).
% 12.37/8.38 tff(6474,plain,
% 12.37/8.38 (~until6(s55)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6473, 6471])).
% 12.37/8.38 tff(6475,plain,
% 12.37/8.38 (~xuntil7(s54)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5078, 6474])).
% 12.37/8.38 tff(6476,plain,
% 12.37/8.38 (~always5(s54)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3899, 6472])).
% 12.37/8.38 tff(6477,plain,
% 12.37/8.38 (xuntil7(s54) | (~until6(s54))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5072, 4345, 6476])).
% 12.37/8.38 tff(6478,plain,
% 12.37/8.38 (~until6(s54)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6477, 6475])).
% 12.37/8.38 tff(6479,plain,
% 12.37/8.38 (~xuntil7(s53)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5065, 6478])).
% 12.37/8.38 tff(6480,plain,
% 12.37/8.38 (~always5(s53)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3907, 6476])).
% 12.37/8.38 tff(6481,plain,
% 12.37/8.38 (xuntil7(s53) | (~until6(s53))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5059, 4345, 6480])).
% 12.37/8.38 tff(6482,plain,
% 12.37/8.38 (~until6(s53)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6481, 6479])).
% 12.37/8.38 tff(6483,plain,
% 12.37/8.38 (~xuntil7(s52)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5052, 6482])).
% 12.37/8.38 tff(6484,plain,
% 12.37/8.38 (~always5(s52)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3915, 6480])).
% 12.37/8.38 tff(6485,plain,
% 12.37/8.38 (xuntil7(s52) | (~until6(s52))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5046, 4345, 6484])).
% 12.37/8.38 tff(6486,plain,
% 12.37/8.38 (~until6(s52)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6485, 6483])).
% 12.37/8.38 tff(6487,plain,
% 12.37/8.38 (~xuntil7(s51)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5039, 6486])).
% 12.37/8.38 tff(6488,plain,
% 12.37/8.38 (~always5(s51)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3923, 6484])).
% 12.37/8.38 tff(6489,plain,
% 12.37/8.38 (xuntil7(s51) | (~until6(s51))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5033, 4345, 6488])).
% 12.37/8.38 tff(6490,plain,
% 12.37/8.38 (~until6(s51)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6489, 6487])).
% 12.37/8.38 tff(6491,plain,
% 12.37/8.38 (~xuntil7(s50)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5026, 6490])).
% 12.37/8.38 tff(6492,plain,
% 12.37/8.38 (~always5(s50)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3931, 6488])).
% 12.37/8.38 tff(6493,plain,
% 12.37/8.38 (xuntil7(s50) | (~until6(s50))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5020, 4345, 6492])).
% 12.37/8.38 tff(6494,plain,
% 12.37/8.38 (~until6(s50)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6493, 6491])).
% 12.37/8.38 tff(6495,plain,
% 12.37/8.38 (~xuntil7(s49)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5013, 6494])).
% 12.37/8.38 tff(6496,plain,
% 12.37/8.38 (~always5(s49)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3939, 6492])).
% 12.37/8.38 tff(6497,plain,
% 12.37/8.38 (xuntil7(s49) | (~until6(s49))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5007, 4345, 6496])).
% 12.37/8.38 tff(6498,plain,
% 12.37/8.38 (~until6(s49)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6497, 6495])).
% 12.37/8.38 tff(6499,plain,
% 12.37/8.38 (~xuntil7(s48)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[5000, 6498])).
% 12.37/8.38 tff(6500,plain,
% 12.37/8.38 (~always5(s48)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3947, 6496])).
% 12.37/8.38 tff(6501,plain,
% 12.37/8.38 (xuntil7(s48) | (~until6(s48))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4994, 4345, 6500])).
% 12.37/8.38 tff(6502,plain,
% 12.37/8.38 (~until6(s48)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6501, 6499])).
% 12.37/8.38 tff(6503,plain,
% 12.37/8.38 (~xuntil7(s47)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4987, 6502])).
% 12.37/8.38 tff(6504,plain,
% 12.37/8.38 (~always5(s47)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3955, 6500])).
% 12.37/8.38 tff(6505,plain,
% 12.37/8.38 (xuntil7(s47) | (~until6(s47))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4981, 4345, 6504])).
% 12.37/8.38 tff(6506,plain,
% 12.37/8.38 (~until6(s47)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6505, 6503])).
% 12.37/8.38 tff(6507,plain,
% 12.37/8.38 (~xuntil7(s46)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4974, 6506])).
% 12.37/8.38 tff(6508,plain,
% 12.37/8.38 (~always5(s46)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3963, 6504])).
% 12.37/8.38 tff(6509,plain,
% 12.37/8.38 (xuntil7(s46) | (~until6(s46))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4968, 4345, 6508])).
% 12.37/8.38 tff(6510,plain,
% 12.37/8.38 (~until6(s46)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6509, 6507])).
% 12.37/8.38 tff(6511,plain,
% 12.37/8.38 (~xuntil7(s45)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4961, 6510])).
% 12.37/8.38 tff(6512,plain,
% 12.37/8.38 (~always5(s45)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3971, 6508])).
% 12.37/8.38 tff(6513,plain,
% 12.37/8.38 (xuntil7(s45) | (~until6(s45))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4955, 4345, 6512])).
% 12.37/8.38 tff(6514,plain,
% 12.37/8.38 (~until6(s45)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6513, 6511])).
% 12.37/8.38 tff(6515,plain,
% 12.37/8.38 (~xuntil7(s44)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4948, 6514])).
% 12.37/8.38 tff(6516,plain,
% 12.37/8.38 (~always5(s44)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3979, 6512])).
% 12.37/8.38 tff(6517,plain,
% 12.37/8.38 (xuntil7(s44) | (~until6(s44))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4942, 4345, 6516])).
% 12.37/8.38 tff(6518,plain,
% 12.37/8.38 (~until6(s44)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6517, 6515])).
% 12.37/8.38 tff(6519,plain,
% 12.37/8.38 (~xuntil7(s43)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4935, 6518])).
% 12.37/8.38 tff(6520,plain,
% 12.37/8.38 (~always5(s43)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3987, 6516])).
% 12.37/8.38 tff(6521,plain,
% 12.37/8.38 (xuntil7(s43) | (~until6(s43))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4929, 4345, 6520])).
% 12.37/8.38 tff(6522,plain,
% 12.37/8.38 (~until6(s43)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6521, 6519])).
% 12.37/8.38 tff(6523,plain,
% 12.37/8.38 (~xuntil7(s42)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4922, 6522])).
% 12.37/8.38 tff(6524,plain,
% 12.37/8.38 (~always5(s42)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[3995, 6520])).
% 12.37/8.38 tff(6525,plain,
% 12.37/8.38 (xuntil7(s42) | (~until6(s42))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4916, 4345, 6524])).
% 12.37/8.38 tff(6526,plain,
% 12.37/8.38 (~until6(s42)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6525, 6523])).
% 12.37/8.38 tff(6527,plain,
% 12.37/8.38 (~xuntil7(s41)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4909, 6526])).
% 12.37/8.38 tff(6528,plain,
% 12.37/8.38 (~always5(s41)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4003, 6524])).
% 12.37/8.38 tff(6529,plain,
% 12.37/8.38 (xuntil7(s41) | (~until6(s41))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4903, 4345, 6528])).
% 12.37/8.38 tff(6530,plain,
% 12.37/8.38 (~until6(s41)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6529, 6527])).
% 12.37/8.38 tff(6531,plain,
% 12.37/8.38 (~xuntil7(s40)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4896, 6530])).
% 12.37/8.38 tff(6532,plain,
% 12.37/8.38 (~always5(s40)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4011, 6528])).
% 12.37/8.38 tff(6533,plain,
% 12.37/8.38 (xuntil7(s40) | (~until6(s40))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4890, 4345, 6532])).
% 12.37/8.38 tff(6534,plain,
% 12.37/8.38 (~until6(s40)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6533, 6531])).
% 12.37/8.38 tff(6535,plain,
% 12.37/8.38 (~xuntil7(s39)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4883, 6534])).
% 12.37/8.38 tff(6536,plain,
% 12.37/8.38 (~always5(s39)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4019, 6532])).
% 12.37/8.38 tff(6537,plain,
% 12.37/8.38 (xuntil7(s39) | (~until6(s39))),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4877, 4345, 6536])).
% 12.37/8.38 tff(6538,plain,
% 12.37/8.38 (~until6(s39)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[6537, 6535])).
% 12.37/8.38 tff(6539,plain,
% 12.37/8.38 (~xuntil7(s38)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4870, 6538])).
% 12.37/8.38 tff(6540,plain,
% 12.37/8.38 (~always5(s38)),
% 12.37/8.38 inference(unit_resolution,[status(thm)],[4027, 6536])).
% 12.37/8.38 tff(6541,plain,
% 12.37/8.38 (xuntil7(s38) | (~until6(s38))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4864, 4345, 6540])).
% 12.37/8.39 tff(6542,plain,
% 12.37/8.39 (~until6(s38)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6541, 6539])).
% 12.37/8.39 tff(6543,plain,
% 12.37/8.39 (~xuntil7(s37)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4857, 6542])).
% 12.37/8.39 tff(6544,plain,
% 12.37/8.39 (~always5(s37)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4035, 6540])).
% 12.37/8.39 tff(6545,plain,
% 12.37/8.39 (xuntil7(s37) | (~until6(s37))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4851, 4345, 6544])).
% 12.37/8.39 tff(6546,plain,
% 12.37/8.39 (~until6(s37)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6545, 6543])).
% 12.37/8.39 tff(6547,plain,
% 12.37/8.39 (~xuntil7(s36)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4844, 6546])).
% 12.37/8.39 tff(6548,plain,
% 12.37/8.39 (~always5(s36)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4043, 6544])).
% 12.37/8.39 tff(6549,plain,
% 12.37/8.39 (xuntil7(s36) | (~until6(s36))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4838, 4345, 6548])).
% 12.37/8.39 tff(6550,plain,
% 12.37/8.39 (~until6(s36)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6549, 6547])).
% 12.37/8.39 tff(6551,plain,
% 12.37/8.39 (~xuntil7(s35)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4831, 6550])).
% 12.37/8.39 tff(6552,plain,
% 12.37/8.39 (~always5(s35)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4051, 6548])).
% 12.37/8.39 tff(6553,plain,
% 12.37/8.39 (xuntil7(s35) | (~until6(s35))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4825, 4345, 6552])).
% 12.37/8.39 tff(6554,plain,
% 12.37/8.39 (~until6(s35)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6553, 6551])).
% 12.37/8.39 tff(6555,plain,
% 12.37/8.39 (~xuntil7(s34)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4818, 6554])).
% 12.37/8.39 tff(6556,plain,
% 12.37/8.39 (~always5(s34)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4059, 6552])).
% 12.37/8.39 tff(6557,plain,
% 12.37/8.39 (xuntil7(s34) | (~until6(s34))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4812, 4345, 6556])).
% 12.37/8.39 tff(6558,plain,
% 12.37/8.39 (~until6(s34)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6557, 6555])).
% 12.37/8.39 tff(6559,plain,
% 12.37/8.39 (~xuntil7(s33)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4805, 6558])).
% 12.37/8.39 tff(6560,plain,
% 12.37/8.39 (~always5(s33)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4067, 6556])).
% 12.37/8.39 tff(6561,plain,
% 12.37/8.39 (xuntil7(s33) | (~until6(s33))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4799, 4345, 6560])).
% 12.37/8.39 tff(6562,plain,
% 12.37/8.39 (~until6(s33)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6561, 6559])).
% 12.37/8.39 tff(6563,plain,
% 12.37/8.39 (~xuntil7(s32)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4792, 6562])).
% 12.37/8.39 tff(6564,plain,
% 12.37/8.39 (~always5(s32)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4075, 6560])).
% 12.37/8.39 tff(6565,plain,
% 12.37/8.39 (xuntil7(s32) | (~until6(s32))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4786, 4345, 6564])).
% 12.37/8.39 tff(6566,plain,
% 12.37/8.39 (~until6(s32)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6565, 6563])).
% 12.37/8.39 tff(6567,plain,
% 12.37/8.39 (~xuntil7(s31)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4779, 6566])).
% 12.37/8.39 tff(6568,plain,
% 12.37/8.39 (~always5(s31)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4083, 6564])).
% 12.37/8.39 tff(6569,plain,
% 12.37/8.39 (xuntil7(s31) | (~until6(s31))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4773, 4345, 6568])).
% 12.37/8.39 tff(6570,plain,
% 12.37/8.39 (~until6(s31)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6569, 6567])).
% 12.37/8.39 tff(6571,plain,
% 12.37/8.39 (~xuntil7(s30)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4766, 6570])).
% 12.37/8.39 tff(6572,plain,
% 12.37/8.39 (~always5(s30)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4091, 6568])).
% 12.37/8.39 tff(6573,plain,
% 12.37/8.39 (~always5(s29)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4099, 6572])).
% 12.37/8.39 tff(6574,plain,
% 12.37/8.39 (~always5(s28)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4107, 6573])).
% 12.37/8.39 tff(6575,plain,
% 12.37/8.39 (~always5(s27)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4115, 6574])).
% 12.37/8.39 tff(6576,plain,
% 12.37/8.39 (~always5(s26)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4123, 6575])).
% 12.37/8.39 tff(6577,plain,
% 12.37/8.39 (~always5(s25)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4131, 6576])).
% 12.37/8.39 tff(6578,plain,
% 12.37/8.39 (~always5(s24)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4139, 6577])).
% 12.37/8.39 tff(6579,plain,
% 12.37/8.39 (~always5(s23)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4147, 6578])).
% 12.37/8.39 tff(6580,plain,
% 12.37/8.39 (~always5(s22)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4155, 6579])).
% 12.37/8.39 tff(6581,plain,
% 12.37/8.39 (~always5(s21)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4163, 6580])).
% 12.37/8.39 tff(6582,plain,
% 12.37/8.39 (~always5(s20)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4171, 6581])).
% 12.37/8.39 tff(6583,plain,
% 12.37/8.39 (~always5(s19)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4179, 6582])).
% 12.37/8.39 tff(6584,plain,
% 12.37/8.39 (~always5(s18)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4187, 6583])).
% 12.37/8.39 tff(6585,plain,
% 12.37/8.39 (~always5(s17)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4195, 6584])).
% 12.37/8.39 tff(6586,plain,
% 12.37/8.39 (~always5(s16)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4203, 6585])).
% 12.37/8.39 tff(6587,plain,
% 12.37/8.39 (~always5(s15)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4211, 6586])).
% 12.37/8.39 tff(6588,plain,
% 12.37/8.39 (~always5(s14)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4219, 6587])).
% 12.37/8.39 tff(6589,plain,
% 12.37/8.39 (~always5(s13)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4227, 6588])).
% 12.37/8.39 tff(6590,plain,
% 12.37/8.39 (~always5(s12)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4235, 6589])).
% 12.37/8.39 tff(6591,plain,
% 12.37/8.39 (~always5(s11)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4243, 6590])).
% 12.37/8.39 tff(6592,plain,
% 12.37/8.39 (~always5(s10)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4251, 6591])).
% 12.37/8.39 tff(6593,plain,
% 12.37/8.39 (~always5(s9)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4259, 6592])).
% 12.37/8.39 tff(6594,plain,
% 12.37/8.39 (~always5(s8)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4267, 6593])).
% 12.37/8.39 tff(6595,plain,
% 12.37/8.39 (~always5(s7)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4275, 6594])).
% 12.37/8.39 tff(6596,plain,
% 12.37/8.39 (~always5(s6)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4283, 6595])).
% 12.37/8.39 tff(6597,plain,
% 12.37/8.39 (~always5(s5)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4291, 6596])).
% 12.37/8.39 tff(6598,plain,
% 12.37/8.39 (~always5(s4)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4299, 6597])).
% 12.37/8.39 tff(6599,plain,
% 12.37/8.39 (~always5(s3)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4307, 6598])).
% 12.37/8.39 tff(6600,plain,
% 12.37/8.39 (~always5(s2)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4315, 6599])).
% 12.37/8.39 tff(6601,plain,
% 12.37/8.39 (~always5(s1)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4323, 6600])).
% 12.37/8.39 tff(6602,plain,
% 12.37/8.39 (~always5(s0)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4331, 6601])).
% 12.37/8.39 tff(6603,plain,
% 12.37/8.39 (xuntil7(s0)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4352, 6602])).
% 12.37/8.39 tff(6604,plain,
% 12.37/8.39 (until6(s1)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4367, 6603])).
% 12.37/8.39 tff(6605,plain,
% 12.37/8.39 (xuntil7(s1)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4374, 4345, 6604, 6601])).
% 12.37/8.39 tff(6606,plain,
% 12.37/8.39 (until6(s2)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4379, 6605])).
% 12.37/8.39 tff(6607,plain,
% 12.37/8.39 (xuntil7(s2) | (~until6(s2))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4386, 4345, 6600])).
% 12.37/8.39 tff(6608,plain,
% 12.37/8.39 (xuntil7(s2)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6607, 6606])).
% 12.37/8.39 tff(6609,plain,
% 12.37/8.39 (until6(s3)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4392, 6608])).
% 12.37/8.39 tff(6610,plain,
% 12.37/8.39 (xuntil7(s3) | (~until6(s3))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4399, 4345, 6599])).
% 12.37/8.39 tff(6611,plain,
% 12.37/8.39 (xuntil7(s3)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6610, 6609])).
% 12.37/8.39 tff(6612,plain,
% 12.37/8.39 (until6(s4)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4405, 6611])).
% 12.37/8.39 tff(6613,plain,
% 12.37/8.39 (xuntil7(s4) | (~until6(s4))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4412, 4345, 6598])).
% 12.37/8.39 tff(6614,plain,
% 12.37/8.39 (xuntil7(s4)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6613, 6612])).
% 12.37/8.39 tff(6615,plain,
% 12.37/8.39 (until6(s5)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4418, 6614])).
% 12.37/8.39 tff(6616,plain,
% 12.37/8.39 (xuntil7(s5) | (~until6(s5))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4425, 4345, 6597])).
% 12.37/8.39 tff(6617,plain,
% 12.37/8.39 (xuntil7(s5)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6616, 6615])).
% 12.37/8.39 tff(6618,plain,
% 12.37/8.39 (until6(s6)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4431, 6617])).
% 12.37/8.39 tff(6619,plain,
% 12.37/8.39 (xuntil7(s6) | (~until6(s6))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4438, 4345, 6596])).
% 12.37/8.39 tff(6620,plain,
% 12.37/8.39 (xuntil7(s6)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[6619, 6618])).
% 12.37/8.39 tff(6621,plain,
% 12.37/8.39 (until6(s7)),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4444, 6620])).
% 12.37/8.39 tff(6622,plain,
% 12.37/8.39 (xuntil7(s7) | (~until6(s7))),
% 12.37/8.39 inference(unit_resolution,[status(thm)],[4451, 4345, 6595])).
% 12.37/8.39 tff(6623,plain,
% 12.37/8.39 (xuntil7(s7)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6622, 6621])).
% 12.46/8.39 tff(6624,plain,
% 12.46/8.39 (until6(s8)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4457, 6623])).
% 12.46/8.39 tff(6625,plain,
% 12.46/8.39 (xuntil7(s8) | (~until6(s8))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4520, 4345, 6594])).
% 12.46/8.39 tff(6626,plain,
% 12.46/8.39 (xuntil7(s8)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6625, 6624])).
% 12.46/8.39 tff(6627,plain,
% 12.46/8.39 (until6(s9)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4526, 6626])).
% 12.46/8.39 tff(6628,plain,
% 12.46/8.39 (xuntil7(s9) | (~until6(s9))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4533, 4345, 6593])).
% 12.46/8.39 tff(6629,plain,
% 12.46/8.39 (xuntil7(s9)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6628, 6627])).
% 12.46/8.39 tff(6630,plain,
% 12.46/8.39 (until6(s10)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4538, 6629])).
% 12.46/8.39 tff(6631,plain,
% 12.46/8.39 (xuntil7(s10) | (~until6(s10))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4545, 4345, 6592])).
% 12.46/8.39 tff(6632,plain,
% 12.46/8.39 (xuntil7(s10)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6631, 6630])).
% 12.46/8.39 tff(6633,plain,
% 12.46/8.39 (until6(s11)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4551, 6632])).
% 12.46/8.39 tff(6634,plain,
% 12.46/8.39 (xuntil7(s11) | (~until6(s11))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4558, 4345, 6591])).
% 12.46/8.39 tff(6635,plain,
% 12.46/8.39 (xuntil7(s11)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6634, 6633])).
% 12.46/8.39 tff(6636,plain,
% 12.46/8.39 (until6(s12)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4564, 6635])).
% 12.46/8.39 tff(6637,plain,
% 12.46/8.39 (xuntil7(s12) | (~until6(s12))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4507, 4345, 6590])).
% 12.46/8.39 tff(6638,plain,
% 12.46/8.39 (xuntil7(s12)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6637, 6636])).
% 12.46/8.39 tff(6639,plain,
% 12.46/8.39 (until6(s13)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4499, 6638])).
% 12.46/8.39 tff(6640,plain,
% 12.46/8.39 (xuntil7(s13) | (~until6(s13))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4493, 4345, 6589])).
% 12.46/8.39 tff(6641,plain,
% 12.46/8.39 (xuntil7(s13)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6640, 6639])).
% 12.46/8.39 tff(6642,plain,
% 12.46/8.39 (until6(s14)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4485, 6641])).
% 12.46/8.39 tff(6643,plain,
% 12.46/8.39 (xuntil7(s14) | (~until6(s14))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4480, 4345, 6588])).
% 12.46/8.39 tff(6644,plain,
% 12.46/8.39 (xuntil7(s14)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6643, 6642])).
% 12.46/8.39 tff(6645,plain,
% 12.46/8.39 (until6(s15)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4473, 6644])).
% 12.46/8.39 tff(6646,plain,
% 12.46/8.39 (xuntil7(s15) | (~until6(s15))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4467, 4345, 6587])).
% 12.46/8.39 tff(6647,plain,
% 12.46/8.39 (xuntil7(s15)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6646, 6645])).
% 12.46/8.39 tff(6648,plain,
% 12.46/8.39 (until6(s16)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4571, 6647])).
% 12.46/8.39 tff(6649,plain,
% 12.46/8.39 (xuntil7(s16) | (~until6(s16))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4578, 4345, 6586])).
% 12.46/8.39 tff(6650,plain,
% 12.46/8.39 (xuntil7(s16)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6649, 6648])).
% 12.46/8.39 tff(6651,plain,
% 12.46/8.39 (until6(s17)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4584, 6650])).
% 12.46/8.39 tff(6652,plain,
% 12.46/8.39 (xuntil7(s17) | (~until6(s17))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4591, 4345, 6585])).
% 12.46/8.39 tff(6653,plain,
% 12.46/8.39 (xuntil7(s17)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6652, 6651])).
% 12.46/8.39 tff(6654,plain,
% 12.46/8.39 (until6(s18)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4597, 6653])).
% 12.46/8.39 tff(6655,plain,
% 12.46/8.39 (xuntil7(s18) | (~until6(s18))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4604, 4345, 6584])).
% 12.46/8.39 tff(6656,plain,
% 12.46/8.39 (xuntil7(s18)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6655, 6654])).
% 12.46/8.39 tff(6657,plain,
% 12.46/8.39 (until6(s19)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4610, 6656])).
% 12.46/8.39 tff(6658,plain,
% 12.46/8.39 (xuntil7(s19) | (~until6(s19))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4617, 4345, 6583])).
% 12.46/8.39 tff(6659,plain,
% 12.46/8.39 (xuntil7(s19)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6658, 6657])).
% 12.46/8.39 tff(6660,plain,
% 12.46/8.39 (until6(s20)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4623, 6659])).
% 12.46/8.39 tff(6661,plain,
% 12.46/8.39 (xuntil7(s20) | (~until6(s20))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4630, 4345, 6582])).
% 12.46/8.39 tff(6662,plain,
% 12.46/8.39 (xuntil7(s20)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6661, 6660])).
% 12.46/8.39 tff(6663,plain,
% 12.46/8.39 (until6(s21)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4636, 6662])).
% 12.46/8.39 tff(6664,plain,
% 12.46/8.39 (xuntil7(s21) | (~until6(s21))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4643, 4345, 6581])).
% 12.46/8.39 tff(6665,plain,
% 12.46/8.39 (xuntil7(s21)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6664, 6663])).
% 12.46/8.39 tff(6666,plain,
% 12.46/8.39 (until6(s22)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4649, 6665])).
% 12.46/8.39 tff(6667,plain,
% 12.46/8.39 (xuntil7(s22) | (~until6(s22))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4656, 4345, 6580])).
% 12.46/8.39 tff(6668,plain,
% 12.46/8.39 (xuntil7(s22)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6667, 6666])).
% 12.46/8.39 tff(6669,plain,
% 12.46/8.39 (until6(s23)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4662, 6668])).
% 12.46/8.39 tff(6670,plain,
% 12.46/8.39 (xuntil7(s23) | (~until6(s23))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4669, 4345, 6579])).
% 12.46/8.39 tff(6671,plain,
% 12.46/8.39 (xuntil7(s23)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6670, 6669])).
% 12.46/8.39 tff(6672,plain,
% 12.46/8.39 (until6(s24)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4675, 6671])).
% 12.46/8.39 tff(6673,plain,
% 12.46/8.39 (xuntil7(s24) | (~until6(s24))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4682, 4345, 6578])).
% 12.46/8.39 tff(6674,plain,
% 12.46/8.39 (xuntil7(s24)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6673, 6672])).
% 12.46/8.39 tff(6675,plain,
% 12.46/8.39 (until6(s25)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4688, 6674])).
% 12.46/8.39 tff(6676,plain,
% 12.46/8.39 (xuntil7(s25) | (~until6(s25))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4695, 4345, 6577])).
% 12.46/8.39 tff(6677,plain,
% 12.46/8.39 (xuntil7(s25)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6676, 6675])).
% 12.46/8.39 tff(6678,plain,
% 12.46/8.39 (until6(s26)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4701, 6677])).
% 12.46/8.39 tff(6679,plain,
% 12.46/8.39 (xuntil7(s26) | (~until6(s26))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4708, 4345, 6576])).
% 12.46/8.39 tff(6680,plain,
% 12.46/8.39 (xuntil7(s26)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6679, 6678])).
% 12.46/8.39 tff(6681,plain,
% 12.46/8.39 (until6(s27)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4714, 6680])).
% 12.46/8.39 tff(6682,plain,
% 12.46/8.39 (xuntil7(s27) | (~until6(s27))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4721, 4345, 6575])).
% 12.46/8.39 tff(6683,plain,
% 12.46/8.39 (xuntil7(s27)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6682, 6681])).
% 12.46/8.39 tff(6684,plain,
% 12.46/8.39 (until6(s28)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4727, 6683])).
% 12.46/8.39 tff(6685,plain,
% 12.46/8.39 (xuntil7(s28) | (~until6(s28))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4734, 4345, 6574])).
% 12.46/8.39 tff(6686,plain,
% 12.46/8.39 (xuntil7(s28)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6685, 6684])).
% 12.46/8.39 tff(6687,plain,
% 12.46/8.39 (until6(s29)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4740, 6686])).
% 12.46/8.39 tff(6688,plain,
% 12.46/8.39 (xuntil7(s29) | (~until6(s29))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4747, 4345, 6573])).
% 12.46/8.39 tff(6689,plain,
% 12.46/8.39 (xuntil7(s29)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6688, 6687])).
% 12.46/8.39 tff(6690,plain,
% 12.46/8.39 (until6(s30)),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4753, 6689])).
% 12.46/8.39 tff(6691,plain,
% 12.46/8.39 (xuntil7(s30) | (~until6(s30))),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[4760, 4345, 6572])).
% 12.46/8.39 tff(6692,plain,
% 12.46/8.39 ($false),
% 12.46/8.39 inference(unit_resolution,[status(thm)],[6691, 6690, 6571])).
% 12.46/8.39 tff(6693,plain,(loop), inference(lemma,lemma(discharge,[]))).
% 12.46/8.39 tff(6694,plain,
% 12.46/8.39 (((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.39 inference(rewrite,[status(thm)],[])).
% 12.46/8.39 tff(6695,plain,
% 12.46/8.39 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.39 inference(rewrite,[status(thm)],[])).
% 12.46/8.39 tff(6696,plain,
% 12.46/8.39 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.39 inference(rewrite,[status(thm)],[])).
% 12.46/8.39 tff(6697,plain,
% 12.46/8.39 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.39 inference(rewrite,[status(thm)],[])).
% 12.46/8.39 tff(6698,plain,
% 12.46/8.39 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.40 inference(rewrite,[status(thm)],[])).
% 12.46/8.40 tff(6699,plain,
% 12.46/8.40 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.40 inference(rewrite,[status(thm)],[])).
% 12.46/8.40 tff(6700,plain,
% 12.46/8.40 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.40 inference(rewrite,[status(thm)],[])).
% 12.46/8.40 tff(6701,plain,
% 12.46/8.40 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.40 inference(rewrite,[status(thm)],[])).
% 12.46/8.40 tff(6702,plain,
% 12.46/8.40 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.40 inference(rewrite,[status(thm)],[])).
% 12.46/8.40 tff(6703,plain,
% 12.46/8.40 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.40 inference(rewrite,[status(thm)],[])).
% 12.46/8.40 tff(6704,plain,
% 12.46/8.40 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.41 inference(rewrite,[status(thm)],[])).
% 12.46/8.41 tff(6705,plain,
% 12.46/8.41 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.46/8.41 inference(rewrite,[status(thm)],[])).
% 12.46/8.41 tff(6706,plain,
% 12.46/8.41 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.48/8.41 inference(rewrite,[status(thm)],[])).
% 12.48/8.41 tff(6707,plain,
% 12.48/8.41 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.48/8.41 inference(rewrite,[status(thm)],[])).
% 12.48/8.41 tff(6708,plain,
% 12.48/8.41 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.48/8.42 inference(rewrite,[status(thm)],[])).
% 12.48/8.42 tff(6709,plain,
% 12.48/8.42 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.48/8.42 inference(rewrite,[status(thm)],[])).
% 12.48/8.42 tff(6710,plain,
% 12.48/8.42 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.48/8.42 inference(rewrite,[status(thm)],[])).
% 12.48/8.42 tff(6711,plain,
% 12.48/8.42 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.48/8.42 inference(rewrite,[status(thm)],[])).
% 12.48/8.42 tff(6712,plain,
% 12.48/8.42 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.48/8.42 inference(rewrite,[status(thm)],[])).
% 12.48/8.42 tff(6713,plain,
% 12.48/8.42 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.42 inference(rewrite,[status(thm)],[])).
% 12.49/8.42 tff(6714,plain,
% 12.49/8.42 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.42 inference(rewrite,[status(thm)],[])).
% 12.49/8.42 tff(6715,plain,
% 12.49/8.42 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.42 inference(rewrite,[status(thm)],[])).
% 12.49/8.42 tff(6716,plain,
% 12.49/8.42 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6717,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6718,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6719,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6720,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6721,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6722,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6723,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6724,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.43 inference(rewrite,[status(thm)],[])).
% 12.49/8.43 tff(6725,plain,
% 12.49/8.43 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6726,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6727,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6728,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6729,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6730,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6731,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6732,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6733,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6734,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6735,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6736,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6737,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6738,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | 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))),
% 12.49/8.44 inference(rewrite,[status(thm)],[])).
% 12.49/8.44 tff(6739,plain,
% 12.49/8.44 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6740,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6741,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6742,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6743,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6744,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6745,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0) | trans(s59, s1) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6746,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6747,plain,
% 12.49/8.45 ((((~loop) | 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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6748,plain,
% 12.49/8.45 ((((~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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6749,plain,
% 12.49/8.45 ((((~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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6750,plain,
% 12.49/8.45 ((((~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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6751,plain,
% 12.49/8.45 ((((~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))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6752,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0) | trans(s59, s1)) | trans(s59, s2)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6753,plain,
% 12.49/8.45 ((((~loop) | trans(s59, s0)) | trans(s59, s1)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1))),
% 12.49/8.45 inference(rewrite,[status(thm)],[])).
% 12.49/8.45 tff(6754,plain,
% 12.49/8.45 (((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) <=> (((~loop) | trans(s59, s0) | trans(s59, s1)) | trans(s59, s2))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6753])).
% 12.49/8.45 tff(6755,plain,
% 12.49/8.45 (((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) <=> ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6754, 6752])).
% 12.49/8.45 tff(6756,plain,
% 12.49/8.45 ((((((~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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6755])).
% 12.49/8.45 tff(6757,plain,
% 12.49/8.45 ((((((~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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6756, 6751])).
% 12.49/8.45 tff(6758,plain,
% 12.49/8.45 (((((((~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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6757])).
% 12.49/8.45 tff(6759,plain,
% 12.49/8.45 (((((((~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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6758, 6750])).
% 12.49/8.45 tff(6760,plain,
% 12.49/8.45 ((((((((~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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6759])).
% 12.49/8.45 tff(6761,plain,
% 12.49/8.45 ((((((((~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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6760, 6749])).
% 12.49/8.45 tff(6762,plain,
% 12.49/8.45 (((((((((~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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6761])).
% 12.49/8.45 tff(6763,plain,
% 12.49/8.45 (((((((((~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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6762, 6748])).
% 12.49/8.45 tff(6764,plain,
% 12.49/8.45 ((((((((((~loop) | 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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6763])).
% 12.49/8.45 tff(6765,plain,
% 12.49/8.45 ((((((((((~loop) | 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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6764, 6747])).
% 12.49/8.45 tff(6766,plain,
% 12.49/8.45 (((((((((((~loop) | trans(s59, s0)) | 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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6765])).
% 12.49/8.45 tff(6767,plain,
% 12.49/8.45 (((((((((((~loop) | trans(s59, s0)) | 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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6766, 6746])).
% 12.49/8.45 tff(6768,plain,
% 12.49/8.45 ((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | 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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6767])).
% 12.49/8.45 tff(6769,plain,
% 12.49/8.45 ((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | 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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6768, 6745])).
% 12.49/8.45 tff(6770,plain,
% 12.49/8.45 (((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | 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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6769])).
% 12.49/8.45 tff(6771,plain,
% 12.49/8.45 (((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | 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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6770, 6744])).
% 12.49/8.45 tff(6772,plain,
% 12.49/8.45 ((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | 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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6771])).
% 12.49/8.45 tff(6773,plain,
% 12.49/8.45 ((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | 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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6772, 6743])).
% 12.49/8.45 tff(6774,plain,
% 12.49/8.45 (((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | 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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6773])).
% 12.49/8.45 tff(6775,plain,
% 12.49/8.45 (((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | 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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6774, 6742])).
% 12.49/8.45 tff(6776,plain,
% 12.49/8.45 ((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | 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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6775])).
% 12.49/8.45 tff(6777,plain,
% 12.49/8.45 ((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | 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))),
% 12.49/8.45 inference(transitivity,[status(thm)],[6776, 6741])).
% 12.49/8.45 tff(6778,plain,
% 12.49/8.45 (((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | 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))),
% 12.49/8.45 inference(monotonicity,[status(thm)],[6777])).
% 12.49/8.45 tff(6779,plain,
% 12.49/8.45 (((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | 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))),
% 12.49/8.46 inference(transitivity,[status(thm)],[6778, 6740])).
% 12.49/8.46 tff(6780,plain,
% 12.49/8.46 ((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | 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))),
% 12.49/8.46 inference(monotonicity,[status(thm)],[6779])).
% 12.49/8.46 tff(6781,plain,
% 12.49/8.46 ((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | 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))),
% 12.49/8.46 inference(transitivity,[status(thm)],[6780, 6739])).
% 12.49/8.46 tff(6782,plain,
% 12.49/8.46 (((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | 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))),
% 12.49/8.46 inference(monotonicity,[status(thm)],[6781])).
% 12.49/8.46 tff(6783,plain,
% 12.49/8.46 (((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | 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))),
% 12.49/8.46 inference(transitivity,[status(thm)],[6782, 6738])).
% 12.49/8.46 tff(6784,plain,
% 12.49/8.46 ((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | 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))),
% 12.49/8.46 inference(monotonicity,[status(thm)],[6783])).
% 12.49/8.46 tff(6785,plain,
% 12.49/8.46 ((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | 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))),
% 12.49/8.46 inference(transitivity,[status(thm)],[6784, 6737])).
% 12.49/8.46 tff(6786,plain,
% 12.49/8.46 (((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.46 inference(monotonicity,[status(thm)],[6785])).
% 12.49/8.46 tff(6787,plain,
% 12.49/8.46 (((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.46 inference(transitivity,[status(thm)],[6786, 6736])).
% 12.49/8.46 tff(6788,plain,
% 12.49/8.46 ((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.46 inference(monotonicity,[status(thm)],[6787])).
% 12.49/8.46 tff(6789,plain,
% 12.49/8.46 ((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.46 inference(transitivity,[status(thm)],[6788, 6735])).
% 12.49/8.46 tff(6790,plain,
% 12.49/8.46 (((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.46 inference(monotonicity,[status(thm)],[6789])).
% 12.49/8.46 tff(6791,plain,
% 12.49/8.46 (((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.46 inference(transitivity,[status(thm)],[6790, 6734])).
% 12.49/8.46 tff(6792,plain,
% 12.49/8.46 ((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.46 inference(monotonicity,[status(thm)],[6791])).
% 12.49/8.46 tff(6793,plain,
% 12.49/8.46 ((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.46 inference(transitivity,[status(thm)],[6792, 6733])).
% 12.49/8.46 tff(6794,plain,
% 12.49/8.46 (((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(monotonicity,[status(thm)],[6793])).
% 12.49/8.47 tff(6795,plain,
% 12.49/8.47 (((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(transitivity,[status(thm)],[6794, 6732])).
% 12.49/8.47 tff(6796,plain,
% 12.49/8.47 ((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(monotonicity,[status(thm)],[6795])).
% 12.49/8.47 tff(6797,plain,
% 12.49/8.47 ((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(transitivity,[status(thm)],[6796, 6731])).
% 12.49/8.47 tff(6798,plain,
% 12.49/8.47 (((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(monotonicity,[status(thm)],[6797])).
% 12.49/8.47 tff(6799,plain,
% 12.49/8.47 (((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(transitivity,[status(thm)],[6798, 6730])).
% 12.49/8.47 tff(6800,plain,
% 12.49/8.47 ((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(monotonicity,[status(thm)],[6799])).
% 12.49/8.47 tff(6801,plain,
% 12.49/8.47 ((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(transitivity,[status(thm)],[6800, 6729])).
% 12.49/8.47 tff(6802,plain,
% 12.49/8.47 (((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(monotonicity,[status(thm)],[6801])).
% 12.49/8.47 tff(6803,plain,
% 12.49/8.47 (((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(transitivity,[status(thm)],[6802, 6728])).
% 12.49/8.47 tff(6804,plain,
% 12.49/8.47 ((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(monotonicity,[status(thm)],[6803])).
% 12.49/8.47 tff(6805,plain,
% 12.49/8.47 ((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.47 inference(transitivity,[status(thm)],[6804, 6727])).
% 12.49/8.47 tff(6806,plain,
% 12.49/8.47 (((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(monotonicity,[status(thm)],[6805])).
% 12.49/8.48 tff(6807,plain,
% 12.49/8.48 (((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(transitivity,[status(thm)],[6806, 6726])).
% 12.49/8.48 tff(6808,plain,
% 12.49/8.48 ((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(monotonicity,[status(thm)],[6807])).
% 12.49/8.48 tff(6809,plain,
% 12.49/8.48 ((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(transitivity,[status(thm)],[6808, 6725])).
% 12.49/8.48 tff(6810,plain,
% 12.49/8.48 (((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(monotonicity,[status(thm)],[6809])).
% 12.49/8.48 tff(6811,plain,
% 12.49/8.48 (((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(transitivity,[status(thm)],[6810, 6724])).
% 12.49/8.48 tff(6812,plain,
% 12.49/8.48 ((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(monotonicity,[status(thm)],[6811])).
% 12.49/8.48 tff(6813,plain,
% 12.49/8.48 ((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(transitivity,[status(thm)],[6812, 6723])).
% 12.49/8.48 tff(6814,plain,
% 12.49/8.48 (((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.48 inference(monotonicity,[status(thm)],[6813])).
% 12.49/8.48 tff(6815,plain,
% 12.49/8.48 (((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(transitivity,[status(thm)],[6814, 6722])).
% 12.49/8.49 tff(6816,plain,
% 12.49/8.49 ((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(monotonicity,[status(thm)],[6815])).
% 12.49/8.49 tff(6817,plain,
% 12.49/8.49 ((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(transitivity,[status(thm)],[6816, 6721])).
% 12.49/8.49 tff(6818,plain,
% 12.49/8.49 (((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(monotonicity,[status(thm)],[6817])).
% 12.49/8.49 tff(6819,plain,
% 12.49/8.49 (((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(transitivity,[status(thm)],[6818, 6720])).
% 12.49/8.49 tff(6820,plain,
% 12.49/8.49 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(monotonicity,[status(thm)],[6819])).
% 12.49/8.49 tff(6821,plain,
% 12.49/8.49 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(transitivity,[status(thm)],[6820, 6719])).
% 12.49/8.49 tff(6822,plain,
% 12.49/8.49 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(monotonicity,[status(thm)],[6821])).
% 12.49/8.49 tff(6823,plain,
% 12.49/8.49 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(transitivity,[status(thm)],[6822, 6718])).
% 12.49/8.49 tff(6824,plain,
% 12.49/8.49 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(monotonicity,[status(thm)],[6823])).
% 12.49/8.49 tff(6825,plain,
% 12.49/8.49 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(transitivity,[status(thm)],[6824, 6717])).
% 12.49/8.49 tff(6826,plain,
% 12.49/8.49 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.49 inference(monotonicity,[status(thm)],[6825])).
% 12.49/8.49 tff(6827,plain,
% 12.49/8.49 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.50 inference(transitivity,[status(thm)],[6826, 6716])).
% 12.49/8.50 tff(6828,plain,
% 12.49/8.50 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.50 inference(monotonicity,[status(thm)],[6827])).
% 12.49/8.50 tff(6829,plain,
% 12.49/8.50 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.50 inference(transitivity,[status(thm)],[6828, 6715])).
% 12.49/8.50 tff(6830,plain,
% 12.49/8.50 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.50 inference(monotonicity,[status(thm)],[6829])).
% 12.49/8.50 tff(6831,plain,
% 12.49/8.50 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.49/8.50 inference(transitivity,[status(thm)],[6830, 6714])).
% 12.49/8.50 tff(6832,plain,
% 12.49/8.50 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.50 inference(monotonicity,[status(thm)],[6831])).
% 12.57/8.50 tff(6833,plain,
% 12.57/8.50 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.50 inference(transitivity,[status(thm)],[6832, 6713])).
% 12.57/8.50 tff(6834,plain,
% 12.57/8.50 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.51 inference(monotonicity,[status(thm)],[6833])).
% 12.57/8.51 tff(6835,plain,
% 12.57/8.51 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.51 inference(transitivity,[status(thm)],[6834, 6712])).
% 12.57/8.51 tff(6836,plain,
% 12.57/8.51 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.51 inference(monotonicity,[status(thm)],[6835])).
% 12.57/8.51 tff(6837,plain,
% 12.57/8.51 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.51 inference(transitivity,[status(thm)],[6836, 6711])).
% 12.57/8.51 tff(6838,plain,
% 12.57/8.51 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.51 inference(monotonicity,[status(thm)],[6837])).
% 12.57/8.51 tff(6839,plain,
% 12.57/8.51 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.51 inference(transitivity,[status(thm)],[6838, 6710])).
% 12.57/8.51 tff(6840,plain,
% 12.57/8.51 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.51 inference(monotonicity,[status(thm)],[6839])).
% 12.57/8.51 tff(6841,plain,
% 12.57/8.51 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.52 inference(transitivity,[status(thm)],[6840, 6709])).
% 12.57/8.52 tff(6842,plain,
% 12.57/8.52 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.52 inference(monotonicity,[status(thm)],[6841])).
% 12.57/8.52 tff(6843,plain,
% 12.57/8.52 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.52 inference(transitivity,[status(thm)],[6842, 6708])).
% 12.57/8.52 tff(6844,plain,
% 12.57/8.52 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.52 inference(monotonicity,[status(thm)],[6843])).
% 12.57/8.52 tff(6845,plain,
% 12.57/8.52 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.52 inference(transitivity,[status(thm)],[6844, 6707])).
% 12.57/8.52 tff(6846,plain,
% 12.57/8.52 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.52 inference(monotonicity,[status(thm)],[6845])).
% 12.57/8.52 tff(6847,plain,
% 12.57/8.52 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.52 inference(transitivity,[status(thm)],[6846, 6706])).
% 12.57/8.52 tff(6848,plain,
% 12.57/8.52 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.53 inference(monotonicity,[status(thm)],[6847])).
% 12.57/8.53 tff(6849,plain,
% 12.57/8.53 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.53 inference(transitivity,[status(thm)],[6848, 6705])).
% 12.57/8.53 tff(6850,plain,
% 12.57/8.53 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.53 inference(monotonicity,[status(thm)],[6849])).
% 12.57/8.53 tff(6851,plain,
% 12.57/8.53 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.53 inference(transitivity,[status(thm)],[6850, 6704])).
% 12.57/8.53 tff(6852,plain,
% 12.57/8.53 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.53 inference(monotonicity,[status(thm)],[6851])).
% 12.57/8.53 tff(6853,plain,
% 12.57/8.53 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.53 inference(transitivity,[status(thm)],[6852, 6703])).
% 12.57/8.53 tff(6854,plain,
% 12.57/8.53 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.54 inference(monotonicity,[status(thm)],[6853])).
% 12.57/8.54 tff(6855,plain,
% 12.57/8.54 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.54 inference(transitivity,[status(thm)],[6854, 6702])).
% 12.57/8.54 tff(6856,plain,
% 12.57/8.54 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.54 inference(monotonicity,[status(thm)],[6855])).
% 12.57/8.54 tff(6857,plain,
% 12.57/8.54 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.54 inference(transitivity,[status(thm)],[6856, 6701])).
% 12.57/8.54 tff(6858,plain,
% 12.57/8.54 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.54 inference(monotonicity,[status(thm)],[6857])).
% 12.57/8.54 tff(6859,plain,
% 12.57/8.54 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.55 inference(transitivity,[status(thm)],[6858, 6700])).
% 12.57/8.55 tff(6860,plain,
% 12.57/8.55 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.55 inference(monotonicity,[status(thm)],[6859])).
% 12.57/8.55 tff(6861,plain,
% 12.57/8.55 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.55 inference(transitivity,[status(thm)],[6860, 6699])).
% 12.57/8.55 tff(6862,plain,
% 12.57/8.55 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.55 inference(monotonicity,[status(thm)],[6861])).
% 12.57/8.55 tff(6863,plain,
% 12.57/8.55 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.55 inference(transitivity,[status(thm)],[6862, 6698])).
% 12.57/8.55 tff(6864,plain,
% 12.57/8.55 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.55 inference(monotonicity,[status(thm)],[6863])).
% 12.57/8.55 tff(6865,plain,
% 12.57/8.55 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.56 inference(transitivity,[status(thm)],[6864, 6697])).
% 12.57/8.56 tff(6866,plain,
% 12.57/8.56 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.56 inference(monotonicity,[status(thm)],[6865])).
% 12.57/8.56 tff(6867,plain,
% 12.57/8.56 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.56 inference(transitivity,[status(thm)],[6866, 6696])).
% 12.57/8.56 tff(6868,plain,
% 12.57/8.56 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.56 inference(monotonicity,[status(thm)],[6867])).
% 12.57/8.56 tff(6869,plain,
% 12.57/8.56 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s59, s0)) | trans(s59, s1)) | trans(s59, s2)) | trans(s59, s3)) | trans(s59, s4)) | trans(s59, s5)) | trans(s59, s6)) | trans(s59, s7)) | trans(s59, s8)) | trans(s59, s9)) | trans(s59, s10)) | 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))),
% 12.57/8.56 inference(transitivity,[status(thm)],[6868, 6695])).
% 12.57/8.56 tff(6870,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')).
% 12.57/8.56 tff(6871,plain,
% 12.57/8.56 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6870, 6869])).
% 12.57/8.57 tff(6872,plain,
% 12.57/8.57 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6871, 6694])).
% 12.57/8.57 tff(6873,plain,
% 12.57/8.57 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6872, 6694])).
% 12.57/8.57 tff(6874,plain,
% 12.57/8.57 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6873, 6694])).
% 12.57/8.57 tff(6875,plain,
% 12.57/8.57 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6874, 6694])).
% 12.57/8.57 tff(6876,plain,
% 12.57/8.57 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6875, 6694])).
% 12.57/8.57 tff(6877,plain,
% 12.57/8.57 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6876, 6694])).
% 12.57/8.57 tff(6878,plain,
% 12.57/8.57 ((~loop) | trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6877, 6694])).
% 12.57/8.57 tff(6879,plain,
% 12.57/8.57 (trans(s59, s0) | trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s4) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6878, 6693])).
% 12.57/8.57 tff(6880,plain,
% 12.57/8.57 (trans(s59, s4)),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6879, 6426, 6415, 6394, 6383, 6372, 6361, 6350, 6339, 6328, 6317, 6306, 6295, 6284, 6273, 6262, 6251, 6240, 6229, 6218, 6207, 6196, 6185, 6174, 6163, 6152, 6141, 6130, 6119, 6108, 6097, 6086, 6075, 6064, 6053, 6042, 6031, 6020, 6009, 5998, 5987, 5976, 5965, 5954, 5943, 5932, 5921, 5910, 5899, 5888, 5877, 5866, 5855, 5844, 5833, 5822, 5781, 5770, 5759, 5748])).
% 12.57/8.57 tff(6881,plain,
% 12.57/8.57 (((~![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)))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6882,plain,
% 12.57/8.57 (((~last(s59)) | (~trans(s59, s4)) | (~xuntil7(s59)) | until2p8(s4)) <=> (until2p8(s4) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s4)))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6883,plain,
% 12.57/8.57 (((~![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))))),
% 12.57/8.57 inference(monotonicity,[status(thm)],[6882])).
% 12.57/8.57 tff(6884,plain,
% 12.57/8.57 (((~![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)))),
% 12.57/8.57 inference(transitivity,[status(thm)],[6883, 6881])).
% 12.57/8.57 tff(6885,plain,
% 12.57/8.57 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s59)) | (~trans(s59, s4)) | (~xuntil7(s59)) | until2p8(s4))),
% 12.57/8.57 inference(quant_inst,[status(thm)],[])).
% 12.57/8.57 tff(6886,plain,
% 12.57/8.57 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s59)) | (~xuntil7(s59)) | (~trans(s59, s4))),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6885, 6884])).
% 12.57/8.57 tff(6887,plain,
% 12.57/8.57 ($false),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6886, 5148, 6880, 5736, 5726, 5138])).
% 12.57/8.57 tff(6888,plain,(always5(s59)), inference(lemma,lemma(discharge,[]))).
% 12.57/8.57 tff(6889,plain,
% 12.57/8.57 (^[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))))),
% 12.57/8.57 inference(bind,[status(th)],[])).
% 12.57/8.57 tff(6890,plain,
% 12.57/8.57 (![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)))),
% 12.57/8.57 inference(quant_intro,[status(thm)],[6889])).
% 12.57/8.57 tff(6891,plain,
% 12.57/8.57 (![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)))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6892,plain,
% 12.57/8.57 (^[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))))),
% 12.57/8.57 inference(bind,[status(th)],[])).
% 12.57/8.57 tff(6893,plain,
% 12.57/8.57 (![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)))),
% 12.57/8.57 inference(quant_intro,[status(thm)],[6892])).
% 12.57/8.57 tff(6894,axiom,(![X: $i] : ((~m_counter_cell_v_carry_out(c_bit2, X)) | (~always5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty1')).
% 12.57/8.57 tff(6895,plain,
% 12.57/8.57 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6894, 6893])).
% 12.57/8.57 tff(6896,plain,
% 12.57/8.57 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6895, 6891])).
% 12.57/8.57 tff(6897,plain,(
% 12.57/8.57 ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 12.57/8.57 inference(skolemize,[status(sab)],[6896])).
% 12.57/8.57 tff(6898,plain,
% 12.57/8.57 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6897, 6890])).
% 12.57/8.57 tff(6899,plain,
% 12.57/8.57 (((~![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)))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6900,plain,
% 12.57/8.57 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s59)) | (~m_counter_cell_v_carry_out(c_bit2, s59)))),
% 12.57/8.57 inference(quant_inst,[status(thm)],[])).
% 12.57/8.57 tff(6901,plain,
% 12.57/8.57 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s59)) | (~m_counter_cell_v_carry_out(c_bit2, s59))),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6900, 6899])).
% 12.57/8.57 tff(6902,plain,
% 12.57/8.57 (~m_counter_cell_v_carry_out(c_bit2, s59)),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6901, 6898, 6888])).
% 12.57/8.57 tff(6903,plain,
% 12.57/8.57 (((~![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))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6904,plain,
% 12.57/8.57 ((~![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))),
% 12.57/8.57 inference(quant_inst,[status(thm)],[])).
% 12.57/8.57 tff(6905,plain,
% 12.57/8.57 ((~![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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6904, 6903])).
% 12.57/8.57 tff(6906,plain,
% 12.57/8.57 ((~m_counter_cell_v_carry_in(c_bit2, s59)) | (~m_counter_cell_v_value(c_bit2, s59))),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6905, 1368, 6902])).
% 12.57/8.57 tff(6907,plain,
% 12.57/8.57 (~m_counter_cell_v_carry_in(c_bit2, s59)),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6906, 3849])).
% 12.57/8.57 tff(6908,assumption,(m_counter_cell_v_carry_out(c_bit1, s59)), introduced(assumption)).
% 12.57/8.57 tff(6909,assumption,(~m_counter_cell_v_carry_in(c_bit2, s59)), introduced(assumption)).
% 12.57/8.57 tff(6910,plain,
% 12.57/8.57 (^[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)))),
% 12.57/8.57 inference(bind,[status(th)],[])).
% 12.57/8.57 tff(6911,plain,
% 12.57/8.57 (![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))),
% 12.57/8.57 inference(quant_intro,[status(thm)],[6910])).
% 12.57/8.57 tff(6912,plain,
% 12.57/8.57 (![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))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6913,plain,
% 12.57/8.57 (^[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)))),
% 12.57/8.57 inference(bind,[status(th)],[])).
% 12.57/8.57 tff(6914,plain,
% 12.57/8.57 (![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))),
% 12.57/8.57 inference(quant_intro,[status(thm)],[6913])).
% 12.57/8.57 tff(6915,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')).
% 12.57/8.57 tff(6916,plain,
% 12.57/8.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6915, 6914])).
% 12.57/8.57 tff(6917,plain,
% 12.57/8.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6916, 6912])).
% 12.57/8.57 tff(6918,plain,(
% 12.57/8.57 ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 12.57/8.57 inference(skolemize,[status(sab)],[6917])).
% 12.57/8.57 tff(6919,plain,
% 12.57/8.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6918, 6911])).
% 12.57/8.57 tff(6920,plain,
% 12.57/8.57 (((~![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))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6921,plain,
% 12.57/8.57 ((~![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))),
% 12.57/8.57 inference(quant_inst,[status(thm)],[])).
% 12.57/8.57 tff(6922,plain,
% 12.57/8.57 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s59)) | m_counter_cell_v_carry_in(c_bit2, s59)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 12.57/8.57 tff(6923,plain,
% 12.57/8.57 ($false),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6922, 6919, 6909, 6908])).
% 12.57/8.57 tff(6924,plain,(m_counter_cell_v_carry_in(c_bit2, s59) | (~m_counter_cell_v_carry_out(c_bit1, s59))), inference(lemma,lemma(discharge,[]))).
% 12.57/8.57 tff(6925,plain,
% 12.57/8.57 (~m_counter_cell_v_carry_out(c_bit1, s59)),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6924, 6907])).
% 12.57/8.57 tff(6926,plain,
% 12.57/8.57 (((~![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, s58)) | m_counter_cell_v_carry_in(c_bit2, s58))) <=> ((~![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, s58)) | m_counter_cell_v_carry_in(c_bit2, s58))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6927,plain,
% 12.57/8.57 ((~![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, s58)) | m_counter_cell_v_carry_in(c_bit2, s58))),
% 12.57/8.57 inference(quant_inst,[status(thm)],[])).
% 12.57/8.57 tff(6928,plain,
% 12.57/8.57 ((~![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, s58)) | m_counter_cell_v_carry_in(c_bit2, s58)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6927, 6926])).
% 12.57/8.57 tff(6929,plain,
% 12.57/8.57 (~m_counter_cell_v_carry_out(c_bit1, s58)),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6928, 6919, 3823])).
% 12.57/8.57 tff(6930,assumption,(m_counter_cell_v_value(c_bit1, s58)), introduced(assumption)).
% 12.57/8.57 tff(6931,plain,
% 12.57/8.57 (((~![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))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6932,plain,
% 12.57/8.57 ((~![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))),
% 12.57/8.57 inference(quant_inst,[status(thm)],[])).
% 12.57/8.57 tff(6933,plain,
% 12.57/8.57 ((~![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)),
% 12.57/8.57 inference(modus_ponens,[status(thm)],[6932, 6931])).
% 12.57/8.57 tff(6934,plain,
% 12.57/8.57 ((~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit1, s58)),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6933, 1368, 6930])).
% 12.57/8.57 tff(6935,plain,
% 12.57/8.57 (~m_counter_cell_v_carry_in(c_bit1, s58)),
% 12.57/8.57 inference(unit_resolution,[status(thm)],[6934, 6929])).
% 12.57/8.57 tff(6936,plain,
% 12.57/8.57 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6937,plain,
% 12.57/8.57 (((~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)))),
% 12.57/8.57 inference(rewrite,[status(thm)],[])).
% 12.57/8.57 tff(6938,plain,
% 12.57/8.57 (((~![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))))),
% 12.57/8.57 inference(monotonicity,[status(thm)],[6937])).
% 12.57/8.57 tff(6939,plain,
% 12.57/8.57 (((~![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)))),
% 12.57/8.58 inference(transitivity,[status(thm)],[6938, 6936])).
% 12.57/8.58 tff(6940,plain,
% 12.57/8.58 ((~![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)))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6941,plain,
% 12.57/8.58 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6940, 6939])).
% 12.57/8.58 tff(6942,plain,
% 12.57/8.58 (m_counter_cell_v_carry_in(c_bit1, s58) | (~node1(c_bit1, s58))),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6941, 1517, 6930])).
% 12.57/8.58 tff(6943,plain,
% 12.57/8.58 (~node1(c_bit1, s58)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6942, 6935])).
% 12.57/8.58 tff(6944,plain,
% 12.57/8.58 (((~![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))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6945,plain,
% 12.57/8.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit1, s58, s59))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6946,plain,
% 12.57/8.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit1, s58, s59)),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6945, 6944])).
% 12.57/8.58 tff(6947,plain,
% 12.57/8.58 (node3(c_bit1, s58, s59)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6946, 21, 3837])).
% 12.57/8.58 tff(6948,plain,
% 12.57/8.58 (((~![Y: $i, 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)))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6949,plain,
% 12.57/8.58 ((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)))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6950,plain,
% 12.57/8.58 (((~![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))))),
% 12.57/8.58 inference(monotonicity,[status(thm)],[6949])).
% 12.57/8.58 tff(6951,plain,
% 12.57/8.58 (((~![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)))),
% 12.57/8.58 inference(transitivity,[status(thm)],[6950, 6948])).
% 12.57/8.58 tff(6952,plain,
% 12.57/8.58 ((~![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))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6953,plain,
% 12.57/8.58 ((~![Y: $i, 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))),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6952, 6951])).
% 12.57/8.58 tff(6954,plain,
% 12.57/8.58 (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6953, 106, 6947])).
% 12.57/8.58 tff(6955,plain,
% 12.57/8.58 (m_counter_cell_v_value(c_bit1, s59)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6954, 6943])).
% 12.57/8.58 tff(6956,assumption,(~m_counter_cell_v_carry_in(c_bit0, s58)), introduced(assumption)).
% 12.57/8.58 tff(6957,plain,
% 12.57/8.58 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s58)),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6958,plain,
% 12.57/8.58 ($false),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6957, 65, 6956])).
% 12.57/8.58 tff(6959,plain,(m_counter_cell_v_carry_in(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 12.57/8.58 tff(6960,plain,
% 12.57/8.58 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6961,plain,
% 12.57/8.58 (((~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)))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6962,plain,
% 12.57/8.58 (((~![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))))),
% 12.57/8.58 inference(monotonicity,[status(thm)],[6961])).
% 12.57/8.58 tff(6963,plain,
% 12.57/8.58 (((~![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)))),
% 12.57/8.58 inference(transitivity,[status(thm)],[6962, 6960])).
% 12.57/8.58 tff(6964,plain,
% 12.57/8.58 ((~![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))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6965,plain,
% 12.57/8.58 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6964, 6963])).
% 12.57/8.58 tff(6966,plain,
% 12.57/8.58 (m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6965, 77, 6959])).
% 12.57/8.58 tff(6967,plain,
% 12.57/8.58 (~node1(c_bit0, s58)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6966, 3763])).
% 12.57/8.58 tff(6968,plain,
% 12.57/8.58 (((~![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))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6969,plain,
% 12.57/8.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit0, s58, s59))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6970,plain,
% 12.57/8.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit0, s58, s59)),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6969, 6968])).
% 12.57/8.58 tff(6971,plain,
% 12.57/8.58 (node3(c_bit0, s58, s59)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6970, 21, 3837])).
% 12.57/8.58 tff(6972,plain,
% 12.57/8.58 (((~![Y: $i, 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)))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6973,plain,
% 12.57/8.58 ((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)))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6974,plain,
% 12.57/8.58 (((~![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))))),
% 12.57/8.58 inference(monotonicity,[status(thm)],[6973])).
% 12.57/8.58 tff(6975,plain,
% 12.57/8.58 (((~![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)))),
% 12.57/8.58 inference(transitivity,[status(thm)],[6974, 6972])).
% 12.57/8.58 tff(6976,plain,
% 12.57/8.58 ((~![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))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6977,plain,
% 12.57/8.58 ((~![Y: $i, 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))),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6976, 6975])).
% 12.57/8.58 tff(6978,plain,
% 12.57/8.58 (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6977, 106, 6971])).
% 12.57/8.58 tff(6979,plain,
% 12.57/8.58 (m_counter_cell_v_value(c_bit0, s59)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6978, 6967])).
% 12.57/8.58 tff(6980,assumption,(~m_counter_cell_v_carry_in(c_bit0, s59)), introduced(assumption)).
% 12.57/8.58 tff(6981,plain,
% 12.57/8.58 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s59)),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6982,plain,
% 12.57/8.58 ($false),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6981, 65, 6980])).
% 12.57/8.58 tff(6983,plain,(m_counter_cell_v_carry_in(c_bit0, s59)), inference(lemma,lemma(discharge,[]))).
% 12.57/8.58 tff(6984,plain,
% 12.57/8.58 (((~![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))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6985,plain,
% 12.57/8.58 ((~![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))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6986,plain,
% 12.57/8.58 ((~![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)),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6985, 6984])).
% 12.57/8.58 tff(6987,plain,
% 12.57/8.58 ((~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6986, 1368, 6983])).
% 12.57/8.58 tff(6988,plain,
% 12.57/8.58 (m_counter_cell_v_carry_out(c_bit0, s59)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6987, 6979])).
% 12.57/8.58 tff(6989,plain,
% 12.57/8.58 (((~![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))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6990,plain,
% 12.57/8.58 ((~![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))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6991,plain,
% 12.57/8.58 ((~![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)),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6990, 6989])).
% 12.57/8.58 tff(6992,plain,
% 12.57/8.58 (m_counter_cell_v_carry_in(c_bit1, s59)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6991, 1383, 6988])).
% 12.57/8.58 tff(6993,assumption,(m_counter_cell_v_carry_in(c_bit1, s59)), introduced(assumption)).
% 12.57/8.58 tff(6994,assumption,(~m_counter_cell_v_carry_out(c_bit1, s59)), introduced(assumption)).
% 12.57/8.58 tff(6995,assumption,(m_counter_cell_v_value(c_bit1, s59)), introduced(assumption)).
% 12.57/8.58 tff(6996,plain,
% 12.57/8.58 (((~![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))),
% 12.57/8.58 inference(rewrite,[status(thm)],[])).
% 12.57/8.58 tff(6997,plain,
% 12.57/8.58 ((~![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))),
% 12.57/8.58 inference(quant_inst,[status(thm)],[])).
% 12.57/8.58 tff(6998,plain,
% 12.57/8.58 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | m_counter_cell_v_carry_out(c_bit1, s59)),
% 12.57/8.58 inference(modus_ponens,[status(thm)],[6997, 6996])).
% 12.57/8.58 tff(6999,plain,
% 12.57/8.58 ($false),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[6998, 1368, 6995, 6994, 6993])).
% 12.57/8.58 tff(7000,plain,((~m_counter_cell_v_value(c_bit1, s59)) | m_counter_cell_v_carry_out(c_bit1, s59) | (~m_counter_cell_v_carry_in(c_bit1, s59))), inference(lemma,lemma(discharge,[]))).
% 12.57/8.58 tff(7001,plain,
% 12.57/8.58 ((~m_counter_cell_v_value(c_bit1, s59)) | m_counter_cell_v_carry_out(c_bit1, s59)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[7000, 6992])).
% 12.57/8.58 tff(7002,plain,
% 12.57/8.58 ($false),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[7001, 6955, 6925])).
% 12.57/8.58 tff(7003,plain,((~m_counter_cell_v_value(c_bit2, s58)) | (~m_counter_cell_v_value(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit2, s58)), inference(lemma,lemma(discharge,[]))).
% 12.57/8.58 tff(7004,plain,
% 12.57/8.58 ((~m_counter_cell_v_value(c_bit2, s58)) | (~m_counter_cell_v_value(c_bit1, s58))),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[7003, 3816])).
% 12.57/8.58 tff(7005,plain,
% 12.57/8.58 (~m_counter_cell_v_value(c_bit2, s58)),
% 12.57/8.58 inference(unit_resolution,[status(thm)],[7004, 3746])).
% 12.57/8.58 tff(7006,plain,
% 12.57/8.58 (((~![I0: $i, X: $i] : (m_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, s58) | m_counter_cell_v_value(c_bit2, s58) | (~node2(c_bit2, 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_bit2, s58) | m_counter_cell_v_value(c_bit2, s58) | (~node2(c_bit2, s58)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7007,plain,
% 12.65/8.58 ((~![I0: $i, X: $i] : (m_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, s58) | m_counter_cell_v_value(c_bit2, s58) | (~node2(c_bit2, s58)))),
% 12.65/8.58 inference(quant_inst,[status(thm)],[])).
% 12.65/8.58 tff(7008,plain,
% 12.65/8.58 ((~![I0: $i, X: $i] : (m_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, s58) | m_counter_cell_v_value(c_bit2, s58) | (~node2(c_bit2, s58))),
% 12.65/8.58 inference(modus_ponens,[status(thm)],[7007, 7006])).
% 12.65/8.58 tff(7009,plain,
% 12.65/8.58 (m_counter_cell_v_value(c_bit2, s58) | (~node2(c_bit2, s58))),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7008, 1449, 3808])).
% 12.65/8.58 tff(7010,plain,
% 12.65/8.58 (~node2(c_bit2, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7009, 7005])).
% 12.65/8.58 tff(7011,plain,
% 12.65/8.58 (((~![Y: $i, 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, s59)) | node2(c_bit2, s58) | (~node3(c_bit2, 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_bit2, s59)) | node2(c_bit2, s58) | (~node3(c_bit2, s58, s59)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7012,plain,
% 12.65/8.58 ((node2(c_bit2, s58) | (~node3(c_bit2, s58, s59)) | (~m_counter_cell_v_value(c_bit2, s59))) <=> ((~m_counter_cell_v_value(c_bit2, s59)) | node2(c_bit2, s58) | (~node3(c_bit2, s58, s59)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7013,plain,
% 12.65/8.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s58) | (~node3(c_bit2, s58, s59)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s59)) | node2(c_bit2, s58) | (~node3(c_bit2, s58, s59))))),
% 12.65/8.58 inference(monotonicity,[status(thm)],[7012])).
% 12.65/8.58 tff(7014,plain,
% 12.65/8.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s58) | (~node3(c_bit2, s58, s59)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s59)) | node2(c_bit2, s58) | (~node3(c_bit2, s58, s59)))),
% 12.65/8.58 inference(transitivity,[status(thm)],[7013, 7011])).
% 12.65/8.58 tff(7015,plain,
% 12.65/8.58 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s58) | (~node3(c_bit2, s58, s59)) | (~m_counter_cell_v_value(c_bit2, s59)))),
% 12.65/8.58 inference(quant_inst,[status(thm)],[])).
% 12.65/8.58 tff(7016,plain,
% 12.65/8.58 ((~![Y: $i, 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, s59)) | node2(c_bit2, s58) | (~node3(c_bit2, s58, s59))),
% 12.65/8.58 inference(modus_ponens,[status(thm)],[7015, 7014])).
% 12.65/8.58 tff(7017,plain,
% 12.65/8.58 ((~m_counter_cell_v_value(c_bit2, s59)) | node2(c_bit2, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7016, 141, 3841])).
% 12.65/8.58 tff(7018,plain,
% 12.65/8.58 (~m_counter_cell_v_value(c_bit2, s59)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7017, 7010])).
% 12.65/8.58 tff(7019,plain,
% 12.65/8.58 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s58)) | node3(c_bit2, s59, s58))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s58)) | node3(c_bit2, s59, s58))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7020,plain,
% 12.65/8.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s58)) | node3(c_bit2, s59, s58))),
% 12.65/8.58 inference(quant_inst,[status(thm)],[])).
% 12.65/8.58 tff(7021,plain,
% 12.65/8.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s58)) | node3(c_bit2, s59, s58)),
% 12.65/8.58 inference(modus_ponens,[status(thm)],[7020, 7019])).
% 12.65/8.58 tff(7022,plain,
% 12.65/8.58 ((~trans(s59, s58)) | node3(c_bit2, s59, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7021, 21])).
% 12.65/8.58 tff(7023,plain,
% 12.65/8.58 (node3(c_bit2, s59, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7022, 6308])).
% 12.65/8.58 tff(7024,assumption,(~m_counter_cell_v_value(c_bit2, s59)), introduced(assumption)).
% 12.65/8.58 tff(7025,plain,
% 12.65/8.58 (node1(c_bit2, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[3848, 7024])).
% 12.65/8.58 tff(7026,plain,
% 12.65/8.58 ((~m_counter_cell_v_value(c_bit2, s58)) | (~node1(c_bit2, s58))),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[3829, 1517, 3808])).
% 12.65/8.58 tff(7027,plain,
% 12.65/8.58 (~m_counter_cell_v_value(c_bit2, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7026, 7025])).
% 12.65/8.58 tff(7028,plain,
% 12.65/8.58 (((~![Y: $i, 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, s59) | (~node3(c_bit2, 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_bit2, s58) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s58)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7029,plain,
% 12.65/8.58 ((node1(c_bit2, s59) | (~node3(c_bit2, s59, s58)) | m_counter_cell_v_value(c_bit2, s58)) <=> (m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s58)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7030,plain,
% 12.65/8.58 (((~![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, 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, s59) | (~node3(c_bit2, s59, s58))))),
% 12.65/8.58 inference(monotonicity,[status(thm)],[7029])).
% 12.65/8.58 tff(7031,plain,
% 12.65/8.58 (((~![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, 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, s59) | (~node3(c_bit2, s59, s58)))),
% 12.65/8.58 inference(transitivity,[status(thm)],[7030, 7028])).
% 12.65/8.58 tff(7032,plain,
% 12.65/8.58 ((~![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, s58)) | m_counter_cell_v_value(c_bit2, s58))),
% 12.65/8.58 inference(quant_inst,[status(thm)],[])).
% 12.65/8.58 tff(7033,plain,
% 12.65/8.58 ((~![Y: $i, 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, s59) | (~node3(c_bit2, s59, s58))),
% 12.65/8.58 inference(modus_ponens,[status(thm)],[7032, 7031])).
% 12.65/8.58 tff(7034,plain,
% 12.65/8.58 (node1(c_bit2, s59)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7033, 106, 7027, 7023])).
% 12.65/8.58 tff(7035,plain,
% 12.65/8.58 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7036,plain,
% 12.65/8.58 (((~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)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7037,plain,
% 12.65/8.58 (((~![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))))),
% 12.65/8.58 inference(monotonicity,[status(thm)],[7036])).
% 12.65/8.58 tff(7038,plain,
% 12.65/8.58 (((~![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)))),
% 12.65/8.58 inference(transitivity,[status(thm)],[7037, 7035])).
% 12.65/8.58 tff(7039,plain,
% 12.65/8.58 ((~![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))),
% 12.65/8.58 inference(quant_inst,[status(thm)],[])).
% 12.65/8.58 tff(7040,plain,
% 12.65/8.58 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.58 inference(modus_ponens,[status(thm)],[7039, 7038])).
% 12.65/8.58 tff(7041,plain,
% 12.65/8.58 ((~m_counter_cell_v_carry_in(c_bit2, s59)) | (~node1(c_bit2, s59))),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7040, 77, 7024])).
% 12.65/8.58 tff(7042,plain,
% 12.65/8.58 (~m_counter_cell_v_carry_in(c_bit2, s59)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7041, 7034])).
% 12.65/8.58 tff(7043,plain,
% 12.65/8.58 (~m_counter_cell_v_carry_out(c_bit1, s59)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[6924, 7042])).
% 12.65/8.58 tff(7044,plain,
% 12.65/8.58 (~m_counter_cell_v_value(c_bit1, s59)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7001, 7043])).
% 12.65/8.58 tff(7045,plain,
% 12.65/8.58 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7046,plain,
% 12.65/8.58 (((~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)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7047,plain,
% 12.65/8.58 (((~![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))))),
% 12.65/8.58 inference(monotonicity,[status(thm)],[7046])).
% 12.65/8.58 tff(7048,plain,
% 12.65/8.58 (((~![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)))),
% 12.65/8.58 inference(transitivity,[status(thm)],[7047, 7045])).
% 12.65/8.58 tff(7049,plain,
% 12.65/8.58 ((~![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))),
% 12.65/8.58 inference(quant_inst,[status(thm)],[])).
% 12.65/8.58 tff(7050,plain,
% 12.65/8.58 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.58 inference(modus_ponens,[status(thm)],[7049, 7048])).
% 12.65/8.58 tff(7051,plain,
% 12.65/8.58 (m_counter_cell_v_value(c_bit1, s59) | (~node1(c_bit1, s59))),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7050, 77, 6992])).
% 12.65/8.58 tff(7052,plain,
% 12.65/8.58 (~node1(c_bit1, s59)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7051, 7044])).
% 12.65/8.58 tff(7053,plain,
% 12.65/8.58 (node1(c_bit1, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[6954, 7044])).
% 12.65/8.58 tff(7054,plain,
% 12.65/8.58 ((~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58))),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[6941, 1517, 3781])).
% 12.65/8.58 tff(7055,plain,
% 12.65/8.58 (~m_counter_cell_v_value(c_bit1, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7054, 7053])).
% 12.65/8.58 tff(7056,plain,
% 12.65/8.58 (((~![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))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7057,plain,
% 12.65/8.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s58)) | node3(c_bit1, s59, s58))),
% 12.65/8.58 inference(quant_inst,[status(thm)],[])).
% 12.65/8.58 tff(7058,plain,
% 12.65/8.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s58)) | node3(c_bit1, s59, s58)),
% 12.65/8.58 inference(modus_ponens,[status(thm)],[7057, 7056])).
% 12.65/8.58 tff(7059,plain,
% 12.65/8.58 ((~trans(s59, s58)) | node3(c_bit1, s59, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7058, 21])).
% 12.65/8.58 tff(7060,plain,
% 12.65/8.58 (node3(c_bit1, s59, s58)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7059, 6308])).
% 12.65/8.58 tff(7061,plain,
% 12.65/8.58 (((~![Y: $i, 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)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7062,plain,
% 12.65/8.58 ((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)))),
% 12.65/8.58 inference(rewrite,[status(thm)],[])).
% 12.65/8.58 tff(7063,plain,
% 12.65/8.58 (((~![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))))),
% 12.65/8.58 inference(monotonicity,[status(thm)],[7062])).
% 12.65/8.58 tff(7064,plain,
% 12.65/8.58 (((~![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)))),
% 12.65/8.58 inference(transitivity,[status(thm)],[7063, 7061])).
% 12.65/8.58 tff(7065,plain,
% 12.65/8.58 ((~![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))),
% 12.65/8.58 inference(quant_inst,[status(thm)],[])).
% 12.65/8.58 tff(7066,plain,
% 12.65/8.58 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59) | (~node3(c_bit1, s59, s58))),
% 12.65/8.58 inference(modus_ponens,[status(thm)],[7065, 7064])).
% 12.65/8.58 tff(7067,plain,
% 12.65/8.58 (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s59)),
% 12.65/8.58 inference(unit_resolution,[status(thm)],[7066, 106, 7060])).
% 12.65/8.59 tff(7068,plain,
% 12.65/8.59 ($false),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7067, 7055, 7052])).
% 12.65/8.59 tff(7069,plain,((~trans(s59, s58)) | m_counter_cell_v_value(c_bit2, s59)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.59 tff(7070,plain,
% 12.65/8.59 (~trans(s59, s58)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7069, 7018])).
% 12.65/8.59 tff(7071,plain,
% 12.65/8.59 (~node1(c_bit1, s58)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7054, 3746])).
% 12.65/8.59 tff(7072,plain,
% 12.65/8.59 (m_counter_cell_v_value(c_bit1, s59)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[6954, 7071])).
% 12.65/8.59 tff(7073,plain,
% 12.65/8.59 (m_counter_cell_v_carry_out(c_bit1, s59)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7001, 7072])).
% 12.65/8.59 tff(7074,plain,
% 12.65/8.59 (m_counter_cell_v_carry_in(c_bit2, s59)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[6924, 7073])).
% 12.65/8.59 tff(7075,plain,
% 12.65/8.59 (~node1(c_bit2, s59)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7040, 77, 7074, 7018])).
% 12.65/8.59 tff(7076,assumption,(~node1(c_bit2, s59)), introduced(assumption)).
% 12.65/8.59 tff(7077,assumption,(node3(c_bit2, s59, s59)), introduced(assumption)).
% 12.65/8.59 tff(7078,plain,
% 12.65/8.59 (((~![Y: $i, 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, s59) | (~node3(c_bit2, s59, 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, s59) | (~node3(c_bit2, s59, s59)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7079,plain,
% 12.65/8.59 ((node1(c_bit2, s59) | (~node3(c_bit2, s59, s59)) | m_counter_cell_v_value(c_bit2, s59)) <=> (m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s59)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7080,plain,
% 12.65/8.59 (((~![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, 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, s59) | (~node3(c_bit2, s59, s59))))),
% 12.65/8.59 inference(monotonicity,[status(thm)],[7079])).
% 12.65/8.59 tff(7081,plain,
% 12.65/8.59 (((~![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, 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, s59) | (~node3(c_bit2, s59, s59)))),
% 12.65/8.59 inference(transitivity,[status(thm)],[7080, 7078])).
% 12.65/8.59 tff(7082,plain,
% 12.65/8.59 ((~![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, s59)) | m_counter_cell_v_value(c_bit2, s59))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7083,plain,
% 12.65/8.59 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s59))),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7082, 7081])).
% 12.65/8.59 tff(7084,plain,
% 12.65/8.59 ($false),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7083, 106, 7024, 7077, 7076])).
% 12.65/8.59 tff(7085,plain,((~node3(c_bit2, s59, s59)) | m_counter_cell_v_value(c_bit2, s59) | node1(c_bit2, s59)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.59 tff(7086,plain,
% 12.65/8.59 (~node3(c_bit2, s59, s59)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7085, 7075, 7018])).
% 12.65/8.59 tff(7087,plain,
% 12.65/8.59 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s59)) | node3(c_bit2, s59, s59))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s59)) | node3(c_bit2, s59, s59))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7088,plain,
% 12.65/8.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s59)) | node3(c_bit2, s59, s59))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7089,plain,
% 12.65/8.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s59)) | node3(c_bit2, s59, s59)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7088, 7087])).
% 12.65/8.59 tff(7090,plain,
% 12.65/8.59 ((~trans(s59, s59)) | node3(c_bit2, s59, s59)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7089, 21])).
% 12.65/8.59 tff(7091,plain,
% 12.65/8.59 (~trans(s59, s59)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7090, 7086])).
% 12.65/8.59 tff(7092,plain,
% 12.65/8.59 (((~![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))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7093,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7094,plain,
% 12.65/8.59 ((~![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)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7093, 7092])).
% 12.65/8.59 tff(7095,plain,
% 12.65/8.59 ((~m_counter_cell_v_value(c_bit1, s55)) | m_counter_cell_v_carry_out(c_bit1, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7094, 1368, 3593])).
% 12.65/8.59 tff(7096,plain,
% 12.65/8.59 (m_counter_cell_v_carry_out(c_bit1, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7095, 3556])).
% 12.65/8.59 tff(7097,plain,
% 12.65/8.59 (((~![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))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7098,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7099,plain,
% 12.65/8.59 ((~![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)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7098, 7097])).
% 12.65/8.59 tff(7100,plain,
% 12.65/8.59 (m_counter_cell_v_carry_in(c_bit2, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7099, 6919, 7096])).
% 12.65/8.59 tff(7101,plain,
% 12.65/8.59 (((~![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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7102,plain,
% 12.65/8.59 ((~![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)))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7103,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7102, 7101])).
% 12.65/8.59 tff(7104,plain,
% 12.65/8.59 (~node4(c_bit1, s56)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7103, 1221, 3654])).
% 12.65/8.59 tff(7105,plain,
% 12.65/8.59 (((~![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))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7106,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7107,plain,
% 12.65/8.59 ((~![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)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7106, 7105])).
% 12.65/8.59 tff(7108,plain,
% 12.65/8.59 (~m_counter_cell_v_carry_out(c_bit1, s56)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7107, 1235, 7104])).
% 12.65/8.59 tff(7109,plain,
% 12.65/8.59 (((~![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))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7110,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7111,plain,
% 12.65/8.59 ((~![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)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7110, 7109])).
% 12.65/8.59 tff(7112,plain,
% 12.65/8.59 (~m_counter_cell_v_carry_in(c_bit2, s56)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7111, 3802, 7108])).
% 12.65/8.59 tff(7113,plain,
% 12.65/8.59 (((~![Y: $i, 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, s56) | node1(c_bit1, s55) | (~node3(c_bit1, 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_bit1, s56) | node1(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7114,plain,
% 12.65/8.59 ((node1(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | m_counter_cell_v_value(c_bit1, s56)) <=> (m_counter_cell_v_value(c_bit1, s56) | node1(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7115,plain,
% 12.65/8.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | m_counter_cell_v_value(c_bit1, 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_bit1, s56) | node1(c_bit1, s55) | (~node3(c_bit1, s55, s56))))),
% 12.65/8.59 inference(monotonicity,[status(thm)],[7114])).
% 12.65/8.59 tff(7116,plain,
% 12.65/8.59 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | m_counter_cell_v_value(c_bit1, 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_bit1, s56) | node1(c_bit1, s55) | (~node3(c_bit1, s55, s56)))),
% 12.65/8.59 inference(transitivity,[status(thm)],[7115, 7113])).
% 12.65/8.59 tff(7117,plain,
% 12.65/8.59 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s55) | (~node3(c_bit1, s55, s56)) | m_counter_cell_v_value(c_bit1, s56))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7118,plain,
% 12.65/8.59 ((~![Y: $i, 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, s56) | node1(c_bit1, s55) | (~node3(c_bit1, s55, s56))),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7117, 7116])).
% 12.65/8.59 tff(7119,plain,
% 12.65/8.59 (m_counter_cell_v_value(c_bit1, s56) | node1(c_bit1, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7118, 106, 3609])).
% 12.65/8.59 tff(7120,plain,
% 12.65/8.59 (node1(c_bit1, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7119, 3654])).
% 12.65/8.59 tff(7121,plain,
% 12.65/8.59 (((~![I0: $i, X: $i] : ((~node1(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, s55)) | m_counter_cell_v_value(c_bit1, s55) | (~node1(c_bit1, 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_bit1, s55)) | m_counter_cell_v_value(c_bit1, s55) | (~node1(c_bit1, s55)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7122,plain,
% 12.65/8.59 (((~node1(c_bit1, s55)) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | m_counter_cell_v_value(c_bit1, s55)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s55)) | m_counter_cell_v_value(c_bit1, s55) | (~node1(c_bit1, s55)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7123,plain,
% 12.65/8.59 (((~![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, s55)) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | m_counter_cell_v_value(c_bit1, 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_bit1, s55)) | m_counter_cell_v_value(c_bit1, s55) | (~node1(c_bit1, s55))))),
% 12.65/8.59 inference(monotonicity,[status(thm)],[7122])).
% 12.65/8.59 tff(7124,plain,
% 12.65/8.59 (((~![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, s55)) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | m_counter_cell_v_value(c_bit1, 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_bit1, s55)) | m_counter_cell_v_value(c_bit1, s55) | (~node1(c_bit1, s55)))),
% 12.65/8.59 inference(transitivity,[status(thm)],[7123, 7121])).
% 12.65/8.59 tff(7125,plain,
% 12.65/8.59 ((~![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, s55)) | (~m_counter_cell_v_carry_in(c_bit1, s55)) | m_counter_cell_v_value(c_bit1, s55))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7126,plain,
% 12.65/8.59 ((~![I0: $i, X: $i] : ((~node1(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, s55)) | m_counter_cell_v_value(c_bit1, s55) | (~node1(c_bit1, s55))),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7125, 7124])).
% 12.65/8.59 tff(7127,plain,
% 12.65/8.59 (m_counter_cell_v_value(c_bit1, s55) | (~node1(c_bit1, s55))),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7126, 77, 3593])).
% 12.65/8.59 tff(7128,plain,
% 12.65/8.59 (m_counter_cell_v_value(c_bit1, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7127, 7120])).
% 12.65/8.59 tff(7129,plain,
% 12.65/8.59 (m_counter_cell_v_carry_out(c_bit1, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7095, 7128])).
% 12.65/8.59 tff(7130,plain,
% 12.65/8.59 (m_counter_cell_v_carry_in(c_bit2, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7099, 6919, 7129])).
% 12.65/8.59 tff(7131,assumption,(~m_counter_cell_v_value(c_bit2, s55)), introduced(assumption)).
% 12.65/8.59 tff(7132,plain,
% 12.65/8.59 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7133,plain,
% 12.65/8.59 (((~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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7134,plain,
% 12.65/8.59 (((~![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))))),
% 12.65/8.59 inference(monotonicity,[status(thm)],[7133])).
% 12.65/8.59 tff(7135,plain,
% 12.65/8.59 (((~![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)))),
% 12.65/8.59 inference(transitivity,[status(thm)],[7134, 7132])).
% 12.65/8.59 tff(7136,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7137,plain,
% 12.65/8.59 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7136, 7135])).
% 12.65/8.59 tff(7138,plain,
% 12.65/8.59 ((~m_counter_cell_v_carry_in(c_bit2, s55)) | (~node1(c_bit2, s55))),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7137, 77, 7131])).
% 12.65/8.59 tff(7139,plain,
% 12.65/8.59 (~node1(c_bit2, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7138, 7130])).
% 12.65/8.59 tff(7140,plain,
% 12.65/8.59 (((~![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))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7141,plain,
% 12.65/8.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit2, s55, s56))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7142,plain,
% 12.65/8.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit2, s55, s56)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7141, 7140])).
% 12.65/8.59 tff(7143,plain,
% 12.65/8.59 (node3(c_bit2, s55, s56)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7142, 21, 3605])).
% 12.65/8.59 tff(7144,plain,
% 12.65/8.59 (((~![Y: $i, 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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7145,plain,
% 12.65/8.59 ((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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7146,plain,
% 12.65/8.59 (((~![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))))),
% 12.65/8.59 inference(monotonicity,[status(thm)],[7145])).
% 12.65/8.59 tff(7147,plain,
% 12.65/8.59 (((~![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)))),
% 12.65/8.59 inference(transitivity,[status(thm)],[7146, 7144])).
% 12.65/8.59 tff(7148,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7149,plain,
% 12.65/8.59 ((~![Y: $i, 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))),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7148, 7147])).
% 12.65/8.59 tff(7150,plain,
% 12.65/8.59 (m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s55)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7149, 106, 7143])).
% 12.65/8.59 tff(7151,plain,
% 12.65/8.59 (m_counter_cell_v_value(c_bit2, s56)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7150, 7139])).
% 12.65/8.59 tff(7152,plain,
% 12.65/8.59 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7153,plain,
% 12.65/8.59 (((~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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7154,plain,
% 12.65/8.59 (((~![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))))),
% 12.65/8.59 inference(monotonicity,[status(thm)],[7153])).
% 12.65/8.59 tff(7155,plain,
% 12.65/8.59 (((~![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)))),
% 12.65/8.59 inference(transitivity,[status(thm)],[7154, 7152])).
% 12.65/8.59 tff(7156,plain,
% 12.65/8.59 ((~![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)))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7157,plain,
% 12.65/8.59 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7156, 7155])).
% 12.65/8.59 tff(7158,plain,
% 12.65/8.59 (m_counter_cell_v_carry_in(c_bit2, s56) | (~node1(c_bit2, s56))),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7157, 1517, 7151])).
% 12.65/8.59 tff(7159,plain,
% 12.65/8.59 (~node1(c_bit2, s56)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7158, 7112])).
% 12.65/8.59 tff(7160,plain,
% 12.65/8.59 (~node2(c_bit1, s56)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[3659, 3654])).
% 12.65/8.59 tff(7161,plain,
% 12.65/8.59 (~m_counter_cell_v_value(c_bit1, s57)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[3678, 7160])).
% 12.65/8.59 tff(7162,plain,
% 12.65/8.59 (((~![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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7163,plain,
% 12.65/8.59 ((~![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)))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7164,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7163, 7162])).
% 12.65/8.59 tff(7165,plain,
% 12.65/8.59 (~node4(c_bit1, s57)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7164, 1221, 7161])).
% 12.65/8.59 tff(7166,plain,
% 12.65/8.59 (((~![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))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7167,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7168,plain,
% 12.65/8.59 ((~![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)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7167, 7166])).
% 12.65/8.59 tff(7169,plain,
% 12.65/8.59 (~m_counter_cell_v_carry_out(c_bit1, s57)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7168, 1235, 7165])).
% 12.65/8.59 tff(7170,plain,
% 12.65/8.59 (((~![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))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7171,plain,
% 12.65/8.59 ((~![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))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7172,plain,
% 12.65/8.59 ((~![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)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7171, 7170])).
% 12.65/8.59 tff(7173,plain,
% 12.65/8.59 (~m_counter_cell_v_carry_in(c_bit2, s57)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7172, 3802, 7169])).
% 12.65/8.59 tff(7174,plain,
% 12.65/8.59 (~node1(c_bit1, s57)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[3726, 7161])).
% 12.65/8.59 tff(7175,plain,
% 12.65/8.59 (m_counter_cell_v_value(c_bit1, s58)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[3745, 7174])).
% 12.65/8.59 tff(7176,plain,
% 12.65/8.59 (~m_counter_cell_v_value(c_bit2, s58)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7004, 7175])).
% 12.65/8.59 tff(7177,plain,
% 12.65/8.59 (((~![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))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7178,plain,
% 12.65/8.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit2, s57, s58))),
% 12.65/8.59 inference(quant_inst,[status(thm)],[])).
% 12.65/8.59 tff(7179,plain,
% 12.65/8.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit2, s57, s58)),
% 12.65/8.59 inference(modus_ponens,[status(thm)],[7178, 7177])).
% 12.65/8.59 tff(7180,plain,
% 12.65/8.59 (node3(c_bit2, s57, s58)),
% 12.65/8.59 inference(unit_resolution,[status(thm)],[7179, 21, 3734])).
% 12.65/8.59 tff(7181,plain,
% 12.65/8.59 (((~![Y: $i, 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)))),
% 12.65/8.59 inference(rewrite,[status(thm)],[])).
% 12.65/8.59 tff(7182,plain,
% 12.65/8.59 ((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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7183,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7182])).
% 12.65/8.60 tff(7184,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7183, 7181])).
% 12.65/8.60 tff(7185,plain,
% 12.65/8.60 ((~![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))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7186,plain,
% 12.65/8.60 ((~![Y: $i, 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))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7185, 7184])).
% 12.65/8.60 tff(7187,plain,
% 12.65/8.60 (m_counter_cell_v_value(c_bit2, s58) | node1(c_bit2, s57)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7186, 106, 7180])).
% 12.65/8.60 tff(7188,plain,
% 12.65/8.60 (node1(c_bit2, s57)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7187, 7176])).
% 12.65/8.60 tff(7189,plain,
% 12.65/8.60 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7190,plain,
% 12.65/8.60 (((~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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7191,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7190])).
% 12.65/8.60 tff(7192,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7191, 7189])).
% 12.65/8.60 tff(7193,plain,
% 12.65/8.60 ((~![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)))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7194,plain,
% 12.65/8.60 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7193, 7192])).
% 12.65/8.60 tff(7195,plain,
% 12.65/8.60 (m_counter_cell_v_carry_in(c_bit2, s57) | (~m_counter_cell_v_value(c_bit2, s57))),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7194, 1517, 7188])).
% 12.65/8.60 tff(7196,plain,
% 12.65/8.60 (~m_counter_cell_v_value(c_bit2, s57)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7195, 7173])).
% 12.65/8.60 tff(7197,plain,
% 12.65/8.60 (((~![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))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7198,plain,
% 12.65/8.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit2, s56, s57))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7199,plain,
% 12.65/8.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit2, s56, s57)),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7198, 7197])).
% 12.65/8.60 tff(7200,plain,
% 12.65/8.60 (node3(c_bit2, s56, s57)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7199, 21, 3667])).
% 12.65/8.60 tff(7201,plain,
% 12.65/8.60 (((~![Y: $i, 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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7202,plain,
% 12.65/8.60 ((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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7203,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7202])).
% 12.65/8.60 tff(7204,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7203, 7201])).
% 12.65/8.60 tff(7205,plain,
% 12.65/8.60 ((~![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))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7206,plain,
% 12.65/8.60 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56) | (~node3(c_bit2, s56, s57))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7205, 7204])).
% 12.65/8.60 tff(7207,plain,
% 12.65/8.60 (m_counter_cell_v_value(c_bit2, s57) | node1(c_bit2, s56)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7206, 106, 7200])).
% 12.65/8.60 tff(7208,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7207, 7196, 7159])).
% 12.65/8.60 tff(7209,plain,(m_counter_cell_v_value(c_bit1, s56) | m_counter_cell_v_value(c_bit2, s55)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7210,plain,
% 12.65/8.60 (m_counter_cell_v_value(c_bit2, s55)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7209, 3617])).
% 12.65/8.60 tff(7211,plain,
% 12.65/8.60 (((~![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))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7212,plain,
% 12.65/8.60 ((~![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))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7213,plain,
% 12.65/8.60 ((~![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)),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7212, 7211])).
% 12.65/8.60 tff(7214,plain,
% 12.65/8.60 ((~m_counter_cell_v_carry_in(c_bit2, s55)) | m_counter_cell_v_carry_out(c_bit2, s55)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7213, 1368, 7210])).
% 12.65/8.60 tff(7215,plain,
% 12.65/8.60 (m_counter_cell_v_carry_out(c_bit2, s55)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7214, 7100])).
% 12.65/8.60 tff(7216,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7217,plain,
% 12.65/8.60 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s55)) | (~m_counter_cell_v_carry_out(c_bit2, s55)))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7218,plain,
% 12.65/8.60 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s55)) | (~m_counter_cell_v_carry_out(c_bit2, s55))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7217, 7216])).
% 12.65/8.60 tff(7219,plain,
% 12.65/8.60 (~always5(s55)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7218, 6898, 7215])).
% 12.65/8.60 tff(7220,assumption,(~always5(s55)), introduced(assumption)).
% 12.65/8.60 tff(7221,plain,
% 12.65/8.60 (~always5(s54)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3899, 7220])).
% 12.65/8.60 tff(7222,plain,
% 12.65/8.60 (~always5(s53)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3907, 7221])).
% 12.65/8.60 tff(7223,plain,
% 12.65/8.60 (~always5(s52)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3915, 7222])).
% 12.65/8.60 tff(7224,plain,
% 12.65/8.60 (~always5(s51)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3923, 7223])).
% 12.65/8.60 tff(7225,plain,
% 12.65/8.60 (~always5(s50)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3931, 7224])).
% 12.65/8.60 tff(7226,plain,
% 12.65/8.60 (~always5(s49)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3939, 7225])).
% 12.65/8.60 tff(7227,plain,
% 12.65/8.60 (~always5(s48)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3947, 7226])).
% 12.65/8.60 tff(7228,plain,
% 12.65/8.60 (~always5(s47)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3955, 7227])).
% 12.65/8.60 tff(7229,plain,
% 12.65/8.60 (~always5(s46)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3963, 7228])).
% 12.65/8.60 tff(7230,plain,
% 12.65/8.60 (~always5(s45)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3971, 7229])).
% 12.65/8.60 tff(7231,plain,
% 12.65/8.60 (~always5(s44)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3979, 7230])).
% 12.65/8.60 tff(7232,plain,
% 12.65/8.60 (~always5(s43)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3987, 7231])).
% 12.65/8.60 tff(7233,plain,
% 12.65/8.60 (~always5(s42)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3995, 7232])).
% 12.65/8.60 tff(7234,plain,
% 12.65/8.60 (~always5(s41)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4003, 7233])).
% 12.65/8.60 tff(7235,plain,
% 12.65/8.60 (~always5(s40)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4011, 7234])).
% 12.65/8.60 tff(7236,plain,
% 12.65/8.60 (~always5(s39)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4019, 7235])).
% 12.65/8.60 tff(7237,plain,
% 12.65/8.60 (~always5(s38)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4027, 7236])).
% 12.65/8.60 tff(7238,plain,
% 12.65/8.60 (~always5(s37)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4035, 7237])).
% 12.65/8.60 tff(7239,plain,
% 12.65/8.60 (~always5(s36)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4043, 7238])).
% 12.65/8.60 tff(7240,plain,
% 12.65/8.60 (~always5(s35)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4051, 7239])).
% 12.65/8.60 tff(7241,plain,
% 12.65/8.60 (~always5(s34)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4059, 7240])).
% 12.65/8.60 tff(7242,plain,
% 12.65/8.60 (~always5(s33)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4067, 7241])).
% 12.65/8.60 tff(7243,plain,
% 12.65/8.60 (~always5(s32)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4075, 7242])).
% 12.65/8.60 tff(7244,plain,
% 12.65/8.60 (~always5(s31)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4083, 7243])).
% 12.65/8.60 tff(7245,plain,
% 12.65/8.60 (~always5(s30)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4091, 7244])).
% 12.65/8.60 tff(7246,assumption,(~trans(s59, s59)), introduced(assumption)).
% 12.65/8.60 tff(7247,assumption,(~always5(s51)), introduced(assumption)).
% 12.65/8.60 tff(7248,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s51) | (~trans(s59, s51)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s51) | (~trans(s59, s51)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7249,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s51)) | always5(s51)) <=> ((~always5(s59)) | always5(s51) | (~trans(s59, s51)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7250,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s51) | (~trans(s59, s51))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7249])).
% 12.65/8.60 tff(7251,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s51) | (~trans(s59, s51)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7250, 7248])).
% 12.65/8.60 tff(7252,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s51)) | always5(s51))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7253,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s51) | (~trans(s59, s51))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7252, 7251])).
% 12.65/8.60 tff(7254,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7253, 5772, 3860, 6888, 7247])).
% 12.65/8.60 tff(7255,plain,((~trans(s59, s51)) | always5(s51)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7256,plain,
% 12.65/8.60 (~trans(s59, s51)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7255, 7224])).
% 12.65/8.60 tff(7257,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7258,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s55)) | always5(s55)) <=> ((~always5(s59)) | always5(s55) | (~trans(s59, s55)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7259,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7258])).
% 12.65/8.60 tff(7260,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7259, 7257])).
% 12.65/8.60 tff(7261,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s55)) | always5(s55))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7262,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s55) | (~trans(s59, s55))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7261, 7260])).
% 12.65/8.60 tff(7263,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7262, 5761, 3860, 6888, 7220])).
% 12.65/8.60 tff(7264,plain,((~trans(s59, s55)) | always5(s55)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7265,plain,
% 12.65/8.60 (~trans(s59, s55)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7264, 7220])).
% 12.65/8.60 tff(7266,assumption,(~trans(s59, s58)), introduced(assumption)).
% 12.65/8.60 tff(7267,assumption,(~trans(s59, s56)), introduced(assumption)).
% 12.65/8.60 tff(7268,assumption,(~always5(s37)), introduced(assumption)).
% 12.65/8.60 tff(7269,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s37) | (~trans(s59, s37)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s37) | (~trans(s59, s37)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7270,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s37)) | always5(s37)) <=> ((~always5(s59)) | always5(s37) | (~trans(s59, s37)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7271,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s37) | (~trans(s59, s37))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7270])).
% 12.65/8.60 tff(7272,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s37) | (~trans(s59, s37)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7271, 7269])).
% 12.65/8.60 tff(7273,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s37)) | always5(s37))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7274,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s37) | (~trans(s59, s37))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7273, 7272])).
% 12.65/8.60 tff(7275,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7274, 5739, 3860, 6888, 7268])).
% 12.65/8.60 tff(7276,plain,((~trans(s59, s37)) | always5(s37)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7277,plain,
% 12.65/8.60 (~trans(s59, s37)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7276, 7238])).
% 12.65/8.60 tff(7278,assumption,(~always5(s54)), introduced(assumption)).
% 12.65/8.60 tff(7279,plain,
% 12.65/8.60 (~always5(s53)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3907, 7278])).
% 12.65/8.60 tff(7280,plain,
% 12.65/8.60 (~always5(s52)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3915, 7279])).
% 12.65/8.60 tff(7281,plain,
% 12.65/8.60 (~always5(s51)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3923, 7280])).
% 12.65/8.60 tff(7282,plain,
% 12.65/8.60 (~always5(s50)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3931, 7281])).
% 12.65/8.60 tff(7283,plain,
% 12.65/8.60 (~always5(s49)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3939, 7282])).
% 12.65/8.60 tff(7284,plain,
% 12.65/8.60 (~always5(s48)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3947, 7283])).
% 12.65/8.60 tff(7285,plain,
% 12.65/8.60 (~always5(s47)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3955, 7284])).
% 12.65/8.60 tff(7286,plain,
% 12.65/8.60 (~always5(s46)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3963, 7285])).
% 12.65/8.60 tff(7287,plain,
% 12.65/8.60 (~always5(s45)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3971, 7286])).
% 12.65/8.60 tff(7288,plain,
% 12.65/8.60 (~always5(s44)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3979, 7287])).
% 12.65/8.60 tff(7289,plain,
% 12.65/8.60 (~always5(s43)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3987, 7288])).
% 12.65/8.60 tff(7290,plain,
% 12.65/8.60 (~always5(s42)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[3995, 7289])).
% 12.65/8.60 tff(7291,plain,
% 12.65/8.60 (~always5(s41)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4003, 7290])).
% 12.65/8.60 tff(7292,plain,
% 12.65/8.60 (~always5(s40)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4011, 7291])).
% 12.65/8.60 tff(7293,plain,
% 12.65/8.60 (~always5(s39)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4019, 7292])).
% 12.65/8.60 tff(7294,assumption,(~always5(s39)), introduced(assumption)).
% 12.65/8.60 tff(7295,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7296,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s39)) | always5(s39)) <=> ((~always5(s59)) | always5(s39) | (~trans(s59, s39)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7297,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7296])).
% 12.65/8.60 tff(7298,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7297, 7295])).
% 12.65/8.60 tff(7299,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s39)) | always5(s39))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7300,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s39) | (~trans(s59, s39))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7299, 7298])).
% 12.65/8.60 tff(7301,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7300, 6253, 3860, 6888, 7294])).
% 12.65/8.60 tff(7302,plain,((~trans(s59, s39)) | always5(s39)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7303,plain,
% 12.65/8.60 (~trans(s59, s39)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7302, 7293])).
% 12.65/8.60 tff(7304,assumption,(~trans(s59, s37)), introduced(assumption)).
% 12.65/8.60 tff(7305,assumption,(~trans(s59, s55)), introduced(assumption)).
% 12.65/8.60 tff(7306,assumption,(~trans(s59, s51)), introduced(assumption)).
% 12.65/8.60 tff(7307,plain,
% 12.65/8.60 (~always5(s38)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4027, 7293])).
% 12.65/8.60 tff(7308,plain,
% 12.65/8.60 (~always5(s37)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4035, 7307])).
% 12.65/8.60 tff(7309,plain,
% 12.65/8.60 (~always5(s36)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4043, 7308])).
% 12.65/8.60 tff(7310,plain,
% 12.65/8.60 (~always5(s35)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4051, 7309])).
% 12.65/8.60 tff(7311,plain,
% 12.65/8.60 (~always5(s34)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4059, 7310])).
% 12.65/8.60 tff(7312,plain,
% 12.65/8.60 (~always5(s33)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4067, 7311])).
% 12.65/8.60 tff(7313,plain,
% 12.65/8.60 (~always5(s32)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4075, 7312])).
% 12.65/8.60 tff(7314,plain,
% 12.65/8.60 (~always5(s31)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4083, 7313])).
% 12.65/8.60 tff(7315,plain,
% 12.65/8.60 (~always5(s30)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4091, 7314])).
% 12.65/8.60 tff(7316,plain,
% 12.65/8.60 (~always5(s29)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4099, 7315])).
% 12.65/8.60 tff(7317,plain,
% 12.65/8.60 (~always5(s28)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4107, 7316])).
% 12.65/8.60 tff(7318,assumption,(~always5(s28)), introduced(assumption)).
% 12.65/8.60 tff(7319,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7320,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s28)) | always5(s28)) <=> ((~always5(s59)) | always5(s28) | (~trans(s59, s28)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7321,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7320])).
% 12.65/8.60 tff(7322,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7321, 7319])).
% 12.65/8.60 tff(7323,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s28)) | always5(s28))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7324,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s28) | (~trans(s59, s28))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7323, 7322])).
% 12.65/8.60 tff(7325,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7324, 6044, 3860, 6888, 7318])).
% 12.65/8.60 tff(7326,plain,((~trans(s59, s28)) | always5(s28)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7327,plain,
% 12.65/8.60 (~trans(s59, s28)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7326, 7317])).
% 12.65/8.60 tff(7328,plain,
% 12.65/8.60 (~always5(s27)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4115, 7317])).
% 12.65/8.60 tff(7329,assumption,(~always5(s27)), introduced(assumption)).
% 12.65/8.60 tff(7330,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7331,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s27)) | always5(s27)) <=> ((~always5(s59)) | always5(s27) | (~trans(s59, s27)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7332,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7331])).
% 12.65/8.60 tff(7333,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7332, 7330])).
% 12.65/8.60 tff(7334,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s27)) | always5(s27))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7335,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s27) | (~trans(s59, s27))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7334, 7333])).
% 12.65/8.60 tff(7336,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7335, 6187, 3860, 6888, 7329])).
% 12.65/8.60 tff(7337,plain,((~trans(s59, s27)) | always5(s27)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7338,plain,
% 12.65/8.60 (~trans(s59, s27)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7337, 7328])).
% 12.65/8.60 tff(7339,assumption,(~always5(s29)), introduced(assumption)).
% 12.65/8.60 tff(7340,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7341,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s29)) | always5(s29)) <=> ((~always5(s59)) | always5(s29) | (~trans(s59, s29)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7342,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7341])).
% 12.65/8.60 tff(7343,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7342, 7340])).
% 12.65/8.60 tff(7344,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s29)) | always5(s29))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7345,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s29) | (~trans(s59, s29))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7344, 7343])).
% 12.65/8.60 tff(7346,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7345, 5890, 3860, 6888, 7339])).
% 12.65/8.60 tff(7347,plain,((~trans(s59, s29)) | always5(s29)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7348,plain,
% 12.65/8.60 (~trans(s59, s29)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7347, 7316])).
% 12.65/8.60 tff(7349,plain,
% 12.65/8.60 (~always5(s26)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4123, 7328])).
% 12.65/8.60 tff(7350,plain,
% 12.65/8.60 (~always5(s25)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4131, 7349])).
% 12.65/8.60 tff(7351,plain,
% 12.65/8.60 (~always5(s24)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4139, 7350])).
% 12.65/8.60 tff(7352,plain,
% 12.65/8.60 (~always5(s23)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4147, 7351])).
% 12.65/8.60 tff(7353,plain,
% 12.65/8.60 (~always5(s22)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4155, 7352])).
% 12.65/8.60 tff(7354,plain,
% 12.65/8.60 (~always5(s21)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4163, 7353])).
% 12.65/8.60 tff(7355,plain,
% 12.65/8.60 (~always5(s20)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4171, 7354])).
% 12.65/8.60 tff(7356,plain,
% 12.65/8.60 (~always5(s19)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4179, 7355])).
% 12.65/8.60 tff(7357,plain,
% 12.65/8.60 (~always5(s18)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[4187, 7356])).
% 12.65/8.60 tff(7358,assumption,(~always5(s18)), introduced(assumption)).
% 12.65/8.60 tff(7359,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7360,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s18)) | always5(s18)) <=> ((~always5(s59)) | always5(s18) | (~trans(s59, s18)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7361,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7360])).
% 12.65/8.60 tff(7362,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7361, 7359])).
% 12.65/8.60 tff(7363,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s18)) | always5(s18))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7364,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s18) | (~trans(s59, s18))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7363, 7362])).
% 12.65/8.60 tff(7365,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7364, 6033, 3860, 6888, 7358])).
% 12.65/8.60 tff(7366,plain,((~trans(s59, s18)) | always5(s18)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7367,plain,
% 12.65/8.60 (~trans(s59, s18)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7366, 7357])).
% 12.65/8.60 tff(7368,assumption,(~always5(s34)), introduced(assumption)).
% 12.65/8.60 tff(7369,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7370,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s34)) | always5(s34)) <=> ((~always5(s59)) | always5(s34) | (~trans(s59, s34)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7371,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7370])).
% 12.65/8.60 tff(7372,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7371, 7369])).
% 12.65/8.60 tff(7373,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s34)) | always5(s34))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7374,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s34) | (~trans(s59, s34))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7373, 7372])).
% 12.65/8.60 tff(7375,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7374, 5923, 3860, 6888, 7368])).
% 12.65/8.60 tff(7376,plain,((~trans(s59, s34)) | always5(s34)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7377,plain,
% 12.65/8.60 (~trans(s59, s34)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7376, 7311])).
% 12.65/8.60 tff(7378,assumption,(~always5(s48)), introduced(assumption)).
% 12.65/8.60 tff(7379,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7380,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s48)) | always5(s48)) <=> ((~always5(s59)) | always5(s48) | (~trans(s59, s48)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7381,plain,
% 12.65/8.60 (((~![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))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7380])).
% 12.65/8.60 tff(7382,plain,
% 12.65/8.60 (((~![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)))),
% 12.65/8.60 inference(transitivity,[status(thm)],[7381, 7379])).
% 12.65/8.60 tff(7383,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s48)) | always5(s48))),
% 12.65/8.60 inference(quant_inst,[status(thm)],[])).
% 12.65/8.60 tff(7384,plain,
% 12.65/8.60 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s48) | (~trans(s59, s48))),
% 12.65/8.60 inference(modus_ponens,[status(thm)],[7383, 7382])).
% 12.65/8.60 tff(7385,plain,
% 12.65/8.60 ($false),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7384, 5857, 3860, 6888, 7378])).
% 12.65/8.60 tff(7386,plain,((~trans(s59, s48)) | always5(s48)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.60 tff(7387,plain,
% 12.65/8.60 (~trans(s59, s48)),
% 12.65/8.60 inference(unit_resolution,[status(thm)],[7386, 7284])).
% 12.65/8.60 tff(7388,assumption,(~always5(s45)), introduced(assumption)).
% 12.65/8.60 tff(7389,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s45) | (~trans(s59, s45)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s45) | (~trans(s59, s45)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7390,plain,
% 12.65/8.60 (((~always5(s59)) | (~trans(s59, s45)) | always5(s45)) <=> ((~always5(s59)) | always5(s45) | (~trans(s59, s45)))),
% 12.65/8.60 inference(rewrite,[status(thm)],[])).
% 12.65/8.60 tff(7391,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s45) | (~trans(s59, s45))))),
% 12.65/8.60 inference(monotonicity,[status(thm)],[7390])).
% 12.65/8.60 tff(7392,plain,
% 12.65/8.60 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s45) | (~trans(s59, s45)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7391, 7389])).
% 12.65/8.61 tff(7393,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s45)) | always5(s45))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7394,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s45) | (~trans(s59, s45))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7393, 7392])).
% 12.65/8.61 tff(7395,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7394, 6165, 3860, 6888, 7388])).
% 12.65/8.61 tff(7396,plain,((~trans(s59, s45)) | always5(s45)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7397,plain,
% 12.65/8.61 (~trans(s59, s45)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7396, 7287])).
% 12.65/8.61 tff(7398,assumption,(~always5(s46)), introduced(assumption)).
% 12.65/8.61 tff(7399,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7400,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s46)) | always5(s46)) <=> ((~always5(s59)) | always5(s46) | (~trans(s59, s46)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7401,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7400])).
% 12.65/8.61 tff(7402,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7401, 7399])).
% 12.65/8.61 tff(7403,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s46)) | always5(s46))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7404,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s46) | (~trans(s59, s46))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7403, 7402])).
% 12.65/8.61 tff(7405,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7404, 6275, 3860, 6888, 7398])).
% 12.65/8.61 tff(7406,plain,((~trans(s59, s46)) | always5(s46)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7407,plain,
% 12.65/8.61 (~trans(s59, s46)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7406, 7286])).
% 12.65/8.61 tff(7408,assumption,(~always5(s47)), introduced(assumption)).
% 12.65/8.61 tff(7409,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7410,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s47)) | always5(s47)) <=> ((~always5(s59)) | always5(s47) | (~trans(s59, s47)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7411,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7410])).
% 12.65/8.61 tff(7412,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7411, 7409])).
% 12.65/8.61 tff(7413,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s47)) | always5(s47))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7414,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s47) | (~trans(s59, s47))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7413, 7412])).
% 12.65/8.61 tff(7415,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7414, 6121, 3860, 6888, 7408])).
% 12.65/8.61 tff(7416,plain,((~trans(s59, s47)) | always5(s47)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7417,plain,
% 12.65/8.61 (~trans(s59, s47)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7416, 7285])).
% 12.65/8.61 tff(7418,assumption,(~always5(s49)), introduced(assumption)).
% 12.65/8.61 tff(7419,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s49) | (~trans(s59, s49)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s49) | (~trans(s59, s49)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7420,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s49)) | always5(s49)) <=> ((~always5(s59)) | always5(s49) | (~trans(s59, s49)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7421,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s49) | (~trans(s59, s49))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7420])).
% 12.65/8.61 tff(7422,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s49) | (~trans(s59, s49)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7421, 7419])).
% 12.65/8.61 tff(7423,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s49)) | always5(s49))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7424,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s49) | (~trans(s59, s49))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7423, 7422])).
% 12.65/8.61 tff(7425,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7424, 6286, 3860, 6888, 7418])).
% 12.65/8.61 tff(7426,plain,((~trans(s59, s49)) | always5(s49)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7427,plain,
% 12.65/8.61 (~trans(s59, s49)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7426, 7283])).
% 12.65/8.61 tff(7428,assumption,(~always5(s50)), introduced(assumption)).
% 12.65/8.61 tff(7429,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7430,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s50)) | always5(s50)) <=> ((~always5(s59)) | always5(s50) | (~trans(s59, s50)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7431,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7430])).
% 12.65/8.61 tff(7432,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7431, 7429])).
% 12.65/8.61 tff(7433,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s50)) | always5(s50))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7434,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s50) | (~trans(s59, s50))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7433, 7432])).
% 12.65/8.61 tff(7435,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7434, 6209, 3860, 6888, 7428])).
% 12.65/8.61 tff(7436,plain,((~trans(s59, s50)) | always5(s50)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7437,plain,
% 12.65/8.61 (~trans(s59, s50)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7436, 7282])).
% 12.65/8.61 tff(7438,assumption,(~always5(s53)), introduced(assumption)).
% 12.65/8.61 tff(7439,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s53) | (~trans(s59, s53)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s53) | (~trans(s59, s53)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7440,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s53)) | always5(s53)) <=> ((~always5(s59)) | always5(s53) | (~trans(s59, s53)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7441,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s53) | (~trans(s59, s53))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7440])).
% 12.65/8.61 tff(7442,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s53) | (~trans(s59, s53)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7441, 7439])).
% 12.65/8.61 tff(7443,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s53)) | always5(s53))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7444,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s53) | (~trans(s59, s53))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7443, 7442])).
% 12.65/8.61 tff(7445,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7444, 6011, 3860, 6888, 7438])).
% 12.65/8.61 tff(7446,plain,((~trans(s59, s53)) | always5(s53)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7447,plain,
% 12.65/8.61 (~trans(s59, s53)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7446, 7279])).
% 12.65/8.61 tff(7448,assumption,(~always5(s52)), introduced(assumption)).
% 12.65/8.61 tff(7449,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7450,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s52)) | always5(s52)) <=> ((~always5(s59)) | always5(s52) | (~trans(s59, s52)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7451,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7450])).
% 12.65/8.61 tff(7452,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7451, 7449])).
% 12.65/8.61 tff(7453,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s52)) | always5(s52))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7454,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s52) | (~trans(s59, s52))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7453, 7452])).
% 12.65/8.61 tff(7455,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7454, 6264, 3860, 6888, 7448])).
% 12.65/8.61 tff(7456,plain,((~trans(s59, s52)) | always5(s52)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7457,plain,
% 12.65/8.61 (~trans(s59, s52)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7456, 7280])).
% 12.65/8.61 tff(7458,assumption,(~always5(s44)), introduced(assumption)).
% 12.65/8.61 tff(7459,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7460,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s44)) | always5(s44)) <=> ((~always5(s59)) | always5(s44) | (~trans(s59, s44)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7461,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7460])).
% 12.65/8.61 tff(7462,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7461, 7459])).
% 12.65/8.61 tff(7463,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s44)) | always5(s44))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7464,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s44) | (~trans(s59, s44))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7463, 7462])).
% 12.65/8.61 tff(7465,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7464, 5978, 3860, 6888, 7458])).
% 12.65/8.61 tff(7466,plain,((~trans(s59, s44)) | always5(s44)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7467,plain,
% 12.65/8.61 (~trans(s59, s44)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7466, 7288])).
% 12.65/8.61 tff(7468,assumption,(~always5(s23)), introduced(assumption)).
% 12.65/8.61 tff(7469,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s23) | (~trans(s59, s23)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s23) | (~trans(s59, s23)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7470,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s23)) | always5(s23)) <=> ((~always5(s59)) | always5(s23) | (~trans(s59, s23)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7471,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s23) | (~trans(s59, s23))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7470])).
% 12.65/8.61 tff(7472,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s23) | (~trans(s59, s23)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7471, 7469])).
% 12.65/8.61 tff(7473,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s23)) | always5(s23))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7474,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s23) | (~trans(s59, s23))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7473, 7472])).
% 12.65/8.61 tff(7475,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7474, 6330, 3860, 6888, 7468])).
% 12.65/8.61 tff(7476,plain,((~trans(s59, s23)) | always5(s23)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7477,plain,
% 12.65/8.61 (~trans(s59, s23)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7476, 7352])).
% 12.65/8.61 tff(7478,assumption,(~always5(s36)), introduced(assumption)).
% 12.65/8.61 tff(7479,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7480,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s36)) | always5(s36)) <=> ((~always5(s59)) | always5(s36) | (~trans(s59, s36)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7481,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7480])).
% 12.65/8.61 tff(7482,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7481, 7479])).
% 12.65/8.61 tff(7483,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s36)) | always5(s36))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7484,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s36) | (~trans(s59, s36))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7483, 7482])).
% 12.65/8.61 tff(7485,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7484, 5967, 3860, 6888, 7478])).
% 12.65/8.61 tff(7486,plain,((~trans(s59, s36)) | always5(s36)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7487,plain,
% 12.65/8.61 (~trans(s59, s36)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7486, 7309])).
% 12.65/8.61 tff(7488,assumption,(~always5(s43)), introduced(assumption)).
% 12.65/8.61 tff(7489,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7490,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s43)) | always5(s43)) <=> ((~always5(s59)) | always5(s43) | (~trans(s59, s43)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7491,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7490])).
% 12.65/8.61 tff(7492,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7491, 7489])).
% 12.65/8.61 tff(7493,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s43)) | always5(s43))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7494,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s43) | (~trans(s59, s43))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7493, 7492])).
% 12.65/8.61 tff(7495,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7494, 5934, 3860, 6888, 7488])).
% 12.65/8.61 tff(7496,plain,((~trans(s59, s43)) | always5(s43)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7497,plain,
% 12.65/8.61 (~trans(s59, s43)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7496, 7289])).
% 12.65/8.61 tff(7498,assumption,(~always5(s40)), introduced(assumption)).
% 12.65/8.61 tff(7499,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7500,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s40)) | always5(s40)) <=> ((~always5(s59)) | always5(s40) | (~trans(s59, s40)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7501,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7500])).
% 12.65/8.61 tff(7502,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7501, 7499])).
% 12.65/8.61 tff(7503,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s40)) | always5(s40))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7504,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s40) | (~trans(s59, s40))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7503, 7502])).
% 12.65/8.61 tff(7505,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7504, 6176, 3860, 6888, 7498])).
% 12.65/8.61 tff(7506,plain,((~trans(s59, s40)) | always5(s40)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7507,plain,
% 12.65/8.61 (~trans(s59, s40)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7506, 7292])).
% 12.65/8.61 tff(7508,assumption,(~always5(s38)), introduced(assumption)).
% 12.65/8.61 tff(7509,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7510,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s38)) | always5(s38)) <=> ((~always5(s59)) | always5(s38) | (~trans(s59, s38)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7511,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7510])).
% 12.65/8.61 tff(7512,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7511, 7509])).
% 12.65/8.61 tff(7513,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s38)) | always5(s38))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7514,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s38) | (~trans(s59, s38))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7513, 7512])).
% 12.65/8.61 tff(7515,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7514, 5901, 3860, 6888, 7508])).
% 12.65/8.61 tff(7516,plain,((~trans(s59, s38)) | always5(s38)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7517,plain,
% 12.65/8.61 (~trans(s59, s38)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7516, 7307])).
% 12.65/8.61 tff(7518,assumption,(~always5(s35)), introduced(assumption)).
% 12.65/8.61 tff(7519,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7520,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s35)) | always5(s35)) <=> ((~always5(s59)) | always5(s35) | (~trans(s59, s35)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7521,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7520])).
% 12.65/8.61 tff(7522,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7521, 7519])).
% 12.65/8.61 tff(7523,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s35)) | always5(s35))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7524,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s35) | (~trans(s59, s35))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7523, 7522])).
% 12.65/8.61 tff(7525,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7524, 6099, 3860, 6888, 7518])).
% 12.65/8.61 tff(7526,plain,((~trans(s59, s35)) | always5(s35)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7527,plain,
% 12.65/8.61 (~trans(s59, s35)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7526, 7310])).
% 12.65/8.61 tff(7528,assumption,(~always5(s41)), introduced(assumption)).
% 12.65/8.61 tff(7529,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s41) | (~trans(s59, s41)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s41) | (~trans(s59, s41)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7530,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s41)) | always5(s41)) <=> ((~always5(s59)) | always5(s41) | (~trans(s59, s41)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7531,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s41) | (~trans(s59, s41))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7530])).
% 12.65/8.61 tff(7532,plain,
% 12.65/8.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s41) | (~trans(s59, s41)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7531, 7529])).
% 12.65/8.61 tff(7533,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s41)) | always5(s41))),
% 12.65/8.61 inference(quant_inst,[status(thm)],[])).
% 12.65/8.61 tff(7534,plain,
% 12.65/8.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s41) | (~trans(s59, s41))),
% 12.65/8.61 inference(modus_ponens,[status(thm)],[7533, 7532])).
% 12.65/8.61 tff(7535,plain,
% 12.65/8.61 ($false),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7534, 5912, 3860, 6888, 7528])).
% 12.65/8.61 tff(7536,plain,((~trans(s59, s41)) | always5(s41)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.61 tff(7537,plain,
% 12.65/8.61 (~trans(s59, s41)),
% 12.65/8.61 inference(unit_resolution,[status(thm)],[7536, 7291])).
% 12.65/8.61 tff(7538,assumption,(~always5(s20)), introduced(assumption)).
% 12.65/8.61 tff(7539,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7540,plain,
% 12.65/8.61 (((~always5(s59)) | (~trans(s59, s20)) | always5(s20)) <=> ((~always5(s59)) | always5(s20) | (~trans(s59, s20)))),
% 12.65/8.61 inference(rewrite,[status(thm)],[])).
% 12.65/8.61 tff(7541,plain,
% 12.65/8.61 (((~![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))))),
% 12.65/8.61 inference(monotonicity,[status(thm)],[7540])).
% 12.65/8.61 tff(7542,plain,
% 12.65/8.61 (((~![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)))),
% 12.65/8.61 inference(transitivity,[status(thm)],[7541, 7539])).
% 12.65/8.62 tff(7543,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s20)) | always5(s20))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7544,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s20) | (~trans(s59, s20))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7543, 7542])).
% 12.65/8.62 tff(7545,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7544, 5989, 3860, 6888, 7538])).
% 12.65/8.62 tff(7546,plain,((~trans(s59, s20)) | always5(s20)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7547,plain,
% 12.65/8.62 (~trans(s59, s20)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7546, 7355])).
% 12.65/8.62 tff(7548,assumption,(~always5(s33)), introduced(assumption)).
% 12.65/8.62 tff(7549,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s33) | (~trans(s59, s33)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s33) | (~trans(s59, s33)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7550,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s33)) | always5(s33)) <=> ((~always5(s59)) | always5(s33) | (~trans(s59, s33)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7551,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s33) | (~trans(s59, s33))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7550])).
% 12.65/8.62 tff(7552,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s33) | (~trans(s59, s33)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7551, 7549])).
% 12.65/8.62 tff(7553,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s33)) | always5(s33))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7554,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s33) | (~trans(s59, s33))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7553, 7552])).
% 12.65/8.62 tff(7555,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7554, 6088, 3860, 6888, 7548])).
% 12.65/8.62 tff(7556,plain,((~trans(s59, s33)) | always5(s33)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7557,plain,
% 12.65/8.62 (~trans(s59, s33)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7556, 7312])).
% 12.65/8.62 tff(7558,assumption,(~always5(s32)), introduced(assumption)).
% 12.65/8.62 tff(7559,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7560,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s32)) | always5(s32)) <=> ((~always5(s59)) | always5(s32) | (~trans(s59, s32)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7561,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7560])).
% 12.65/8.62 tff(7562,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7561, 7559])).
% 12.65/8.62 tff(7563,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s32)) | always5(s32))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7564,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s32) | (~trans(s59, s32))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7563, 7562])).
% 12.65/8.62 tff(7565,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7564, 5879, 3860, 6888, 7558])).
% 12.65/8.62 tff(7566,plain,((~trans(s59, s32)) | always5(s32)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7567,plain,
% 12.65/8.62 (~trans(s59, s32)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7566, 7313])).
% 12.65/8.62 tff(7568,assumption,(~always5(s31)), introduced(assumption)).
% 12.65/8.62 tff(7569,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s31) | (~trans(s59, s31)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s31) | (~trans(s59, s31)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7570,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s31)) | always5(s31)) <=> ((~always5(s59)) | always5(s31) | (~trans(s59, s31)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7571,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s31) | (~trans(s59, s31))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7570])).
% 12.65/8.62 tff(7572,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s31) | (~trans(s59, s31)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7571, 7569])).
% 12.65/8.62 tff(7573,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s31)) | always5(s31))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7574,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s31) | (~trans(s59, s31))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7573, 7572])).
% 12.65/8.62 tff(7575,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7574, 6242, 3860, 6888, 7568])).
% 12.65/8.62 tff(7576,plain,((~trans(s59, s31)) | always5(s31)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7577,plain,
% 12.65/8.62 (~trans(s59, s31)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7576, 7314])).
% 12.65/8.62 tff(7578,assumption,(~always5(s26)), introduced(assumption)).
% 12.65/8.62 tff(7579,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7580,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s26)) | always5(s26)) <=> ((~always5(s59)) | always5(s26) | (~trans(s59, s26)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7581,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7580])).
% 12.65/8.62 tff(7582,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7581, 7579])).
% 12.65/8.62 tff(7583,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s26)) | always5(s26))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7584,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s26) | (~trans(s59, s26))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7583, 7582])).
% 12.65/8.62 tff(7585,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7584, 5835, 3860, 6888, 7578])).
% 12.65/8.62 tff(7586,plain,((~trans(s59, s26)) | always5(s26)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7587,plain,
% 12.65/8.62 (~trans(s59, s26)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7586, 7349])).
% 12.65/8.62 tff(7588,assumption,(~always5(s19)), introduced(assumption)).
% 12.65/8.62 tff(7589,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7590,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s19)) | always5(s19)) <=> ((~always5(s59)) | always5(s19) | (~trans(s59, s19)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7591,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7590])).
% 12.65/8.62 tff(7592,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7591, 7589])).
% 12.65/8.62 tff(7593,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s19)) | always5(s19))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7594,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s19) | (~trans(s59, s19))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7593, 7592])).
% 12.65/8.62 tff(7595,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7594, 6297, 3860, 6888, 7588])).
% 12.65/8.62 tff(7596,plain,((~trans(s59, s19)) | always5(s19)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7597,plain,
% 12.65/8.62 (~trans(s59, s19)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7596, 7356])).
% 12.65/8.62 tff(7598,assumption,(~always5(s21)), introduced(assumption)).
% 12.65/8.62 tff(7599,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s21) | (~trans(s59, s21)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s21) | (~trans(s59, s21)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7600,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s21)) | always5(s21)) <=> ((~always5(s59)) | always5(s21) | (~trans(s59, s21)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7601,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s21)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s21) | (~trans(s59, s21))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7600])).
% 12.65/8.62 tff(7602,plain,
% 12.65/8.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s21)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s21) | (~trans(s59, s21)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7601, 7599])).
% 12.65/8.62 tff(7603,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s21)) | always5(s21))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7604,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s21) | (~trans(s59, s21))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7603, 7602])).
% 12.65/8.62 tff(7605,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7604, 6319, 3860, 6888, 7598])).
% 12.65/8.62 tff(7606,plain,((~trans(s59, s21)) | always5(s21)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7607,plain,
% 12.65/8.62 (~trans(s59, s21)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7606, 7354])).
% 12.65/8.62 tff(7608,assumption,(~always5(s22)), introduced(assumption)).
% 12.65/8.62 tff(7609,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7610,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s22)) | always5(s22)) <=> ((~always5(s59)) | always5(s22) | (~trans(s59, s22)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7611,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7610])).
% 12.65/8.62 tff(7612,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7611, 7609])).
% 12.65/8.62 tff(7613,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s22)) | always5(s22))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7614,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s22) | (~trans(s59, s22))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7613, 7612])).
% 12.65/8.62 tff(7615,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7614, 6000, 3860, 6888, 7608])).
% 12.65/8.62 tff(7616,plain,((~trans(s59, s22)) | always5(s22)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7617,plain,
% 12.65/8.62 (~trans(s59, s22)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7616, 7353])).
% 12.65/8.62 tff(7618,assumption,(~always5(s24)), introduced(assumption)).
% 12.65/8.62 tff(7619,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7620,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s24)) | always5(s24)) <=> ((~always5(s59)) | always5(s24) | (~trans(s59, s24)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7621,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7620])).
% 12.65/8.62 tff(7622,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7621, 7619])).
% 12.65/8.62 tff(7623,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s24)) | always5(s24))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7624,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s24) | (~trans(s59, s24))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7623, 7622])).
% 12.65/8.62 tff(7625,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7624, 6110, 3860, 6888, 7618])).
% 12.65/8.62 tff(7626,plain,((~trans(s59, s24)) | always5(s24)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7627,plain,
% 12.65/8.62 (~trans(s59, s24)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7626, 7351])).
% 12.65/8.62 tff(7628,assumption,(~always5(s30)), introduced(assumption)).
% 12.65/8.62 tff(7629,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7630,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s30)) | always5(s30)) <=> ((~always5(s59)) | always5(s30) | (~trans(s59, s30)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7631,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7630])).
% 12.65/8.62 tff(7632,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7631, 7629])).
% 12.65/8.62 tff(7633,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s30)) | always5(s30))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7634,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s30) | (~trans(s59, s30))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7633, 7632])).
% 12.65/8.62 tff(7635,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7634, 6022, 3860, 6888, 7628])).
% 12.65/8.62 tff(7636,plain,((~trans(s59, s30)) | always5(s30)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7637,plain,
% 12.65/8.62 (~trans(s59, s30)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7636, 7315])).
% 12.65/8.62 tff(7638,assumption,(~always5(s42)), introduced(assumption)).
% 12.65/8.62 tff(7639,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7640,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s42)) | always5(s42)) <=> ((~always5(s59)) | always5(s42) | (~trans(s59, s42)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7641,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7640])).
% 12.65/8.62 tff(7642,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7641, 7639])).
% 12.65/8.62 tff(7643,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s42)) | always5(s42))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7644,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s42) | (~trans(s59, s42))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7643, 7642])).
% 12.65/8.62 tff(7645,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7644, 6352, 3860, 6888, 7638])).
% 12.65/8.62 tff(7646,plain,((~trans(s59, s42)) | always5(s42)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7647,plain,
% 12.65/8.62 (~trans(s59, s42)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7646, 7290])).
% 12.65/8.62 tff(7648,assumption,(~trans(s59, s25)), introduced(assumption)).
% 12.65/8.62 tff(7649,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7650,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s54)) | always5(s54)) <=> ((~always5(s59)) | always5(s54) | (~trans(s59, s54)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7651,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7650])).
% 12.65/8.62 tff(7652,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7651, 7649])).
% 12.65/8.62 tff(7653,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s54)) | always5(s54))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7654,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s54) | (~trans(s59, s54))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7653, 7652])).
% 12.65/8.62 tff(7655,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7654, 6374, 3860, 6888, 7278])).
% 12.65/8.62 tff(7656,plain,((~trans(s59, s54)) | always5(s54)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7657,plain,
% 12.65/8.62 (~trans(s59, s54)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7656, 7278])).
% 12.65/8.62 tff(7658,plain,
% 12.65/8.62 (~always5(s17)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[4195, 7357])).
% 12.65/8.62 tff(7659,assumption,(~always5(s17)), introduced(assumption)).
% 12.65/8.62 tff(7660,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7661,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s17)) | always5(s17)) <=> ((~always5(s59)) | always5(s17) | (~trans(s59, s17)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7662,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7661])).
% 12.65/8.62 tff(7663,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7662, 7660])).
% 12.65/8.62 tff(7664,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s17)) | always5(s17))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7665,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s17) | (~trans(s59, s17))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7664, 7663])).
% 12.65/8.62 tff(7666,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7665, 6154, 3860, 6888, 7659])).
% 12.65/8.62 tff(7667,plain,((~trans(s59, s17)) | always5(s17)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7668,plain,
% 12.65/8.62 (~trans(s59, s17)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7667, 7658])).
% 12.65/8.62 tff(7669,plain,
% 12.65/8.62 (~always5(s16)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[4203, 7658])).
% 12.65/8.62 tff(7670,assumption,(~always5(s16)), introduced(assumption)).
% 12.65/8.62 tff(7671,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7672,plain,
% 12.65/8.62 (((~always5(s59)) | (~trans(s59, s16)) | always5(s16)) <=> ((~always5(s59)) | always5(s16) | (~trans(s59, s16)))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7673,plain,
% 12.65/8.62 (((~![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))))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7672])).
% 12.65/8.62 tff(7674,plain,
% 12.65/8.62 (((~![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)))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7673, 7671])).
% 12.65/8.62 tff(7675,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s16)) | always5(s16))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7676,plain,
% 12.65/8.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s16) | (~trans(s59, s16))),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7675, 7674])).
% 12.65/8.62 tff(7677,plain,
% 12.65/8.62 ($false),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7676, 6341, 3860, 6888, 7670])).
% 12.65/8.62 tff(7678,plain,((~trans(s59, s16)) | always5(s16)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.62 tff(7679,plain,
% 12.65/8.62 (~trans(s59, s16)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7678, 7669])).
% 12.65/8.62 tff(7680,plain,
% 12.65/8.62 (((~![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))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7681,plain,
% 12.65/8.62 ((~![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))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7682,plain,
% 12.65/8.62 ((~![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)),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7681, 7680])).
% 12.65/8.62 tff(7683,plain,
% 12.65/8.62 ((~m_counter_cell_v_value(c_bit1, s7)) | m_counter_cell_v_carry_out(c_bit1, s7)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7682, 1368, 1657])).
% 12.65/8.62 tff(7684,plain,
% 12.65/8.62 (m_counter_cell_v_carry_out(c_bit1, s7)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7683, 1648])).
% 12.65/8.62 tff(7685,plain,
% 12.65/8.62 (((~![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))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7686,plain,
% 12.65/8.62 ((~![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))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7687,plain,
% 12.65/8.62 ((~![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)),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7686, 7685])).
% 12.65/8.62 tff(7688,plain,
% 12.65/8.62 (m_counter_cell_v_carry_in(c_bit2, s7)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7687, 6919, 7684])).
% 12.65/8.62 tff(7689,plain,
% 12.65/8.62 (((~![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))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7690,plain,
% 12.65/8.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit2, s5, s6))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7691,plain,
% 12.65/8.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit2, s5, s6)),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7690, 7689])).
% 12.65/8.62 tff(7692,plain,
% 12.65/8.62 (node3(c_bit2, s5, s6)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7691, 21, 246])).
% 12.65/8.62 tff(7693,plain,
% 12.65/8.62 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7694,plain,
% 12.65/8.62 ((m_counter_cell_v_value(c_bit1, s5) | (~node4(c_bit1, s5))) <=> ((~node4(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7695,plain,
% 12.65/8.62 (((~![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)))) | ((~node4(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5)))),
% 12.65/8.62 inference(monotonicity,[status(thm)],[7694])).
% 12.65/8.62 tff(7696,plain,
% 12.65/8.62 (((~![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)))) | (~node4(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 12.65/8.62 inference(transitivity,[status(thm)],[7695, 7693])).
% 12.65/8.62 tff(7697,plain,
% 12.65/8.62 ((~![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)))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7698,plain,
% 12.65/8.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5)),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7697, 7696])).
% 12.65/8.62 tff(7699,plain,
% 12.65/8.62 (~node4(c_bit1, s5)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7698, 1221, 1595])).
% 12.65/8.62 tff(7700,plain,
% 12.65/8.62 (((~![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))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7701,plain,
% 12.65/8.62 ((~![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))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7702,plain,
% 12.65/8.62 ((~![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)),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7701, 7700])).
% 12.65/8.62 tff(7703,plain,
% 12.65/8.62 (~m_counter_cell_v_carry_out(c_bit1, s5)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7702, 1235, 7699])).
% 12.65/8.62 tff(7704,plain,
% 12.65/8.62 (((~![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))),
% 12.65/8.62 inference(rewrite,[status(thm)],[])).
% 12.65/8.62 tff(7705,plain,
% 12.65/8.62 ((~![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))),
% 12.65/8.62 inference(quant_inst,[status(thm)],[])).
% 12.65/8.62 tff(7706,plain,
% 12.65/8.62 ((~![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)),
% 12.65/8.62 inference(modus_ponens,[status(thm)],[7705, 7704])).
% 12.65/8.62 tff(7707,plain,
% 12.65/8.62 (~m_counter_cell_v_carry_in(c_bit2, s5)),
% 12.65/8.62 inference(unit_resolution,[status(thm)],[7706, 3802, 7703])).
% 12.65/8.63 tff(7708,plain,
% 12.65/8.63 (((~![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)))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7709,plain,
% 12.65/8.63 ((~![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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7710,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7709, 7708])).
% 12.65/8.63 tff(7711,plain,
% 12.65/8.63 (~node4(c_bit1, s1)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7710, 1221, 1466])).
% 12.65/8.63 tff(7712,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7713,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7714,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7713, 7712])).
% 12.65/8.63 tff(7715,plain,
% 12.65/8.63 (~m_counter_cell_v_carry_out(c_bit1, s1)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7714, 1235, 7711])).
% 12.65/8.63 tff(7716,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7717,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7718,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7717, 7716])).
% 12.65/8.63 tff(7719,plain,
% 12.65/8.63 (~m_counter_cell_v_carry_in(c_bit2, s1)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7718, 3802, 7715])).
% 12.65/8.63 tff(7720,assumption,(m_counter_cell_v_value(c_bit2, s0)), introduced(assumption)).
% 12.65/8.63 tff(7721,plain,
% 12.65/8.63 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit2, s0))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7722,plain,
% 12.65/8.63 ($false),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7721, 55, 7720])).
% 12.65/8.63 tff(7723,plain,(~m_counter_cell_v_value(c_bit2, s0)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.63 tff(7724,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7725,plain,
% 12.65/8.63 ((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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7726,plain,
% 12.65/8.63 (((~![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)))),
% 12.65/8.63 inference(monotonicity,[status(thm)],[7725])).
% 12.65/8.63 tff(7727,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(transitivity,[status(thm)],[7726, 7724])).
% 12.65/8.63 tff(7728,plain,
% 12.65/8.63 ((~![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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7729,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7728, 7727])).
% 12.65/8.63 tff(7730,plain,
% 12.65/8.63 (~node4(c_bit1, s0)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7729, 3055, 1439])).
% 12.65/8.63 tff(7731,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7732,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7733,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7732, 7731])).
% 12.65/8.63 tff(7734,plain,
% 12.65/8.63 (~m_counter_cell_v_carry_out(c_bit1, s0)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7733, 1235, 7730])).
% 12.65/8.63 tff(7735,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7736,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7737,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7736, 7735])).
% 12.65/8.63 tff(7738,plain,
% 12.65/8.63 (~m_counter_cell_v_carry_in(c_bit2, s0)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7737, 3802, 7734])).
% 12.65/8.63 tff(7739,plain,
% 12.65/8.63 (((~![I0: $i, 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_bit2, s0) | m_counter_cell_v_carry_in(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)))) | m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0) | (~node2(c_bit2, s0)))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7740,plain,
% 12.65/8.63 ((m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0))) <=> (m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0) | (~node2(c_bit2, s0)))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7741,plain,
% 12.65/8.63 (((~![I0: $i, X: $i] : (m_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)))) | (m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0) | (~node2(c_bit2, s0))))),
% 12.65/8.63 inference(monotonicity,[status(thm)],[7740])).
% 12.65/8.63 tff(7742,plain,
% 12.65/8.63 (((~![I0: $i, X: $i] : (m_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)))) | m_counter_cell_v_value(c_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0) | (~node2(c_bit2, s0)))),
% 12.65/8.63 inference(transitivity,[status(thm)],[7741, 7739])).
% 12.65/8.63 tff(7743,plain,
% 12.65/8.63 ((~![I0: $i, X: $i] : (m_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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7744,plain,
% 12.65/8.63 ((~![I0: $i, 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_bit2, s0) | m_counter_cell_v_carry_in(c_bit2, s0) | (~node2(c_bit2, s0))),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7743, 7742])).
% 12.65/8.63 tff(7745,plain,
% 12.65/8.63 (m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0))),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7744, 1449, 7738])).
% 12.65/8.63 tff(7746,plain,
% 12.65/8.63 (~node2(c_bit2, s0)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7745, 7723])).
% 12.65/8.63 tff(7747,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7748,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit2, s0, s1))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7749,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit2, s0, s1)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7748, 7747])).
% 12.65/8.63 tff(7750,plain,
% 12.65/8.63 (node3(c_bit2, s0, s1)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7749, 21, 92])).
% 12.65/8.63 tff(7751,plain,
% 12.65/8.63 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~node3(c_bit2, s0, s1)) | node2(c_bit2, s0) | (~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)))) | (~node3(c_bit2, s0, s1)) | node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7752,plain,
% 12.65/8.63 ((node2(c_bit2, s0) | (~node3(c_bit2, s0, s1)) | (~m_counter_cell_v_value(c_bit2, s1))) <=> ((~node3(c_bit2, s0, s1)) | node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7753,plain,
% 12.65/8.63 (((~![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)))) | ((~node3(c_bit2, s0, s1)) | node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1))))),
% 12.65/8.63 inference(monotonicity,[status(thm)],[7752])).
% 12.65/8.63 tff(7754,plain,
% 12.65/8.63 (((~![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)))) | (~node3(c_bit2, s0, s1)) | node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1)))),
% 12.65/8.63 inference(transitivity,[status(thm)],[7753, 7751])).
% 12.65/8.63 tff(7755,plain,
% 12.65/8.63 ((~![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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7756,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit2, s0, s1)) | node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1))),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7755, 7754])).
% 12.65/8.63 tff(7757,plain,
% 12.65/8.63 (node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1))),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7756, 141, 7750])).
% 12.65/8.63 tff(7758,plain,
% 12.65/8.63 (~m_counter_cell_v_value(c_bit2, s1)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7757, 7746])).
% 12.65/8.63 tff(7759,plain,
% 12.65/8.63 (((~![I0: $i, 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_bit2, s1) | (~node2(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)))) | m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1)) | m_counter_cell_v_carry_in(c_bit2, s1))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7760,plain,
% 12.65/8.63 ((m_counter_cell_v_carry_in(c_bit2, s1) | m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1))) <=> (m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1)) | m_counter_cell_v_carry_in(c_bit2, s1))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7761,plain,
% 12.65/8.63 (((~![I0: $i, X: $i] : (m_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)))) | (m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1)) | m_counter_cell_v_carry_in(c_bit2, s1)))),
% 12.65/8.63 inference(monotonicity,[status(thm)],[7760])).
% 12.65/8.63 tff(7762,plain,
% 12.65/8.63 (((~![I0: $i, X: $i] : (m_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)))) | m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1)) | m_counter_cell_v_carry_in(c_bit2, s1))),
% 12.65/8.63 inference(transitivity,[status(thm)],[7761, 7759])).
% 12.65/8.63 tff(7763,plain,
% 12.65/8.63 ((~![I0: $i, X: $i] : (m_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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7764,plain,
% 12.65/8.63 ((~![I0: $i, 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_bit2, s1) | (~node2(c_bit2, s1)) | m_counter_cell_v_carry_in(c_bit2, s1)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7763, 7762])).
% 12.65/8.63 tff(7765,plain,
% 12.65/8.63 ((~node2(c_bit2, s1)) | m_counter_cell_v_carry_in(c_bit2, s1)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7764, 1449, 7758])).
% 12.65/8.63 tff(7766,plain,
% 12.65/8.63 (~node2(c_bit2, s1)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7765, 7719])).
% 12.65/8.63 tff(7767,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7768,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit2, s1, s2))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7769,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit2, s1, s2)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7768, 7767])).
% 12.65/8.63 tff(7770,plain,
% 12.65/8.63 (node3(c_bit2, s1, s2)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7769, 21, 43])).
% 12.65/8.63 tff(7771,plain,
% 12.65/8.63 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, 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)))) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)) | node2(c_bit2, s1))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7772,plain,
% 12.65/8.63 ((node2(c_bit2, s1) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2))) <=> ((~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)) | node2(c_bit2, s1))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7773,plain,
% 12.65/8.63 (((~![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)))) | ((~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)) | node2(c_bit2, s1)))),
% 12.65/8.63 inference(monotonicity,[status(thm)],[7772])).
% 12.65/8.63 tff(7774,plain,
% 12.65/8.63 (((~![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)))) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)) | node2(c_bit2, s1))),
% 12.65/8.63 inference(transitivity,[status(thm)],[7773, 7771])).
% 12.65/8.63 tff(7775,plain,
% 12.65/8.63 ((~![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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7776,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)) | node2(c_bit2, s1)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7775, 7774])).
% 12.65/8.63 tff(7777,plain,
% 12.65/8.63 ((~m_counter_cell_v_value(c_bit2, s2)) | node2(c_bit2, s1)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7776, 141, 7770])).
% 12.65/8.63 tff(7778,plain,
% 12.65/8.63 (~m_counter_cell_v_value(c_bit2, s2)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7777, 7766])).
% 12.65/8.63 tff(7779,plain,
% 12.65/8.63 (((~![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)))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7780,plain,
% 12.65/8.63 ((~![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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7781,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7780, 7779])).
% 12.65/8.63 tff(7782,plain,
% 12.65/8.63 (~node4(c_bit1, s2)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7781, 3055, 1507])).
% 12.65/8.63 tff(7783,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7784,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7785,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7784, 7783])).
% 12.65/8.63 tff(7786,plain,
% 12.65/8.63 (~m_counter_cell_v_carry_out(c_bit1, s2)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7785, 1235, 7782])).
% 12.65/8.63 tff(7787,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7788,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7789,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7788, 7787])).
% 12.65/8.63 tff(7790,plain,
% 12.65/8.63 (~m_counter_cell_v_carry_in(c_bit2, s2)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7789, 3802, 7786])).
% 12.65/8.63 tff(7791,plain,
% 12.65/8.63 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit2, s2)) | m_counter_cell_v_value(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) | (~node2(c_bit2, s2)) | m_counter_cell_v_value(c_bit2, s2))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7792,plain,
% 12.65/8.63 ((m_counter_cell_v_carry_in(c_bit2, s2) | m_counter_cell_v_value(c_bit2, s2) | (~node2(c_bit2, s2))) <=> (m_counter_cell_v_carry_in(c_bit2, s2) | (~node2(c_bit2, s2)) | m_counter_cell_v_value(c_bit2, s2))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7793,plain,
% 12.65/8.63 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit2, s2)) | m_counter_cell_v_value(c_bit2, s2)))),
% 12.65/8.63 inference(monotonicity,[status(thm)],[7792])).
% 12.65/8.63 tff(7794,plain,
% 12.65/8.63 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit2, s2)) | m_counter_cell_v_value(c_bit2, s2))),
% 12.65/8.63 inference(transitivity,[status(thm)],[7793, 7791])).
% 12.65/8.63 tff(7795,plain,
% 12.65/8.63 ((~![I0: $i, X: $i] : (m_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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7796,plain,
% 12.65/8.63 ((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit2, s2)) | m_counter_cell_v_value(c_bit2, s2)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7795, 7794])).
% 12.65/8.63 tff(7797,plain,
% 12.65/8.63 ((~node2(c_bit2, s2)) | m_counter_cell_v_value(c_bit2, s2)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7796, 1449, 7790])).
% 12.65/8.63 tff(7798,plain,
% 12.65/8.63 (~node2(c_bit2, s2)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7797, 7778])).
% 12.65/8.63 tff(7799,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7800,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit2, s2, s3))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7801,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit2, s2, s3)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7800, 7799])).
% 12.65/8.63 tff(7802,plain,
% 12.65/8.63 (node3(c_bit2, s2, s3)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7801, 21, 165])).
% 12.65/8.63 tff(7803,plain,
% 12.65/8.63 (((~![Y: $i, 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, s3)) | (~node3(c_bit2, s2, s3)) | node2(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, s3)) | (~node3(c_bit2, s2, s3)) | node2(c_bit2, s2))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7804,plain,
% 12.65/8.63 ((node2(c_bit2, s2) | (~node3(c_bit2, s2, s3)) | (~m_counter_cell_v_value(c_bit2, s3))) <=> ((~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3)) | node2(c_bit2, s2))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7805,plain,
% 12.65/8.63 (((~![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)))) | ((~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3)) | node2(c_bit2, s2)))),
% 12.65/8.63 inference(monotonicity,[status(thm)],[7804])).
% 12.65/8.63 tff(7806,plain,
% 12.65/8.63 (((~![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)))) | (~m_counter_cell_v_value(c_bit2, s3)) | (~node3(c_bit2, s2, s3)) | node2(c_bit2, s2))),
% 12.65/8.63 inference(transitivity,[status(thm)],[7805, 7803])).
% 12.65/8.63 tff(7807,plain,
% 12.65/8.63 ((~![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)))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7808,plain,
% 12.65/8.63 ((~![Y: $i, 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, s3)) | (~node3(c_bit2, s2, s3)) | node2(c_bit2, s2)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7807, 7806])).
% 12.65/8.63 tff(7809,plain,
% 12.65/8.63 ((~m_counter_cell_v_value(c_bit2, s3)) | node2(c_bit2, s2)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7808, 141, 7802])).
% 12.65/8.63 tff(7810,plain,
% 12.65/8.63 (~m_counter_cell_v_value(c_bit2, s3)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7809, 7798])).
% 12.65/8.63 tff(7811,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7812,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7813,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7812, 7811])).
% 12.65/8.63 tff(7814,plain,
% 12.65/8.63 ((~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7813, 1368, 1546])).
% 12.65/8.63 tff(7815,plain,
% 12.65/8.63 (m_counter_cell_v_carry_out(c_bit1, s3)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7814, 1537])).
% 12.65/8.63 tff(7816,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7817,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7818,plain,
% 12.65/8.63 ((~![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)),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7817, 7816])).
% 12.65/8.63 tff(7819,plain,
% 12.65/8.63 (m_counter_cell_v_carry_in(c_bit2, s3)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7818, 6919, 7815])).
% 12.65/8.63 tff(7820,plain,
% 12.65/8.63 (((~![I0: $i, X: $i] : ((~node1(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, s3)) | m_counter_cell_v_value(c_bit2, s3) | (~node1(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_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7821,plain,
% 12.65/8.63 (((~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_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7822,plain,
% 12.65/8.63 (((~![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_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3))))),
% 12.65/8.63 inference(monotonicity,[status(thm)],[7821])).
% 12.65/8.63 tff(7823,plain,
% 12.65/8.63 (((~![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_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3)))),
% 12.65/8.63 inference(transitivity,[status(thm)],[7822, 7820])).
% 12.65/8.63 tff(7824,plain,
% 12.65/8.63 ((~![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))),
% 12.65/8.63 inference(quant_inst,[status(thm)],[])).
% 12.65/8.63 tff(7825,plain,
% 12.65/8.63 ((~![I0: $i, X: $i] : ((~node1(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, s3)) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3))),
% 12.65/8.63 inference(modus_ponens,[status(thm)],[7824, 7823])).
% 12.65/8.63 tff(7826,plain,
% 12.65/8.63 (m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3))),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7825, 77, 7819])).
% 12.65/8.63 tff(7827,plain,
% 12.65/8.63 (~node1(c_bit2, s3)),
% 12.65/8.63 inference(unit_resolution,[status(thm)],[7826, 7810])).
% 12.65/8.63 tff(7828,plain,
% 12.65/8.63 (((~![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))),
% 12.65/8.63 inference(rewrite,[status(thm)],[])).
% 12.65/8.63 tff(7829,plain,
% 12.65/8.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit2, s3, s4))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7830,plain,
% 12.65/8.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit2, s3, s4)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7829, 7828])).
% 12.65/8.64 tff(7831,plain,
% 12.65/8.64 (node3(c_bit2, s3, s4)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7830, 21, 191])).
% 12.65/8.64 tff(7832,plain,
% 12.65/8.64 (((~![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)) | node1(c_bit2, s3) | 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)) | node1(c_bit2, s3) | m_counter_cell_v_value(c_bit2, s4))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7833,plain,
% 12.65/8.64 ((node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4)) <=> ((~node3(c_bit2, s3, s4)) | node1(c_bit2, s3) | m_counter_cell_v_value(c_bit2, s4))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7834,plain,
% 12.65/8.64 (((~![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)) | node1(c_bit2, s3) | m_counter_cell_v_value(c_bit2, s4)))),
% 12.65/8.64 inference(monotonicity,[status(thm)],[7833])).
% 12.65/8.64 tff(7835,plain,
% 12.65/8.64 (((~![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)) | node1(c_bit2, s3) | m_counter_cell_v_value(c_bit2, s4))),
% 12.65/8.64 inference(transitivity,[status(thm)],[7834, 7832])).
% 12.65/8.64 tff(7836,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7837,plain,
% 12.65/8.64 ((~![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)) | node1(c_bit2, s3) | m_counter_cell_v_value(c_bit2, s4)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7836, 7835])).
% 12.65/8.64 tff(7838,plain,
% 12.65/8.64 (node1(c_bit2, s3) | m_counter_cell_v_value(c_bit2, s4)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7837, 106, 7831])).
% 12.65/8.64 tff(7839,plain,
% 12.65/8.64 (m_counter_cell_v_value(c_bit2, s4)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7838, 7827])).
% 12.65/8.64 tff(7840,plain,
% 12.65/8.64 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7841,plain,
% 12.65/8.64 ((m_counter_cell_v_carry_in(c_bit1, s4) | (~node4(c_bit1, s4))) <=> ((~node4(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7842,plain,
% 12.65/8.64 (((~![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)))) | ((~node4(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4)))),
% 12.65/8.64 inference(monotonicity,[status(thm)],[7841])).
% 12.65/8.64 tff(7843,plain,
% 12.65/8.64 (((~![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)))) | (~node4(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4))),
% 12.65/8.64 inference(transitivity,[status(thm)],[7842, 7840])).
% 12.65/8.64 tff(7844,plain,
% 12.65/8.64 ((~![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)))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7845,plain,
% 12.65/8.64 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7844, 7843])).
% 12.65/8.64 tff(7846,plain,
% 12.65/8.64 (~node4(c_bit1, s4)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7845, 3055, 1575])).
% 12.65/8.64 tff(7847,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7848,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7849,plain,
% 12.65/8.64 ((~![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)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7848, 7847])).
% 12.65/8.64 tff(7850,plain,
% 12.65/8.64 (~m_counter_cell_v_carry_out(c_bit1, s4)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7849, 1235, 7846])).
% 12.65/8.64 tff(7851,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7852,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7853,plain,
% 12.65/8.64 ((~![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)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7852, 7851])).
% 12.65/8.64 tff(7854,plain,
% 12.65/8.64 (~m_counter_cell_v_carry_in(c_bit2, s4)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7853, 3802, 7850])).
% 12.65/8.64 tff(7855,plain,
% 12.65/8.64 (((~![I0: $i, X: $i] : ((~node1(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, s4) | (~m_counter_cell_v_value(c_bit2, s4)) | (~node1(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)))) | m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4)) | (~node1(c_bit2, s4)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7856,plain,
% 12.65/8.64 (((~node1(c_bit2, s4)) | m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4))) <=> (m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4)) | (~node1(c_bit2, s4)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7857,plain,
% 12.65/8.64 (((~![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)))) | (m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4)) | (~node1(c_bit2, s4))))),
% 12.65/8.64 inference(monotonicity,[status(thm)],[7856])).
% 12.65/8.64 tff(7858,plain,
% 12.65/8.64 (((~![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)))) | m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4)) | (~node1(c_bit2, s4)))),
% 12.65/8.64 inference(transitivity,[status(thm)],[7857, 7855])).
% 12.65/8.64 tff(7859,plain,
% 12.65/8.64 ((~![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)))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7860,plain,
% 12.65/8.64 ((~![I0: $i, X: $i] : ((~node1(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, s4) | (~m_counter_cell_v_value(c_bit2, s4)) | (~node1(c_bit2, s4))),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7859, 7858])).
% 12.65/8.64 tff(7861,plain,
% 12.65/8.64 ((~m_counter_cell_v_value(c_bit2, s4)) | (~node1(c_bit2, s4))),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7860, 1517, 7854])).
% 12.65/8.64 tff(7862,plain,
% 12.65/8.64 (~node1(c_bit2, s4)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7861, 7839])).
% 12.65/8.64 tff(7863,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7864,plain,
% 12.65/8.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit2, s4, s5))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7865,plain,
% 12.65/8.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit2, s4, s5)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7864, 7863])).
% 12.65/8.64 tff(7866,plain,
% 12.65/8.64 (node3(c_bit2, s4, s5)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7865, 21, 220])).
% 12.65/8.64 tff(7867,plain,
% 12.65/8.64 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | ((~node3(c_bit2, s4, s5)) | node1(c_bit2, s4) | 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))) | (~node3(c_bit2, s4, s5)) | node1(c_bit2, s4) | m_counter_cell_v_value(c_bit2, s5))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7868,plain,
% 12.65/8.64 ((node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)) | m_counter_cell_v_value(c_bit2, s5)) <=> ((~node3(c_bit2, s4, s5)) | node1(c_bit2, s4) | m_counter_cell_v_value(c_bit2, s5))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7869,plain,
% 12.65/8.64 (((~![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))) | ((~node3(c_bit2, s4, s5)) | node1(c_bit2, s4) | m_counter_cell_v_value(c_bit2, s5)))),
% 12.65/8.64 inference(monotonicity,[status(thm)],[7868])).
% 12.65/8.64 tff(7870,plain,
% 12.65/8.64 (((~![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))) | (~node3(c_bit2, s4, s5)) | node1(c_bit2, s4) | m_counter_cell_v_value(c_bit2, s5))),
% 12.65/8.64 inference(transitivity,[status(thm)],[7869, 7867])).
% 12.65/8.64 tff(7871,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7872,plain,
% 12.65/8.64 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit2, s4, s5)) | node1(c_bit2, s4) | m_counter_cell_v_value(c_bit2, s5)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7871, 7870])).
% 12.65/8.64 tff(7873,plain,
% 12.65/8.64 (node1(c_bit2, s4) | m_counter_cell_v_value(c_bit2, s5)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7872, 106, 7866])).
% 12.65/8.64 tff(7874,plain,
% 12.65/8.64 (m_counter_cell_v_value(c_bit2, s5)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7873, 7862])).
% 12.65/8.64 tff(7875,plain,
% 12.65/8.64 (((~![I0: $i, 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, s5)) | m_counter_cell_v_carry_in(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_value(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~node1(c_bit2, s5)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7876,plain,
% 12.65/8.64 (((~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_value(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~node1(c_bit2, s5)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7877,plain,
% 12.65/8.64 (((~![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_value(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~node1(c_bit2, s5))))),
% 12.65/8.64 inference(monotonicity,[status(thm)],[7876])).
% 12.65/8.64 tff(7878,plain,
% 12.65/8.64 (((~![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_value(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~node1(c_bit2, s5)))),
% 12.65/8.64 inference(transitivity,[status(thm)],[7877, 7875])).
% 12.65/8.64 tff(7879,plain,
% 12.65/8.64 ((~![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)))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7880,plain,
% 12.65/8.64 ((~![I0: $i, 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, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~node1(c_bit2, s5))),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7879, 7878])).
% 12.65/8.64 tff(7881,plain,
% 12.65/8.64 (~node1(c_bit2, s5)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7880, 1517, 7874, 7707])).
% 12.65/8.64 tff(7882,plain,
% 12.65/8.64 (((~![Y: $i, 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, s6) | node1(c_bit2, s5) | (~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))) | m_counter_cell_v_value(c_bit2, s6) | node1(c_bit2, s5) | (~node3(c_bit2, s5, s6)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7883,plain,
% 12.65/8.64 ((node1(c_bit2, s5) | (~node3(c_bit2, s5, s6)) | m_counter_cell_v_value(c_bit2, s6)) <=> (m_counter_cell_v_value(c_bit2, s6) | node1(c_bit2, s5) | (~node3(c_bit2, s5, s6)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7884,plain,
% 12.65/8.64 (((~![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))) | (m_counter_cell_v_value(c_bit2, s6) | node1(c_bit2, s5) | (~node3(c_bit2, s5, s6))))),
% 12.65/8.64 inference(monotonicity,[status(thm)],[7883])).
% 12.65/8.64 tff(7885,plain,
% 12.65/8.64 (((~![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))) | m_counter_cell_v_value(c_bit2, s6) | node1(c_bit2, s5) | (~node3(c_bit2, s5, s6)))),
% 12.65/8.64 inference(transitivity,[status(thm)],[7884, 7882])).
% 12.65/8.64 tff(7886,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7887,plain,
% 12.65/8.64 ((~![Y: $i, 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, s6) | node1(c_bit2, s5) | (~node3(c_bit2, s5, s6))),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7886, 7885])).
% 12.65/8.64 tff(7888,plain,
% 12.65/8.64 (m_counter_cell_v_value(c_bit2, s6)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7887, 106, 7881, 7692])).
% 12.65/8.64 tff(7889,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7890,plain,
% 12.65/8.64 ((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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7891,plain,
% 12.65/8.64 (((~![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)))),
% 12.65/8.64 inference(monotonicity,[status(thm)],[7890])).
% 12.65/8.64 tff(7892,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(transitivity,[status(thm)],[7891, 7889])).
% 12.65/8.64 tff(7893,plain,
% 12.65/8.64 ((~![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)))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7894,plain,
% 12.65/8.64 ((~![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)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7893, 7892])).
% 12.65/8.64 tff(7895,plain,
% 12.65/8.64 (~node4(c_bit1, s6)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7894, 3055, 1631])).
% 12.65/8.64 tff(7896,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7897,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7898,plain,
% 12.65/8.64 ((~![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)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7897, 7896])).
% 12.65/8.64 tff(7899,plain,
% 12.65/8.64 (~m_counter_cell_v_carry_out(c_bit1, s6)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7898, 1235, 7895])).
% 12.65/8.64 tff(7900,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7901,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7902,plain,
% 12.65/8.64 ((~![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)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7901, 7900])).
% 12.65/8.64 tff(7903,plain,
% 12.65/8.64 (~m_counter_cell_v_carry_in(c_bit2, s6)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7902, 3802, 7899])).
% 12.65/8.64 tff(7904,plain,
% 12.65/8.64 (((~![I0: $i, 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, s6)) | m_counter_cell_v_carry_in(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_value(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~node1(c_bit2, s6)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7905,plain,
% 12.65/8.64 (((~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_value(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~node1(c_bit2, s6)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7906,plain,
% 12.65/8.64 (((~![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_value(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~node1(c_bit2, s6))))),
% 12.65/8.64 inference(monotonicity,[status(thm)],[7905])).
% 12.65/8.64 tff(7907,plain,
% 12.65/8.64 (((~![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_value(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~node1(c_bit2, s6)))),
% 12.65/8.64 inference(transitivity,[status(thm)],[7906, 7904])).
% 12.65/8.64 tff(7908,plain,
% 12.65/8.64 ((~![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)))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7909,plain,
% 12.65/8.64 ((~![I0: $i, 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, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~node1(c_bit2, s6))),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7908, 7907])).
% 12.65/8.64 tff(7910,plain,
% 12.65/8.64 ((~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6))),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7909, 1517, 7903])).
% 12.65/8.64 tff(7911,plain,
% 12.65/8.64 (~node1(c_bit2, s6)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7910, 7888])).
% 12.65/8.64 tff(7912,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7913,plain,
% 12.65/8.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit2, s6, s7))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7914,plain,
% 12.65/8.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit2, s6, s7)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7913, 7912])).
% 12.65/8.64 tff(7915,plain,
% 12.65/8.64 (node3(c_bit2, s6, s7)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7914, 21, 272])).
% 12.65/8.64 tff(7916,plain,
% 12.65/8.64 (((~![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) | (~node3(c_bit2, s6, s7)) | m_counter_cell_v_value(c_bit2, s7))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7917,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7918,plain,
% 12.65/8.64 ((~![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)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7917, 7916])).
% 12.65/8.64 tff(7919,plain,
% 12.65/8.64 (node1(c_bit2, s6) | m_counter_cell_v_value(c_bit2, s7)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7918, 106, 7915])).
% 12.65/8.64 tff(7920,plain,
% 12.65/8.64 (m_counter_cell_v_value(c_bit2, s7)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7919, 7911])).
% 12.65/8.64 tff(7921,plain,
% 12.65/8.64 (((~![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))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7922,plain,
% 12.65/8.64 ((~![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))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7923,plain,
% 12.65/8.64 ((~![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)),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7922, 7921])).
% 12.65/8.64 tff(7924,plain,
% 12.65/8.64 ((~m_counter_cell_v_carry_in(c_bit2, s7)) | m_counter_cell_v_carry_out(c_bit2, s7)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7923, 1368, 7920])).
% 12.65/8.64 tff(7925,plain,
% 12.65/8.64 (m_counter_cell_v_carry_out(c_bit2, s7)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7924, 7688])).
% 12.65/8.64 tff(7926,plain,
% 12.65/8.64 (((~![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)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7927,plain,
% 12.65/8.64 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s7)) | (~m_counter_cell_v_carry_out(c_bit2, s7)))),
% 12.65/8.64 inference(quant_inst,[status(thm)],[])).
% 12.65/8.64 tff(7928,plain,
% 12.65/8.64 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s7)) | (~m_counter_cell_v_carry_out(c_bit2, s7))),
% 12.65/8.64 inference(modus_ponens,[status(thm)],[7927, 7926])).
% 12.65/8.64 tff(7929,plain,
% 12.65/8.64 (~always5(s7)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[7928, 6898, 7925])).
% 12.65/8.64 tff(7930,plain,
% 12.65/8.64 (~always5(s6)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[4283, 7929])).
% 12.65/8.64 tff(7931,plain,
% 12.65/8.64 (~always5(s5)),
% 12.65/8.64 inference(unit_resolution,[status(thm)],[4291, 7930])).
% 12.65/8.64 tff(7932,plain,
% 12.65/8.64 (((~![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)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7933,plain,
% 12.65/8.64 (((~always5(s59)) | (~trans(s59, s5)) | always5(s5)) <=> ((~always5(s59)) | always5(s5) | (~trans(s59, s5)))),
% 12.65/8.64 inference(rewrite,[status(thm)],[])).
% 12.65/8.64 tff(7934,plain,
% 12.65/8.64 (((~![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))))),
% 12.65/8.65 inference(monotonicity,[status(thm)],[7933])).
% 12.65/8.65 tff(7935,plain,
% 12.65/8.65 (((~![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)))),
% 12.65/8.65 inference(transitivity,[status(thm)],[7934, 7932])).
% 12.65/8.65 tff(7936,plain,
% 12.65/8.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s5)) | always5(s5))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7937,plain,
% 12.65/8.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s5) | (~trans(s59, s5))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7936, 7935])).
% 12.65/8.65 tff(7938,plain,
% 12.65/8.65 ($false),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7937, 6417, 3860, 6888, 7931])).
% 12.65/8.65 tff(7939,plain,(~trans(s59, s5)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.65 tff(7940,plain,
% 12.65/8.65 (~always5(s4)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[4299, 7931])).
% 12.65/8.65 tff(7941,plain,
% 12.65/8.65 (~always5(s3)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[4307, 7940])).
% 12.65/8.65 tff(7942,plain,
% 12.65/8.65 (~always5(s2)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[4315, 7941])).
% 12.65/8.65 tff(7943,plain,
% 12.65/8.65 (~always5(s1)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[4323, 7942])).
% 12.65/8.65 tff(7944,plain,
% 12.65/8.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s1) | (~trans(s59, s1)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s1) | (~trans(s59, s1)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7945,plain,
% 12.65/8.65 (((~always5(s59)) | (~trans(s59, s1)) | always5(s1)) <=> ((~always5(s59)) | always5(s1) | (~trans(s59, s1)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7946,plain,
% 12.65/8.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s1) | (~trans(s59, s1))))),
% 12.65/8.65 inference(monotonicity,[status(thm)],[7945])).
% 12.65/8.65 tff(7947,plain,
% 12.65/8.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s1) | (~trans(s59, s1)))),
% 12.65/8.65 inference(transitivity,[status(thm)],[7946, 7944])).
% 12.65/8.65 tff(7948,plain,
% 12.65/8.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s1)) | always5(s1))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7949,plain,
% 12.65/8.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s1) | (~trans(s59, s1))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7948, 7947])).
% 12.65/8.65 tff(7950,plain,
% 12.65/8.65 ($false),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7949, 5813, 3860, 6888, 7943])).
% 12.65/8.65 tff(7951,plain,(~trans(s59, s1)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.65 tff(7952,plain,
% 12.65/8.65 (((~![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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7953,plain,
% 12.65/8.65 ((~![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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7954,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7953, 7952])).
% 12.65/8.65 tff(7955,plain,
% 12.65/8.65 (~node4(c_bit1, s14)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7954, 3055, 1358])).
% 12.65/8.65 tff(7956,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7957,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7958,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7957, 7956])).
% 12.65/8.65 tff(7959,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_out(c_bit1, s14)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7958, 1235, 7955])).
% 12.65/8.65 tff(7960,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7961,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7962,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7961, 7960])).
% 12.65/8.65 tff(7963,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_in(c_bit2, s14)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7962, 3802, 7959])).
% 12.65/8.65 tff(7964,plain,
% 12.65/8.65 (((~![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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7965,plain,
% 12.65/8.65 ((~![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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7966,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7965, 7964])).
% 12.65/8.65 tff(7967,plain,
% 12.65/8.65 (~node4(c_bit1, s13)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7966, 1221, 1787])).
% 12.65/8.65 tff(7968,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7969,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7970,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7969, 7968])).
% 12.65/8.65 tff(7971,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_out(c_bit1, s13)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7970, 1235, 7967])).
% 12.65/8.65 tff(7972,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7973,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7974,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7973, 7972])).
% 12.65/8.65 tff(7975,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_in(c_bit2, s13)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7974, 3802, 7971])).
% 12.65/8.65 tff(7976,plain,
% 12.65/8.65 (((~![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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7977,plain,
% 12.65/8.65 ((~![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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7978,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7977, 7976])).
% 12.65/8.65 tff(7979,plain,
% 12.65/8.65 (~node4(c_bit1, s10)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7978, 3055, 1403])).
% 12.65/8.65 tff(7980,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7981,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7982,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7981, 7980])).
% 12.65/8.65 tff(7983,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_out(c_bit1, s10)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7982, 1235, 7979])).
% 12.65/8.65 tff(7984,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7985,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7986,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7985, 7984])).
% 12.65/8.65 tff(7987,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_in(c_bit2, s10)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7986, 3802, 7983])).
% 12.65/8.65 tff(7988,plain,
% 12.65/8.65 (((~![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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7989,plain,
% 12.65/8.65 ((~![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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7990,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7989, 7988])).
% 12.65/8.65 tff(7991,plain,
% 12.65/8.65 (~node4(c_bit1, s9)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7990, 1221, 1689])).
% 12.65/8.65 tff(7992,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7993,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7994,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7993, 7992])).
% 12.65/8.65 tff(7995,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_out(c_bit1, s9)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7994, 1235, 7991])).
% 12.65/8.65 tff(7996,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(7997,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(7998,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[7997, 7996])).
% 12.65/8.65 tff(7999,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_in(c_bit2, s9)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[7998, 3802, 7995])).
% 12.65/8.65 tff(8000,plain,
% 12.65/8.65 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s8)) | m_counter_cell_v_value(c_bit1, s8))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s8)) | m_counter_cell_v_value(c_bit1, s8))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8001,plain,
% 12.65/8.65 ((m_counter_cell_v_value(c_bit1, s8) | (~node4(c_bit1, s8))) <=> ((~node4(c_bit1, s8)) | m_counter_cell_v_value(c_bit1, s8))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8002,plain,
% 12.65/8.65 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s8) | (~node4(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s8)) | m_counter_cell_v_value(c_bit1, s8)))),
% 12.65/8.65 inference(monotonicity,[status(thm)],[8001])).
% 12.65/8.65 tff(8003,plain,
% 12.65/8.65 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s8) | (~node4(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s8)) | m_counter_cell_v_value(c_bit1, s8))),
% 12.65/8.65 inference(transitivity,[status(thm)],[8002, 8000])).
% 12.65/8.65 tff(8004,plain,
% 12.65/8.65 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s8) | (~node4(c_bit1, s8)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8005,plain,
% 12.65/8.65 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s8)) | m_counter_cell_v_value(c_bit1, s8)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8004, 8003])).
% 12.65/8.65 tff(8006,plain,
% 12.65/8.65 (~node4(c_bit1, s8)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8005, 1221, 1669])).
% 12.65/8.65 tff(8007,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8008,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8009,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8008, 8007])).
% 12.65/8.65 tff(8010,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_out(c_bit1, s8)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8009, 1235, 8006])).
% 12.65/8.65 tff(8011,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8012,plain,
% 12.65/8.65 ((~![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))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8013,plain,
% 12.65/8.65 ((~![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)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8012, 8011])).
% 12.65/8.65 tff(8014,plain,
% 12.65/8.65 (~m_counter_cell_v_carry_in(c_bit2, s8)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8013, 3802, 8010])).
% 12.65/8.65 tff(8015,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8016,plain,
% 12.65/8.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit2, s7, s8))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8017,plain,
% 12.65/8.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit2, s7, s8)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8016, 8015])).
% 12.65/8.65 tff(8018,plain,
% 12.65/8.65 (node3(c_bit2, s7, s8)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8017, 21, 32])).
% 12.65/8.65 tff(8019,plain,
% 12.65/8.65 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8020,plain,
% 12.65/8.65 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8021,plain,
% 12.65/8.65 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8020, 8019])).
% 12.65/8.65 tff(8022,plain,
% 12.65/8.65 ((~m_counter_cell_v_carry_in(c_bit2, s7)) | (~node2(c_bit2, s7))),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8021, 126, 7920])).
% 12.65/8.65 tff(8023,plain,
% 12.65/8.65 (~node2(c_bit2, s7)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8022, 7688])).
% 12.65/8.65 tff(8024,plain,
% 12.65/8.65 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s7) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s7) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8025,plain,
% 12.65/8.65 ((node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | (~m_counter_cell_v_value(c_bit2, s8))) <=> (node2(c_bit2, s7) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8026,plain,
% 12.65/8.65 (((~![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)))) | (node2(c_bit2, s7) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8))))),
% 12.65/8.65 inference(monotonicity,[status(thm)],[8025])).
% 12.65/8.65 tff(8027,plain,
% 12.65/8.65 (((~![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)))) | node2(c_bit2, s7) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8)))),
% 12.65/8.65 inference(transitivity,[status(thm)],[8026, 8024])).
% 12.65/8.65 tff(8028,plain,
% 12.65/8.65 ((~![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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8029,plain,
% 12.65/8.65 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s7) | (~m_counter_cell_v_value(c_bit2, s8)) | (~node3(c_bit2, s7, s8))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8028, 8027])).
% 12.65/8.65 tff(8030,plain,
% 12.65/8.65 (~m_counter_cell_v_value(c_bit2, s8)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8029, 141, 8023, 8018])).
% 12.65/8.65 tff(8031,plain,
% 12.65/8.65 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit2, s8)) | m_counter_cell_v_value(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) | (~node2(c_bit2, s8)) | m_counter_cell_v_value(c_bit2, s8))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8032,plain,
% 12.65/8.65 ((m_counter_cell_v_carry_in(c_bit2, s8) | m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8))) <=> (m_counter_cell_v_carry_in(c_bit2, s8) | (~node2(c_bit2, s8)) | m_counter_cell_v_value(c_bit2, s8))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8033,plain,
% 12.65/8.65 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit2, s8)) | m_counter_cell_v_value(c_bit2, s8)))),
% 12.65/8.65 inference(monotonicity,[status(thm)],[8032])).
% 12.65/8.65 tff(8034,plain,
% 12.65/8.65 (((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit2, s8)) | m_counter_cell_v_value(c_bit2, s8))),
% 12.65/8.65 inference(transitivity,[status(thm)],[8033, 8031])).
% 12.65/8.65 tff(8035,plain,
% 12.65/8.65 ((~![I0: $i, X: $i] : (m_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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8036,plain,
% 12.65/8.65 ((~![I0: $i, X: $i] : (m_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) | (~node2(c_bit2, s8)) | m_counter_cell_v_value(c_bit2, s8)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8035, 8034])).
% 12.65/8.65 tff(8037,plain,
% 12.65/8.65 (m_counter_cell_v_carry_in(c_bit2, s8) | (~node2(c_bit2, s8))),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8036, 1449, 8030])).
% 12.65/8.65 tff(8038,plain,
% 12.65/8.65 (~node2(c_bit2, s8)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8037, 8014])).
% 12.65/8.65 tff(8039,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8040,plain,
% 12.65/8.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit2, s8, s9))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8041,plain,
% 12.65/8.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit2, s8, s9)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8040, 8039])).
% 12.65/8.65 tff(8042,plain,
% 12.65/8.65 (node3(c_bit2, s8, s9)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8041, 21, 315])).
% 12.65/8.65 tff(8043,plain,
% 12.65/8.65 (((~![Y: $i, 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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8044,plain,
% 12.65/8.65 ((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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8045,plain,
% 12.65/8.65 (((~![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))))),
% 12.65/8.65 inference(monotonicity,[status(thm)],[8044])).
% 12.65/8.65 tff(8046,plain,
% 12.65/8.65 (((~![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)))),
% 12.65/8.65 inference(transitivity,[status(thm)],[8045, 8043])).
% 12.65/8.65 tff(8047,plain,
% 12.65/8.65 ((~![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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8048,plain,
% 12.65/8.65 ((~![Y: $i, 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))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8047, 8046])).
% 12.65/8.65 tff(8049,plain,
% 12.65/8.65 ((~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8048, 141, 8042])).
% 12.65/8.65 tff(8050,plain,
% 12.65/8.65 (~m_counter_cell_v_value(c_bit2, s9)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8049, 8038])).
% 12.65/8.65 tff(8051,plain,
% 12.65/8.65 (((~![I0: $i, X: $i] : (m_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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8052,plain,
% 12.65/8.65 ((~![I0: $i, X: $i] : (m_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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8053,plain,
% 12.65/8.65 ((~![I0: $i, X: $i] : (m_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))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8052, 8051])).
% 12.65/8.65 tff(8054,plain,
% 12.65/8.65 (m_counter_cell_v_carry_in(c_bit2, s9) | (~node2(c_bit2, s9))),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8053, 1449, 8050])).
% 12.65/8.65 tff(8055,plain,
% 12.65/8.65 (~node2(c_bit2, s9)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8054, 7999])).
% 12.65/8.65 tff(8056,plain,
% 12.65/8.65 (((~![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))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8057,plain,
% 12.65/8.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit2, s9, s10))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8058,plain,
% 12.65/8.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit2, s9, s10)),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8057, 8056])).
% 12.65/8.65 tff(8059,plain,
% 12.65/8.65 (node3(c_bit2, s9, s10)),
% 12.65/8.65 inference(unit_resolution,[status(thm)],[8058, 21, 341])).
% 12.65/8.65 tff(8060,plain,
% 12.65/8.65 (((~![Y: $i, 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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8061,plain,
% 12.65/8.65 ((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)))),
% 12.65/8.65 inference(rewrite,[status(thm)],[])).
% 12.65/8.65 tff(8062,plain,
% 12.65/8.65 (((~![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))))),
% 12.65/8.65 inference(monotonicity,[status(thm)],[8061])).
% 12.65/8.65 tff(8063,plain,
% 12.65/8.65 (((~![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)))),
% 12.65/8.65 inference(transitivity,[status(thm)],[8062, 8060])).
% 12.65/8.65 tff(8064,plain,
% 12.65/8.65 ((~![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)))),
% 12.65/8.65 inference(quant_inst,[status(thm)],[])).
% 12.65/8.65 tff(8065,plain,
% 12.65/8.65 ((~![Y: $i, 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))),
% 12.65/8.65 inference(modus_ponens,[status(thm)],[8064, 8063])).
% 12.65/8.66 tff(8066,plain,
% 12.65/8.66 ((~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8065, 141, 8059])).
% 12.65/8.66 tff(8067,plain,
% 12.65/8.66 (~m_counter_cell_v_value(c_bit2, s10)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8066, 8055])).
% 12.65/8.66 tff(8068,plain,
% 12.65/8.66 (((~![I0: $i, X: $i] : (m_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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8069,plain,
% 12.65/8.66 ((~![I0: $i, X: $i] : (m_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)))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8070,plain,
% 12.65/8.66 ((~![I0: $i, X: $i] : (m_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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8069, 8068])).
% 12.65/8.66 tff(8071,plain,
% 12.65/8.66 (~node2(c_bit2, s10)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8070, 1449, 8067, 7987])).
% 12.65/8.66 tff(8072,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8073,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit2, s10, s11))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8074,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit2, s10, s11)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8073, 8072])).
% 12.65/8.66 tff(8075,plain,
% 12.65/8.66 (node3(c_bit2, s10, s11)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8074, 21, 370])).
% 12.65/8.66 tff(8076,plain,
% 12.65/8.66 (((~![Y: $i, 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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8077,plain,
% 12.65/8.66 ((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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8078,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8077])).
% 12.65/8.66 tff(8079,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8078, 8076])).
% 12.65/8.66 tff(8080,plain,
% 12.65/8.66 ((~![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)))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8081,plain,
% 12.65/8.66 ((~![Y: $i, 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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8080, 8079])).
% 12.65/8.66 tff(8082,plain,
% 12.65/8.66 ((~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8081, 141, 8075])).
% 12.65/8.66 tff(8083,plain,
% 12.65/8.66 (~m_counter_cell_v_value(c_bit2, s11)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8082, 8071])).
% 12.65/8.66 tff(8084,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8085,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8086,plain,
% 12.65/8.66 ((~![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)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8085, 8084])).
% 12.65/8.66 tff(8087,plain,
% 12.65/8.66 ((~m_counter_cell_v_value(c_bit1, s11)) | m_counter_cell_v_carry_out(c_bit1, s11)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8086, 1368, 1746])).
% 12.65/8.66 tff(8088,plain,
% 12.65/8.66 (m_counter_cell_v_carry_out(c_bit1, s11)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8087, 1737])).
% 12.65/8.66 tff(8089,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8090,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8091,plain,
% 12.65/8.66 ((~![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)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8090, 8089])).
% 12.65/8.66 tff(8092,plain,
% 12.65/8.66 (m_counter_cell_v_carry_in(c_bit2, s11)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8091, 6919, 8088])).
% 12.65/8.66 tff(8093,plain,
% 12.65/8.66 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8094,plain,
% 12.65/8.66 (((~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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8095,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8094])).
% 12.65/8.66 tff(8096,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8095, 8093])).
% 12.65/8.66 tff(8097,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8098,plain,
% 12.65/8.66 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8097, 8096])).
% 12.65/8.66 tff(8099,plain,
% 12.65/8.66 (m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11))),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8098, 77, 8092])).
% 12.65/8.66 tff(8100,plain,
% 12.65/8.66 (~node1(c_bit2, s11)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8099, 8083])).
% 12.65/8.66 tff(8101,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8102,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit2, s11, s12))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8103,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit2, s11, s12)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8102, 8101])).
% 12.65/8.66 tff(8104,plain,
% 12.65/8.66 (node3(c_bit2, s11, s12)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8103, 21, 396])).
% 12.65/8.66 tff(8105,plain,
% 12.65/8.66 (((~![Y: $i, 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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8106,plain,
% 12.65/8.66 ((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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8107,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8106])).
% 12.65/8.66 tff(8108,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8107, 8105])).
% 12.65/8.66 tff(8109,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8110,plain,
% 12.65/8.66 ((~![Y: $i, 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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8109, 8108])).
% 12.65/8.66 tff(8111,plain,
% 12.65/8.66 (m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8110, 106, 8104])).
% 12.65/8.66 tff(8112,plain,
% 12.65/8.66 (m_counter_cell_v_value(c_bit2, s12)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8111, 8100])).
% 12.65/8.66 tff(8113,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8114,plain,
% 12.65/8.66 ((~![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)))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8115,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8114, 8113])).
% 12.65/8.66 tff(8116,plain,
% 12.65/8.66 (~node4(c_bit1, s12)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8115, 3055, 1775])).
% 12.65/8.66 tff(8117,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8118,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8119,plain,
% 12.65/8.66 ((~![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)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8118, 8117])).
% 12.65/8.66 tff(8120,plain,
% 12.65/8.66 (~m_counter_cell_v_carry_out(c_bit1, s12)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8119, 1235, 8116])).
% 12.65/8.66 tff(8121,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8122,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8123,plain,
% 12.65/8.66 ((~![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)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8122, 8121])).
% 12.65/8.66 tff(8124,plain,
% 12.65/8.66 (~m_counter_cell_v_carry_in(c_bit2, s12)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8123, 3802, 8120])).
% 12.65/8.66 tff(8125,plain,
% 12.65/8.66 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8126,plain,
% 12.65/8.66 (((~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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8127,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8126])).
% 12.65/8.66 tff(8128,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8127, 8125])).
% 12.65/8.66 tff(8129,plain,
% 12.65/8.66 ((~![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)))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8130,plain,
% 12.65/8.66 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8129, 8128])).
% 12.65/8.66 tff(8131,plain,
% 12.65/8.66 ((~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12))),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8130, 1517, 8124])).
% 12.65/8.66 tff(8132,plain,
% 12.65/8.66 (~node1(c_bit2, s12)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8131, 8112])).
% 12.65/8.66 tff(8133,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8134,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit2, s12, s13))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8135,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit2, s12, s13)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8134, 8133])).
% 12.65/8.66 tff(8136,plain,
% 12.65/8.66 (node3(c_bit2, s12, s13)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8135, 21, 14])).
% 12.65/8.66 tff(8137,plain,
% 12.65/8.66 (((~![Y: $i, 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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8138,plain,
% 12.65/8.66 ((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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8139,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8138])).
% 12.65/8.66 tff(8140,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8139, 8137])).
% 12.65/8.66 tff(8141,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8142,plain,
% 12.65/8.66 ((~![Y: $i, 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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8141, 8140])).
% 12.65/8.66 tff(8143,plain,
% 12.65/8.66 (m_counter_cell_v_value(c_bit2, s13) | node1(c_bit2, s12)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8142, 106, 8136])).
% 12.65/8.66 tff(8144,plain,
% 12.65/8.66 (m_counter_cell_v_value(c_bit2, s13)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8143, 8132])).
% 12.65/8.66 tff(8145,plain,
% 12.65/8.66 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8146,plain,
% 12.65/8.66 (((~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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8147,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8146])).
% 12.65/8.66 tff(8148,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8147, 8145])).
% 12.65/8.66 tff(8149,plain,
% 12.65/8.66 ((~![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)))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8150,plain,
% 12.65/8.66 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8149, 8148])).
% 12.65/8.66 tff(8151,plain,
% 12.65/8.66 (m_counter_cell_v_carry_in(c_bit2, s13) | (~node1(c_bit2, s13))),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8150, 1517, 8144])).
% 12.65/8.66 tff(8152,plain,
% 12.65/8.66 (~node1(c_bit2, s13)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8151, 7975])).
% 12.65/8.66 tff(8153,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8154,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit2, s13, s14))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8155,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit2, s13, s14)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8154, 8153])).
% 12.65/8.66 tff(8156,plain,
% 12.65/8.66 (node3(c_bit2, s13, s14)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8155, 21, 439])).
% 12.65/8.66 tff(8157,plain,
% 12.65/8.66 (((~![Y: $i, 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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8158,plain,
% 12.65/8.66 ((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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8159,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8158])).
% 12.65/8.66 tff(8160,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8159, 8157])).
% 12.65/8.66 tff(8161,plain,
% 12.65/8.66 ((~![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))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8162,plain,
% 12.65/8.66 ((~![Y: $i, 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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8161, 8160])).
% 12.65/8.66 tff(8163,plain,
% 12.65/8.66 (m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8162, 106, 8156])).
% 12.65/8.66 tff(8164,plain,
% 12.65/8.66 (m_counter_cell_v_value(c_bit2, s14)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8163, 8152])).
% 12.65/8.66 tff(8165,plain,
% 12.65/8.66 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8166,plain,
% 12.65/8.66 (((~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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8167,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8166])).
% 12.65/8.66 tff(8168,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8167, 8165])).
% 12.65/8.66 tff(8169,plain,
% 12.65/8.66 ((~![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)))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8170,plain,
% 12.65/8.66 ((~![I0: $i, X: $i] : ((~node1(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))),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8169, 8168])).
% 12.65/8.66 tff(8171,plain,
% 12.65/8.66 (m_counter_cell_v_carry_in(c_bit2, s14) | (~node1(c_bit2, s14))),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8170, 1517, 8164])).
% 12.65/8.66 tff(8172,plain,
% 12.65/8.66 (~node1(c_bit2, s14)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8171, 7963])).
% 12.65/8.66 tff(8173,plain,
% 12.65/8.66 (((~![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))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8174,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit2, s14, s15))),
% 12.65/8.66 inference(quant_inst,[status(thm)],[])).
% 12.65/8.66 tff(8175,plain,
% 12.65/8.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit2, s14, s15)),
% 12.65/8.66 inference(modus_ponens,[status(thm)],[8174, 8173])).
% 12.65/8.66 tff(8176,plain,
% 12.65/8.66 (node3(c_bit2, s14, s15)),
% 12.65/8.66 inference(unit_resolution,[status(thm)],[8175, 21, 468])).
% 12.65/8.66 tff(8177,plain,
% 12.65/8.66 (((~![Y: $i, 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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8178,plain,
% 12.65/8.66 ((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)))),
% 12.65/8.66 inference(rewrite,[status(thm)],[])).
% 12.65/8.66 tff(8179,plain,
% 12.65/8.66 (((~![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))))),
% 12.65/8.66 inference(monotonicity,[status(thm)],[8178])).
% 12.65/8.66 tff(8180,plain,
% 12.65/8.66 (((~![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)))),
% 12.65/8.66 inference(transitivity,[status(thm)],[8179, 8177])).
% 12.65/8.66 tff(8181,plain,
% 12.65/8.67 ((~![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))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8182,plain,
% 12.65/8.67 ((~![Y: $i, 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))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8181, 8180])).
% 12.65/8.67 tff(8183,plain,
% 12.65/8.67 (m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8182, 106, 8176])).
% 12.65/8.67 tff(8184,plain,
% 12.65/8.67 (m_counter_cell_v_value(c_bit2, s15)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8183, 8172])).
% 12.65/8.67 tff(8185,plain,
% 12.65/8.67 (((~![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))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8186,plain,
% 12.65/8.67 ((~![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))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8187,plain,
% 12.65/8.67 ((~![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)),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8186, 8185])).
% 12.65/8.67 tff(8188,plain,
% 12.65/8.67 ((~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8187, 1368, 1836])).
% 12.65/8.67 tff(8189,plain,
% 12.65/8.67 (m_counter_cell_v_carry_out(c_bit1, s15)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8188, 1827])).
% 12.65/8.67 tff(8190,plain,
% 12.65/8.67 (((~![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))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8191,plain,
% 12.65/8.67 ((~![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))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8192,plain,
% 12.65/8.67 ((~![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)),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8191, 8190])).
% 12.65/8.67 tff(8193,plain,
% 12.65/8.67 (m_counter_cell_v_carry_in(c_bit2, s15)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8192, 6919, 8189])).
% 12.65/8.67 tff(8194,plain,
% 12.65/8.67 (((~![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))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8195,plain,
% 12.65/8.67 ((~![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))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8196,plain,
% 12.65/8.67 ((~![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)),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8195, 8194])).
% 12.65/8.67 tff(8197,plain,
% 12.65/8.67 ((~m_counter_cell_v_value(c_bit2, s15)) | m_counter_cell_v_carry_out(c_bit2, s15)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8196, 1368, 8193])).
% 12.65/8.67 tff(8198,plain,
% 12.65/8.67 (m_counter_cell_v_carry_out(c_bit2, s15)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8197, 8184])).
% 12.65/8.67 tff(8199,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8200,plain,
% 12.65/8.67 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s15)) | (~m_counter_cell_v_carry_out(c_bit2, s15)))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8201,plain,
% 12.65/8.67 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s15)) | (~m_counter_cell_v_carry_out(c_bit2, s15))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8200, 8199])).
% 12.65/8.67 tff(8202,plain,
% 12.65/8.67 (~always5(s15)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8201, 6898, 8198])).
% 12.65/8.67 tff(8203,plain,
% 12.65/8.67 (~always5(s14)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[4219, 8202])).
% 12.65/8.67 tff(8204,plain,
% 12.65/8.67 (~always5(s13)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[4227, 8203])).
% 12.65/8.67 tff(8205,plain,
% 12.65/8.67 (~always5(s12)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[4235, 8204])).
% 12.65/8.67 tff(8206,plain,
% 12.65/8.67 (~always5(s11)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[4243, 8205])).
% 12.65/8.67 tff(8207,plain,
% 12.65/8.67 (~always5(s10)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[4251, 8206])).
% 12.65/8.67 tff(8208,plain,
% 12.65/8.67 (~always5(s9)),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[4259, 8207])).
% 12.65/8.67 tff(8209,plain,
% 12.65/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s9) | (~trans(s59, s9)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s9) | (~trans(s59, s9)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8210,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s9)) | always5(s9)) <=> ((~always5(s59)) | always5(s9) | (~trans(s59, s9)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8211,plain,
% 12.65/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s9) | (~trans(s59, s9))))),
% 12.65/8.67 inference(monotonicity,[status(thm)],[8210])).
% 12.65/8.67 tff(8212,plain,
% 12.65/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s9) | (~trans(s59, s9)))),
% 12.65/8.67 inference(transitivity,[status(thm)],[8211, 8209])).
% 12.65/8.67 tff(8213,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s9)) | always5(s9))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8214,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s9) | (~trans(s59, s9))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8213, 8212])).
% 12.65/8.67 tff(8215,plain,
% 12.65/8.67 ($false),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8214, 5824, 3860, 6888, 8208])).
% 12.65/8.67 tff(8216,plain,(~trans(s59, s9)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.67 tff(8217,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8218,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s10)) | always5(s10)) <=> ((~always5(s59)) | always5(s10) | (~trans(s59, s10)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8219,plain,
% 12.65/8.67 (((~![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))))),
% 12.65/8.67 inference(monotonicity,[status(thm)],[8218])).
% 12.65/8.67 tff(8220,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(transitivity,[status(thm)],[8219, 8217])).
% 12.65/8.67 tff(8221,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s10)) | always5(s10))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8222,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s10) | (~trans(s59, s10))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8221, 8220])).
% 12.65/8.67 tff(8223,plain,
% 12.65/8.67 ($false),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8222, 5868, 3860, 6888, 8207])).
% 12.65/8.67 tff(8224,plain,(~trans(s59, s10)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.67 tff(8225,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8226,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s12)) | always5(s12)) <=> ((~always5(s59)) | always5(s12) | (~trans(s59, s12)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8227,plain,
% 12.65/8.67 (((~![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))))),
% 12.65/8.67 inference(monotonicity,[status(thm)],[8226])).
% 12.65/8.67 tff(8228,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(transitivity,[status(thm)],[8227, 8225])).
% 12.65/8.67 tff(8229,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s12)) | always5(s12))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8230,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s12) | (~trans(s59, s12))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8229, 8228])).
% 12.65/8.67 tff(8231,plain,
% 12.65/8.67 ($false),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8230, 5945, 3860, 6888, 8205])).
% 12.65/8.67 tff(8232,plain,(~trans(s59, s12)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.67 tff(8233,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8234,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s2)) | always5(s2)) <=> ((~always5(s59)) | always5(s2) | (~trans(s59, s2)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8235,plain,
% 12.65/8.67 (((~![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))))),
% 12.65/8.67 inference(monotonicity,[status(thm)],[8234])).
% 12.65/8.67 tff(8236,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(transitivity,[status(thm)],[8235, 8233])).
% 12.65/8.67 tff(8237,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s2)) | always5(s2))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8238,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s2) | (~trans(s59, s2))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8237, 8236])).
% 12.65/8.67 tff(8239,plain,
% 12.65/8.67 ($false),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8238, 5956, 3860, 6888, 7942])).
% 12.65/8.67 tff(8240,plain,(~trans(s59, s2)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.67 tff(8241,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8242,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s14)) | always5(s14)) <=> ((~always5(s59)) | always5(s14) | (~trans(s59, s14)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8243,plain,
% 12.65/8.67 (((~![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))))),
% 12.65/8.67 inference(monotonicity,[status(thm)],[8242])).
% 12.65/8.67 tff(8244,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(transitivity,[status(thm)],[8243, 8241])).
% 12.65/8.67 tff(8245,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s14)) | always5(s14))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8246,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s14) | (~trans(s59, s14))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8245, 8244])).
% 12.65/8.67 tff(8247,plain,
% 12.65/8.67 ($false),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8246, 6055, 3860, 6888, 8203])).
% 12.65/8.67 tff(8248,plain,(~trans(s59, s14)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.67 tff(8249,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8250,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s7)) | always5(s7)) <=> ((~always5(s59)) | always5(s7) | (~trans(s59, s7)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8251,plain,
% 12.65/8.67 (((~![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))))),
% 12.65/8.67 inference(monotonicity,[status(thm)],[8250])).
% 12.65/8.67 tff(8252,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(transitivity,[status(thm)],[8251, 8249])).
% 12.65/8.67 tff(8253,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s7)) | always5(s7))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8254,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s7) | (~trans(s59, s7))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8253, 8252])).
% 12.65/8.67 tff(8255,plain,
% 12.65/8.67 ($false),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8254, 6066, 3860, 6888, 7929])).
% 12.65/8.67 tff(8256,plain,(~trans(s59, s7)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.67 tff(8257,plain,
% 12.65/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s15) | (~trans(s59, s15)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s15) | (~trans(s59, s15)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8258,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s15)) | always5(s15)) <=> ((~always5(s59)) | always5(s15) | (~trans(s59, s15)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8259,plain,
% 12.65/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s15) | (~trans(s59, s15))))),
% 12.65/8.67 inference(monotonicity,[status(thm)],[8258])).
% 12.65/8.67 tff(8260,plain,
% 12.65/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s15) | (~trans(s59, s15)))),
% 12.65/8.67 inference(transitivity,[status(thm)],[8259, 8257])).
% 12.65/8.67 tff(8261,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s15)) | always5(s15))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8262,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s15) | (~trans(s59, s15))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8261, 8260])).
% 12.65/8.67 tff(8263,plain,
% 12.65/8.67 ($false),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8262, 6077, 3860, 6888, 8202])).
% 12.65/8.67 tff(8264,plain,(~trans(s59, s15)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.67 tff(8265,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8266,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s6)) | always5(s6)) <=> ((~always5(s59)) | always5(s6) | (~trans(s59, s6)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8267,plain,
% 12.65/8.67 (((~![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))))),
% 12.65/8.67 inference(monotonicity,[status(thm)],[8266])).
% 12.65/8.67 tff(8268,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(transitivity,[status(thm)],[8267, 8265])).
% 12.65/8.67 tff(8269,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s6)) | always5(s6))),
% 12.65/8.67 inference(quant_inst,[status(thm)],[])).
% 12.65/8.67 tff(8270,plain,
% 12.65/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s6) | (~trans(s59, s6))),
% 12.65/8.67 inference(modus_ponens,[status(thm)],[8269, 8268])).
% 12.65/8.67 tff(8271,plain,
% 12.65/8.67 ($false),
% 12.65/8.67 inference(unit_resolution,[status(thm)],[8270, 6132, 3860, 6888, 7930])).
% 12.65/8.67 tff(8272,plain,(~trans(s59, s6)), inference(lemma,lemma(discharge,[]))).
% 12.65/8.67 tff(8273,plain,
% 12.65/8.67 (((~![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)))),
% 12.65/8.67 inference(rewrite,[status(thm)],[])).
% 12.65/8.67 tff(8274,plain,
% 12.65/8.67 (((~always5(s59)) | (~trans(s59, s13)) | always5(s13)) <=> ((~always5(s59)) | always5(s13) | (~trans(s59, s13)))),
% 12.74/8.67 inference(rewrite,[status(thm)],[])).
% 12.74/8.67 tff(8275,plain,
% 12.74/8.67 (((~![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))))),
% 12.74/8.67 inference(monotonicity,[status(thm)],[8274])).
% 12.74/8.67 tff(8276,plain,
% 12.74/8.67 (((~![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)))),
% 12.74/8.67 inference(transitivity,[status(thm)],[8275, 8273])).
% 12.74/8.67 tff(8277,plain,
% 12.74/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s13)) | always5(s13))),
% 12.74/8.67 inference(quant_inst,[status(thm)],[])).
% 12.74/8.67 tff(8278,plain,
% 12.74/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s13) | (~trans(s59, s13))),
% 12.74/8.67 inference(modus_ponens,[status(thm)],[8277, 8276])).
% 12.74/8.67 tff(8279,plain,
% 12.74/8.67 ($false),
% 12.74/8.67 inference(unit_resolution,[status(thm)],[8278, 6143, 3860, 6888, 8204])).
% 12.74/8.67 tff(8280,plain,(~trans(s59, s13)), inference(lemma,lemma(discharge,[]))).
% 12.74/8.67 tff(8281,plain,
% 12.74/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s3) | (~trans(s59, s3)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s3) | (~trans(s59, s3)))),
% 12.74/8.67 inference(rewrite,[status(thm)],[])).
% 12.74/8.67 tff(8282,plain,
% 12.74/8.67 (((~always5(s59)) | (~trans(s59, s3)) | always5(s3)) <=> ((~always5(s59)) | always5(s3) | (~trans(s59, s3)))),
% 12.74/8.67 inference(rewrite,[status(thm)],[])).
% 12.74/8.67 tff(8283,plain,
% 12.74/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s3) | (~trans(s59, s3))))),
% 12.74/8.67 inference(monotonicity,[status(thm)],[8282])).
% 12.74/8.67 tff(8284,plain,
% 12.74/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s3) | (~trans(s59, s3)))),
% 12.74/8.67 inference(transitivity,[status(thm)],[8283, 8281])).
% 12.74/8.67 tff(8285,plain,
% 12.74/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s3)) | always5(s3))),
% 12.74/8.67 inference(quant_inst,[status(thm)],[])).
% 12.74/8.67 tff(8286,plain,
% 12.74/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s3) | (~trans(s59, s3))),
% 12.74/8.67 inference(modus_ponens,[status(thm)],[8285, 8284])).
% 12.74/8.67 tff(8287,plain,
% 12.74/8.67 ($false),
% 12.74/8.67 inference(unit_resolution,[status(thm)],[8286, 6198, 3860, 6888, 7941])).
% 12.74/8.67 tff(8288,plain,(~trans(s59, s3)), inference(lemma,lemma(discharge,[]))).
% 12.74/8.67 tff(8289,plain,
% 12.74/8.67 (~always5(s8)),
% 12.74/8.67 inference(unit_resolution,[status(thm)],[4267, 8208])).
% 12.74/8.67 tff(8290,plain,
% 12.74/8.67 (((~![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)))),
% 12.74/8.67 inference(rewrite,[status(thm)],[])).
% 12.74/8.67 tff(8291,plain,
% 12.74/8.67 (((~always5(s59)) | (~trans(s59, s8)) | always5(s8)) <=> ((~always5(s59)) | always5(s8) | (~trans(s59, s8)))),
% 12.74/8.67 inference(rewrite,[status(thm)],[])).
% 12.74/8.67 tff(8292,plain,
% 12.74/8.67 (((~![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))))),
% 12.74/8.67 inference(monotonicity,[status(thm)],[8291])).
% 12.74/8.67 tff(8293,plain,
% 12.74/8.67 (((~![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)))),
% 12.74/8.67 inference(transitivity,[status(thm)],[8292, 8290])).
% 12.74/8.67 tff(8294,plain,
% 12.74/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s8)) | always5(s8))),
% 12.74/8.67 inference(quant_inst,[status(thm)],[])).
% 12.74/8.67 tff(8295,plain,
% 12.74/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s8) | (~trans(s59, s8))),
% 12.74/8.67 inference(modus_ponens,[status(thm)],[8294, 8293])).
% 12.74/8.67 tff(8296,plain,
% 12.74/8.67 ($false),
% 12.74/8.67 inference(unit_resolution,[status(thm)],[8295, 6231, 3860, 6888, 8289])).
% 12.74/8.67 tff(8297,plain,(~trans(s59, s8)), inference(lemma,lemma(discharge,[]))).
% 12.74/8.67 tff(8298,plain,
% 12.74/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s11) | (~trans(s59, s11)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s11) | (~trans(s59, s11)))),
% 12.74/8.67 inference(rewrite,[status(thm)],[])).
% 12.74/8.67 tff(8299,plain,
% 12.74/8.67 (((~always5(s59)) | (~trans(s59, s11)) | always5(s11)) <=> ((~always5(s59)) | always5(s11) | (~trans(s59, s11)))),
% 12.74/8.67 inference(rewrite,[status(thm)],[])).
% 12.74/8.67 tff(8300,plain,
% 12.74/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s11)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | always5(s11) | (~trans(s59, s11))))),
% 12.74/8.67 inference(monotonicity,[status(thm)],[8299])).
% 12.74/8.67 tff(8301,plain,
% 12.74/8.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s11)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s11) | (~trans(s59, s11)))),
% 12.74/8.67 inference(transitivity,[status(thm)],[8300, 8298])).
% 12.74/8.67 tff(8302,plain,
% 12.74/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s11)) | always5(s11))),
% 12.74/8.67 inference(quant_inst,[status(thm)],[])).
% 12.74/8.67 tff(8303,plain,
% 12.74/8.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s11) | (~trans(s59, s11))),
% 12.74/8.67 inference(modus_ponens,[status(thm)],[8302, 8301])).
% 12.74/8.67 tff(8304,plain,
% 12.74/8.67 ($false),
% 12.74/8.67 inference(unit_resolution,[status(thm)],[8303, 6363, 3860, 6888, 8206])).
% 12.74/8.67 tff(8305,plain,(~trans(s59, s11)), inference(lemma,lemma(discharge,[]))).
% 12.74/8.67 tff(8306,plain,
% 12.74/8.67 (((~![I0: $i, X: $i] : ((~m_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)))),
% 12.74/8.67 inference(rewrite,[status(thm)],[])).
% 12.74/8.67 tff(8307,plain,
% 12.74/8.67 ((~![I0: $i, X: $i] : ((~m_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)))),
% 12.74/8.67 inference(quant_inst,[status(thm)],[])).
% 12.74/8.67 tff(8308,plain,
% 12.74/8.67 ((~![I0: $i, X: $i] : ((~m_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))),
% 12.74/8.67 inference(modus_ponens,[status(thm)],[8307, 8306])).
% 12.74/8.67 tff(8309,plain,
% 12.74/8.67 ((~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59))),
% 12.74/8.67 inference(unit_resolution,[status(thm)],[8308, 126, 6983])).
% 12.74/8.67 tff(8310,plain,
% 12.74/8.67 (~node2(c_bit0, s59)),
% 12.74/8.67 inference(unit_resolution,[status(thm)],[8309, 6979])).
% 12.74/8.67 tff(8311,assumption,(node3(c_bit0, s59, s57)), introduced(assumption)).
% 12.74/8.67 tff(8312,assumption,(m_counter_cell_v_value(c_bit0, s57)), introduced(assumption)).
% 12.74/8.67 tff(8313,assumption,(~node2(c_bit0, s59)), introduced(assumption)).
% 12.74/8.68 tff(8314,plain,
% 12.74/8.68 (((~![Y: $i, 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)))),
% 12.74/8.68 inference(rewrite,[status(thm)],[])).
% 12.74/8.68 tff(8315,plain,
% 12.74/8.68 ((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)))),
% 12.74/8.68 inference(rewrite,[status(thm)],[])).
% 12.74/8.68 tff(8316,plain,
% 12.74/8.68 (((~![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))))),
% 12.74/8.68 inference(monotonicity,[status(thm)],[8315])).
% 12.74/8.68 tff(8317,plain,
% 12.74/8.68 (((~![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)))),
% 12.74/8.68 inference(transitivity,[status(thm)],[8316, 8314])).
% 12.74/8.68 tff(8318,plain,
% 12.74/8.68 ((~![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)))),
% 12.74/8.68 inference(quant_inst,[status(thm)],[])).
% 12.74/8.68 tff(8319,plain,
% 12.74/8.68 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s57)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s57))),
% 12.74/8.68 inference(modus_ponens,[status(thm)],[8318, 8317])).
% 12.74/8.68 tff(8320,plain,
% 12.74/8.68 ($false),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8319, 141, 8313, 8312, 8311])).
% 12.74/8.68 tff(8321,plain,((~node3(c_bit0, s59, s57)) | node2(c_bit0, s59) | (~m_counter_cell_v_value(c_bit0, s57))), inference(lemma,lemma(discharge,[]))).
% 12.74/8.68 tff(8322,plain,
% 12.74/8.68 (~node3(c_bit0, s59, s57)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8321, 8310, 3704])).
% 12.74/8.68 tff(8323,plain,
% 12.74/8.68 (((~![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))),
% 12.74/8.68 inference(rewrite,[status(thm)],[])).
% 12.74/8.68 tff(8324,plain,
% 12.74/8.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s57)) | node3(c_bit0, s59, s57))),
% 12.74/8.68 inference(quant_inst,[status(thm)],[])).
% 12.74/8.68 tff(8325,plain,
% 12.74/8.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s57)) | node3(c_bit0, s59, s57)),
% 12.74/8.68 inference(modus_ponens,[status(thm)],[8324, 8323])).
% 12.74/8.68 tff(8326,plain,
% 12.74/8.68 ((~trans(s59, s57)) | node3(c_bit0, s59, s57)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8325, 21])).
% 12.74/8.68 tff(8327,plain,
% 12.74/8.68 (~trans(s59, s57)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8326, 8322])).
% 12.74/8.68 tff(8328,plain,
% 12.74/8.68 (~always5(s0)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[4331, 7943])).
% 12.74/8.68 tff(8329,assumption,(~always5(s0)), introduced(assumption)).
% 12.74/8.68 tff(8330,plain,
% 12.74/8.68 (((~![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)))),
% 12.74/8.68 inference(rewrite,[status(thm)],[])).
% 12.74/8.68 tff(8331,plain,
% 12.74/8.68 (((~always5(s59)) | (~trans(s59, s0)) | always5(s0)) <=> ((~always5(s59)) | always5(s0) | (~trans(s59, s0)))),
% 12.74/8.68 inference(rewrite,[status(thm)],[])).
% 12.74/8.68 tff(8332,plain,
% 12.74/8.68 (((~![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))))),
% 12.74/8.68 inference(monotonicity,[status(thm)],[8331])).
% 12.74/8.68 tff(8333,plain,
% 12.74/8.68 (((~![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)))),
% 12.74/8.68 inference(transitivity,[status(thm)],[8332, 8330])).
% 12.74/8.68 tff(8334,plain,
% 12.74/8.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s0)) | always5(s0))),
% 12.74/8.68 inference(quant_inst,[status(thm)],[])).
% 12.74/8.68 tff(8335,plain,
% 12.74/8.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s0) | (~trans(s59, s0))),
% 12.74/8.68 inference(modus_ponens,[status(thm)],[8334, 8333])).
% 12.74/8.68 tff(8336,plain,
% 12.74/8.68 ($false),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8335, 6406, 3860, 6888, 8329])).
% 12.74/8.68 tff(8337,plain,((~trans(s59, s0)) | always5(s0)), inference(lemma,lemma(discharge,[]))).
% 12.74/8.68 tff(8338,plain,
% 12.74/8.68 (~trans(s59, s0)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8337, 8328])).
% 12.74/8.68 tff(8339,assumption,(~always5(s4)), introduced(assumption)).
% 12.74/8.68 tff(8340,assumption,(always5(s59)), introduced(assumption)).
% 12.74/8.68 tff(8341,assumption,(trans(s59, s4)), introduced(assumption)).
% 12.74/8.68 tff(8342,plain,
% 12.74/8.68 (((~![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)))),
% 12.74/8.68 inference(rewrite,[status(thm)],[])).
% 12.74/8.68 tff(8343,plain,
% 12.74/8.68 (((~always5(s59)) | (~trans(s59, s4)) | always5(s4)) <=> ((~always5(s59)) | always5(s4) | (~trans(s59, s4)))),
% 12.74/8.68 inference(rewrite,[status(thm)],[])).
% 12.74/8.68 tff(8344,plain,
% 12.74/8.68 (((~![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))))),
% 12.74/8.68 inference(monotonicity,[status(thm)],[8343])).
% 12.74/8.68 tff(8345,plain,
% 12.74/8.68 (((~![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)))),
% 12.74/8.68 inference(transitivity,[status(thm)],[8344, 8342])).
% 12.74/8.68 tff(8346,plain,
% 12.74/8.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s4)) | always5(s4))),
% 12.74/8.68 inference(quant_inst,[status(thm)],[])).
% 12.74/8.68 tff(8347,plain,
% 12.74/8.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s4) | (~trans(s59, s4))),
% 12.74/8.68 inference(modus_ponens,[status(thm)],[8346, 8345])).
% 12.74/8.68 tff(8348,plain,
% 12.74/8.68 ($false),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8347, 8341, 3860, 8340, 8339])).
% 12.74/8.68 tff(8349,plain,((~trans(s59, s4)) | (~always5(s59)) | always5(s4)), inference(lemma,lemma(discharge,[]))).
% 12.74/8.68 tff(8350,plain,
% 12.74/8.68 ((~trans(s59, s4)) | always5(s4)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8349, 6888])).
% 12.74/8.68 tff(8351,plain,
% 12.74/8.68 (~trans(s59, s4)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8350, 7940])).
% 12.74/8.68 tff(8352,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[6879, 8351, 8338])).
% 12.74/8.68 tff(8353,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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, s58) | trans(s59, s59)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8352, 8327])).
% 12.74/8.68 tff(8354,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s8) | trans(s59, s9) | trans(s59, s10) | 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, s58) | trans(s59, s59)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8353, 8305])).
% 12.74/8.68 tff(8355,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s2) | trans(s59, s3) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s9) | trans(s59, s10) | 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, s58) | trans(s59, s59)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8354, 8297])).
% 12.74/8.68 tff(8356,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s2) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s9) | trans(s59, s10) | 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, s58) | trans(s59, s59)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8355, 8288])).
% 12.74/8.68 tff(8357,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s2) | trans(s59, s5) | trans(s59, s6) | trans(s59, s7) | trans(s59, s9) | trans(s59, s10) | trans(s59, s12) | 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, s58) | trans(s59, s59)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8356, 8280])).
% 12.74/8.68 tff(8358,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s2) | trans(s59, s5) | trans(s59, s7) | trans(s59, s9) | 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, 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, s58) | trans(s59, s59)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8357, 8272, 8264])).
% 12.74/8.68 tff(8359,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s2) | trans(s59, s5) | trans(s59, s9) | trans(s59, s10) | trans(s59, s12) | 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, s58) | trans(s59, s59)),
% 12.74/8.68 inference(unit_resolution,[status(thm)],[8358, 8256, 8248])).
% 12.74/8.68 tff(8360,plain,
% 12.74/8.68 (trans(s59, s1) | trans(s59, s5) | trans(s59, s9) | trans(s59, s10) | trans(s59, s12) | 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, s58) | trans(s59, s59)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[8359, 8240])).
% 12.74/8.69 tff(8361,plain,
% 12.74/8.69 (trans(s59, s1) | trans(s59, s5) | trans(s59, s9) | 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, s58) | trans(s59, s59)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[8360, 8232, 8224])).
% 12.74/8.69 tff(8362,plain,
% 12.74/8.69 (trans(s59, s1) | trans(s59, s5) | 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, s58) | trans(s59, s59)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[8361, 8216])).
% 12.74/8.69 tff(8363,plain,
% 12.74/8.69 (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, s58) | trans(s59, s59)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[8362, 7951, 7939])).
% 12.74/8.69 tff(8364,plain,
% 12.74/8.69 ($false),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[8363, 7679, 7668, 7266, 7267, 7657, 7648, 7647, 7637, 7627, 7617, 7607, 7597, 7587, 7577, 7567, 7557, 7547, 7537, 7527, 7517, 7507, 7497, 7487, 7477, 7467, 7457, 7447, 7437, 7427, 7417, 7407, 7397, 7387, 7377, 7367, 7348, 7338, 7327, 7306, 7305, 7304, 7303, 7246])).
% 12.74/8.69 tff(8365,plain,(always5(s54) | trans(s59, s58) | trans(s59, s56) | trans(s59, s25) | trans(s59, s51) | trans(s59, s55) | trans(s59, s37) | trans(s59, s59)), inference(lemma,lemma(discharge,[]))).
% 12.74/8.69 tff(8366,plain,
% 12.74/8.69 (trans(s59, s25)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[8365, 7277, 7267, 7221, 7266, 7265, 7256, 7246])).
% 12.74/8.69 tff(8367,assumption,(~always5(s25)), introduced(assumption)).
% 12.74/8.69 tff(8368,plain,
% 12.74/8.69 (((~![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)))),
% 12.74/8.69 inference(rewrite,[status(thm)],[])).
% 12.74/8.69 tff(8369,plain,
% 12.74/8.69 (((~always5(s59)) | (~trans(s59, s25)) | always5(s25)) <=> ((~always5(s59)) | always5(s25) | (~trans(s59, s25)))),
% 12.74/8.69 inference(rewrite,[status(thm)],[])).
% 12.74/8.69 tff(8370,plain,
% 12.74/8.69 (((~![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))))),
% 12.74/8.69 inference(monotonicity,[status(thm)],[8369])).
% 12.74/8.69 tff(8371,plain,
% 12.74/8.69 (((~![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)))),
% 12.74/8.69 inference(transitivity,[status(thm)],[8370, 8368])).
% 12.74/8.69 tff(8372,plain,
% 12.74/8.69 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s25)) | always5(s25))),
% 12.74/8.69 inference(quant_inst,[status(thm)],[])).
% 12.74/8.69 tff(8373,plain,
% 12.74/8.69 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s59)) | always5(s25) | (~trans(s59, s25))),
% 12.74/8.69 inference(modus_ponens,[status(thm)],[8372, 8371])).
% 12.74/8.69 tff(8374,plain,
% 12.74/8.69 ($false),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[8373, 5750, 3860, 6888, 8367])).
% 12.74/8.69 tff(8375,plain,((~trans(s59, s25)) | always5(s25)), inference(lemma,lemma(discharge,[]))).
% 12.74/8.69 tff(8376,plain,
% 12.74/8.69 (always5(s25)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[8375, 8366])).
% 12.74/8.69 tff(8377,plain,
% 12.74/8.69 (always5(s26)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[4131, 8376])).
% 12.74/8.69 tff(8378,plain,
% 12.74/8.69 (always5(s27)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[4123, 8377])).
% 12.74/8.69 tff(8379,plain,
% 12.74/8.69 (always5(s28)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[4115, 8378])).
% 12.74/8.69 tff(8380,plain,
% 12.74/8.69 (always5(s29)),
% 12.74/8.69 inference(unit_resolution,[status(thm)],[4107, 8379])).
% 12.76/8.69 tff(8381,plain,
% 12.76/8.69 ($false),
% 12.76/8.69 inference(unit_resolution,[status(thm)],[4099, 8380, 7245])).
% 12.76/8.69 tff(8382,plain,(always5(s55) | trans(s59, s56) | trans(s59, s58) | trans(s59, s59)), inference(lemma,lemma(discharge,[]))).
% 12.76/8.69 tff(8383,plain,
% 12.76/8.69 (trans(s59, s56)),
% 12.76/8.69 inference(unit_resolution,[status(thm)],[8382, 7219, 7091, 7070])).
% 12.76/8.69 tff(8384,plain,
% 12.76/8.69 (((~![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))),
% 12.76/8.69 inference(rewrite,[status(thm)],[])).
% 12.76/8.69 tff(8385,plain,
% 12.76/8.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s56)) | node3(c_bit2, s59, s56))),
% 12.76/8.69 inference(quant_inst,[status(thm)],[])).
% 12.76/8.69 tff(8386,plain,
% 12.76/8.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s56)) | node3(c_bit2, s59, s56)),
% 12.76/8.69 inference(modus_ponens,[status(thm)],[8385, 8384])).
% 12.76/8.69 tff(8387,plain,
% 12.76/8.69 ((~trans(s59, s56)) | node3(c_bit2, s59, s56)),
% 12.76/8.69 inference(unit_resolution,[status(thm)],[8386, 21])).
% 12.76/8.69 tff(8388,plain,
% 12.76/8.69 (node3(c_bit2, s59, s56)),
% 12.76/8.69 inference(unit_resolution,[status(thm)],[8387, 8383])).
% 12.76/8.69 tff(8389,plain,
% 12.76/8.69 (((~![I0: $i, X: $i] : ((~m_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, s55)) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node2(c_bit2, 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_bit2, s55)) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node2(c_bit2, s55)))),
% 12.76/8.69 inference(rewrite,[status(thm)],[])).
% 12.76/8.69 tff(8390,plain,
% 12.76/8.69 ((~![I0: $i, X: $i] : ((~m_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, s55)) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node2(c_bit2, s55)))),
% 12.76/8.69 inference(quant_inst,[status(thm)],[])).
% 12.76/8.69 tff(8391,plain,
% 12.76/8.69 ((~![I0: $i, X: $i] : ((~m_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, s55)) | (~m_counter_cell_v_value(c_bit2, s55)) | (~node2(c_bit2, s55))),
% 12.76/8.69 inference(modus_ponens,[status(thm)],[8390, 8389])).
% 12.76/8.69 tff(8392,plain,
% 12.76/8.69 ((~m_counter_cell_v_carry_in(c_bit2, s55)) | (~node2(c_bit2, s55))),
% 12.76/8.69 inference(unit_resolution,[status(thm)],[8391, 126, 7210])).
% 12.76/8.69 tff(8393,plain,
% 12.76/8.69 (~node2(c_bit2, s55)),
% 12.76/8.69 inference(unit_resolution,[status(thm)],[8392, 7100])).
% 12.76/8.69 tff(8394,plain,
% 12.76/8.69 (((~![Y: $i, 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, s56)) | node2(c_bit2, s55) | (~node3(c_bit2, 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_bit2, s56)) | node2(c_bit2, s55) | (~node3(c_bit2, s55, s56)))),
% 12.76/8.69 inference(rewrite,[status(thm)],[])).
% 12.76/8.69 tff(8395,plain,
% 12.76/8.69 ((node2(c_bit2, s55) | (~node3(c_bit2, s55, s56)) | (~m_counter_cell_v_value(c_bit2, s56))) <=> ((~m_counter_cell_v_value(c_bit2, s56)) | node2(c_bit2, s55) | (~node3(c_bit2, s55, s56)))),
% 12.76/8.69 inference(rewrite,[status(thm)],[])).
% 12.76/8.69 tff(8396,plain,
% 12.76/8.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s55) | (~node3(c_bit2, s55, s56)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s56)) | node2(c_bit2, s55) | (~node3(c_bit2, s55, s56))))),
% 12.76/8.69 inference(monotonicity,[status(thm)],[8395])).
% 12.76/8.69 tff(8397,plain,
% 12.76/8.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s55) | (~node3(c_bit2, s55, s56)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s56)) | node2(c_bit2, s55) | (~node3(c_bit2, s55, s56)))),
% 12.76/8.69 inference(transitivity,[status(thm)],[8396, 8394])).
% 12.76/8.69 tff(8398,plain,
% 12.76/8.69 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s55) | (~node3(c_bit2, s55, s56)) | (~m_counter_cell_v_value(c_bit2, s56)))),
% 12.76/8.69 inference(quant_inst,[status(thm)],[])).
% 12.76/8.69 tff(8399,plain,
% 12.76/8.69 ((~![Y: $i, 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, s56)) | node2(c_bit2, s55) | (~node3(c_bit2, s55, s56))),
% 12.76/8.69 inference(modus_ponens,[status(thm)],[8398, 8397])).
% 12.76/8.69 tff(8400,plain,
% 12.76/8.69 ((~m_counter_cell_v_value(c_bit2, s56)) | node2(c_bit2, s55)),
% 12.76/8.69 inference(unit_resolution,[status(thm)],[8399, 141, 7143])).
% 12.76/8.69 tff(8401,plain,
% 12.76/8.69 (~m_counter_cell_v_value(c_bit2, s56)),
% 12.76/8.69 inference(unit_resolution,[status(thm)],[8400, 8393])).
% 12.76/8.69 tff(8402,plain,
% 12.76/8.69 (((~![Y: $i, 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)))),
% 12.76/8.69 inference(rewrite,[status(thm)],[])).
% 12.76/8.69 tff(8403,plain,
% 12.76/8.69 ((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)))),
% 12.76/8.69 inference(rewrite,[status(thm)],[])).
% 12.76/8.69 tff(8404,plain,
% 12.76/8.69 (((~![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))))),
% 12.76/8.70 inference(monotonicity,[status(thm)],[8403])).
% 12.76/8.70 tff(8405,plain,
% 12.76/8.70 (((~![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)))),
% 12.76/8.70 inference(transitivity,[status(thm)],[8404, 8402])).
% 12.76/8.70 tff(8406,plain,
% 12.76/8.70 ((~![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))),
% 12.76/8.70 inference(quant_inst,[status(thm)],[])).
% 12.76/8.70 tff(8407,plain,
% 12.76/8.70 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s56) | node1(c_bit2, s59) | (~node3(c_bit2, s59, s56))),
% 12.76/8.70 inference(modus_ponens,[status(thm)],[8406, 8405])).
% 12.76/8.70 tff(8408,plain,
% 12.76/8.70 ($false),
% 12.76/8.70 inference(unit_resolution,[status(thm)],[8407, 106, 8401, 7075, 8388])).
% 12.76/8.70 % SZS output end Proof
%------------------------------------------------------------------------------