TSTP Solution File: SWV418-1.100 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV418-1.100 : 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 35.43s 23.26s
% Output : Proof 36.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SWV418-1.100 : TPTP v8.1.0. Released v3.5.0.
% 0.02/0.12 % 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 03:08:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 35.43/23.26 % SZS status Unsatisfiable
% 35.43/23.26 % SZS output start Proof
% 35.43/23.26 tff(m_counter_cell_v_carry_out_type, type, (
% 35.43/23.26 m_counter_cell_v_carry_out: ( $i * $i ) > $o)).
% 35.43/23.26 tff(s97_type, type, (
% 35.43/23.26 s97: $i)).
% 35.43/23.26 tff(c_bit2_type, type, (
% 35.43/23.26 c_bit2: $i)).
% 35.43/23.26 tff(always5_type, type, (
% 35.43/23.26 always5: $i > $o)).
% 35.43/23.26 tff(s96_type, type, (
% 35.43/23.26 s96: $i)).
% 35.43/23.26 tff(trans_type, type, (
% 35.43/23.26 trans: ( $i * $i ) > $o)).
% 35.43/23.26 tff(s99_type, type, (
% 35.43/23.26 s99: $i)).
% 35.43/23.26 tff(s95_type, type, (
% 35.43/23.26 s95: $i)).
% 35.43/23.26 tff(succ_type, type, (
% 35.43/23.26 succ: ( $i * $i ) > $o)).
% 35.43/23.26 tff(m_counter_cell_v_value_type, type, (
% 35.43/23.26 m_counter_cell_v_value: ( $i * $i ) > $o)).
% 35.43/23.26 tff(node1_type, type, (
% 35.43/23.26 node1: ( $i * $i ) > $o)).
% 35.43/23.26 tff(node4_type, type, (
% 35.43/23.26 node4: ( $i * $i ) > $o)).
% 35.43/23.26 tff(m_counter_cell_v_carry_in_type, type, (
% 35.43/23.26 m_counter_cell_v_carry_in: ( $i * $i ) > $o)).
% 35.43/23.26 tff(c_bit1_type, type, (
% 35.43/23.26 c_bit1: $i)).
% 35.43/23.26 tff(node2_type, type, (
% 35.43/23.26 node2: ( $i * $i ) > $o)).
% 35.43/23.26 tff(s94_type, type, (
% 35.43/23.26 s94: $i)).
% 35.43/23.26 tff(c_bit0_type, type, (
% 35.43/23.26 c_bit0: $i)).
% 35.43/23.26 tff(s93_type, type, (
% 35.43/23.26 s93: $i)).
% 35.43/23.26 tff(s92_type, type, (
% 35.43/23.26 s92: $i)).
% 35.43/23.26 tff(s91_type, type, (
% 35.43/23.26 s91: $i)).
% 35.43/23.26 tff(s90_type, type, (
% 35.43/23.26 s90: $i)).
% 35.43/23.26 tff(s89_type, type, (
% 35.43/23.26 s89: $i)).
% 35.43/23.26 tff(s88_type, type, (
% 35.43/23.26 s88: $i)).
% 35.43/23.26 tff(s87_type, type, (
% 35.43/23.26 s87: $i)).
% 35.43/23.26 tff(s86_type, type, (
% 35.43/23.26 s86: $i)).
% 35.43/23.26 tff(s85_type, type, (
% 35.43/23.26 s85: $i)).
% 35.43/23.26 tff(s84_type, type, (
% 35.43/23.26 s84: $i)).
% 35.43/23.26 tff(s83_type, type, (
% 35.43/23.26 s83: $i)).
% 35.43/23.26 tff(s82_type, type, (
% 35.43/23.26 s82: $i)).
% 35.43/23.26 tff(s81_type, type, (
% 35.43/23.26 s81: $i)).
% 35.43/23.26 tff(s80_type, type, (
% 35.43/23.26 s80: $i)).
% 35.43/23.26 tff(s79_type, type, (
% 35.43/23.26 s79: $i)).
% 35.43/23.26 tff(s78_type, type, (
% 35.43/23.26 s78: $i)).
% 35.43/23.26 tff(s77_type, type, (
% 35.43/23.26 s77: $i)).
% 35.43/23.26 tff(s76_type, type, (
% 35.43/23.26 s76: $i)).
% 35.43/23.26 tff(s75_type, type, (
% 35.43/23.26 s75: $i)).
% 35.43/23.26 tff(s74_type, type, (
% 35.43/23.26 s74: $i)).
% 35.43/23.26 tff(s73_type, type, (
% 35.43/23.26 s73: $i)).
% 35.43/23.26 tff(s72_type, type, (
% 35.43/23.26 s72: $i)).
% 35.43/23.26 tff(s71_type, type, (
% 35.43/23.26 s71: $i)).
% 35.43/23.26 tff(s70_type, type, (
% 35.43/23.26 s70: $i)).
% 35.43/23.26 tff(s69_type, type, (
% 35.43/23.26 s69: $i)).
% 35.43/23.26 tff(s68_type, type, (
% 35.43/23.26 s68: $i)).
% 35.43/23.26 tff(s67_type, type, (
% 35.43/23.26 s67: $i)).
% 35.43/23.26 tff(s66_type, type, (
% 35.43/23.26 s66: $i)).
% 35.43/23.26 tff(s65_type, type, (
% 35.43/23.26 s65: $i)).
% 35.43/23.26 tff(s64_type, type, (
% 35.43/23.26 s64: $i)).
% 35.43/23.26 tff(s63_type, type, (
% 35.43/23.26 s63: $i)).
% 35.43/23.26 tff(s62_type, type, (
% 35.43/23.26 s62: $i)).
% 35.43/23.26 tff(s61_type, type, (
% 35.43/23.26 s61: $i)).
% 35.43/23.26 tff(s60_type, type, (
% 35.43/23.26 s60: $i)).
% 35.43/23.26 tff(node3_type, type, (
% 35.43/23.26 node3: ( $i * $i * $i ) > $o)).
% 35.43/23.26 tff(s59_type, type, (
% 35.43/23.26 s59: $i)).
% 35.43/23.26 tff(s58_type, type, (
% 35.43/23.26 s58: $i)).
% 35.43/23.26 tff(s57_type, type, (
% 35.43/23.26 s57: $i)).
% 35.43/23.26 tff(s56_type, type, (
% 35.43/23.26 s56: $i)).
% 35.43/23.26 tff(s55_type, type, (
% 35.43/23.26 s55: $i)).
% 35.43/23.26 tff(s54_type, type, (
% 35.43/23.26 s54: $i)).
% 35.43/23.26 tff(s53_type, type, (
% 35.43/23.26 s53: $i)).
% 35.43/23.26 tff(s52_type, type, (
% 35.43/23.26 s52: $i)).
% 35.43/23.26 tff(s51_type, type, (
% 35.43/23.26 s51: $i)).
% 35.43/23.26 tff(s50_type, type, (
% 35.43/23.26 s50: $i)).
% 35.43/23.26 tff(s49_type, type, (
% 35.43/23.26 s49: $i)).
% 35.43/23.26 tff(s48_type, type, (
% 35.43/23.26 s48: $i)).
% 35.43/23.26 tff(s47_type, type, (
% 35.43/23.26 s47: $i)).
% 35.43/23.26 tff(s46_type, type, (
% 35.43/23.26 s46: $i)).
% 35.43/23.26 tff(s45_type, type, (
% 35.43/23.26 s45: $i)).
% 35.43/23.26 tff(s44_type, type, (
% 35.43/23.26 s44: $i)).
% 35.43/23.26 tff(s43_type, type, (
% 35.43/23.26 s43: $i)).
% 35.43/23.26 tff(s42_type, type, (
% 35.43/23.26 s42: $i)).
% 35.43/23.26 tff(s41_type, type, (
% 35.43/23.26 s41: $i)).
% 35.43/23.26 tff(s40_type, type, (
% 35.43/23.26 s40: $i)).
% 35.43/23.26 tff(s39_type, type, (
% 35.43/23.26 s39: $i)).
% 35.43/23.26 tff(s38_type, type, (
% 35.43/23.26 s38: $i)).
% 35.43/23.26 tff(s37_type, type, (
% 35.43/23.26 s37: $i)).
% 35.43/23.26 tff(s36_type, type, (
% 35.43/23.27 s36: $i)).
% 35.43/23.27 tff(s35_type, type, (
% 35.43/23.27 s35: $i)).
% 35.43/23.27 tff(s34_type, type, (
% 35.43/23.27 s34: $i)).
% 35.43/23.27 tff(s33_type, type, (
% 35.43/23.27 s33: $i)).
% 35.43/23.27 tff(s32_type, type, (
% 35.43/23.27 s32: $i)).
% 35.43/23.27 tff(s31_type, type, (
% 35.43/23.27 s31: $i)).
% 35.43/23.27 tff(s30_type, type, (
% 35.43/23.27 s30: $i)).
% 35.43/23.27 tff(s29_type, type, (
% 35.43/23.27 s29: $i)).
% 35.43/23.27 tff(s28_type, type, (
% 35.43/23.27 s28: $i)).
% 35.43/23.27 tff(s27_type, type, (
% 35.43/23.27 s27: $i)).
% 35.43/23.27 tff(s26_type, type, (
% 35.43/23.27 s26: $i)).
% 35.43/23.27 tff(s25_type, type, (
% 35.43/23.27 s25: $i)).
% 35.43/23.27 tff(s24_type, type, (
% 35.43/23.27 s24: $i)).
% 35.43/23.27 tff(s23_type, type, (
% 35.43/23.27 s23: $i)).
% 35.43/23.27 tff(s22_type, type, (
% 35.43/23.27 s22: $i)).
% 35.43/23.27 tff(s21_type, type, (
% 35.43/23.27 s21: $i)).
% 35.43/23.27 tff(s20_type, type, (
% 35.43/23.27 s20: $i)).
% 35.43/23.27 tff(s19_type, type, (
% 35.43/23.27 s19: $i)).
% 35.43/23.27 tff(s18_type, type, (
% 35.43/23.27 s18: $i)).
% 35.43/23.27 tff(s17_type, type, (
% 35.43/23.27 s17: $i)).
% 35.43/23.27 tff(s16_type, type, (
% 35.43/23.27 s16: $i)).
% 35.43/23.27 tff(s15_type, type, (
% 35.43/23.27 s15: $i)).
% 35.43/23.27 tff(s14_type, type, (
% 35.43/23.27 s14: $i)).
% 35.43/23.27 tff(s13_type, type, (
% 35.43/23.27 s13: $i)).
% 35.43/23.27 tff(s12_type, type, (
% 35.43/23.27 s12: $i)).
% 35.43/23.27 tff(s11_type, type, (
% 35.43/23.27 s11: $i)).
% 35.43/23.27 tff(s10_type, type, (
% 35.43/23.27 s10: $i)).
% 35.43/23.27 tff(s9_type, type, (
% 35.43/23.27 s9: $i)).
% 35.43/23.27 tff(s8_type, type, (
% 35.43/23.27 s8: $i)).
% 35.43/23.27 tff(s7_type, type, (
% 35.43/23.27 s7: $i)).
% 35.43/23.27 tff(s6_type, type, (
% 35.43/23.27 s6: $i)).
% 35.43/23.27 tff(s5_type, type, (
% 35.43/23.27 s5: $i)).
% 35.43/23.27 tff(s4_type, type, (
% 35.43/23.27 s4: $i)).
% 35.43/23.27 tff(s3_type, type, (
% 35.43/23.27 s3: $i)).
% 35.43/23.27 tff(s2_type, type, (
% 35.43/23.27 s2: $i)).
% 35.43/23.27 tff(s1_type, type, (
% 35.43/23.27 s1: $i)).
% 35.43/23.27 tff(s0_type, type, (
% 35.43/23.27 s0: $i)).
% 35.43/23.27 tff(s98_type, type, (
% 35.43/23.27 s98: $i)).
% 35.43/23.27 tff(xuntil7_type, type, (
% 35.43/23.27 xuntil7: $i > $o)).
% 35.43/23.27 tff(until6_type, type, (
% 35.43/23.27 until6: $i > $o)).
% 35.43/23.27 tff(until2p8_type, type, (
% 35.43/23.27 until2p8: $i > $o)).
% 35.43/23.27 tff(xuntil2p9_type, type, (
% 35.43/23.27 xuntil2p9: $i > $o)).
% 35.43/23.27 tff(last_type, type, (
% 35.43/23.27 last: $i > $o)).
% 35.43/23.27 tff(loop_type, type, (
% 35.43/23.27 loop: $o)).
% 35.43/23.27 tff(1,assumption,(always5(s95)), introduced(assumption)).
% 35.43/23.27 tff(2,plain,
% 35.43/23.27 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | trans(X, Y)) <=> ((~succ(X, Y)) | trans(X, Y)))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(3,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[2])).
% 35.43/23.27 tff(4,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(5,axiom,(![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound101')).
% 35.43/23.27 tff(6,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[5, 4])).
% 35.43/23.27 tff(7,plain,(
% 35.43/23.27 ![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 35.43/23.27 inference(skolemize,[status(sab)],[6])).
% 35.43/23.27 tff(8,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[7, 3])).
% 35.43/23.27 tff(9,plain,
% 35.43/23.27 (succ(s95, s96) <=> succ(s95, s96)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(10,axiom,(succ(s95, s96)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound96')).
% 35.43/23.27 tff(11,plain,
% 35.43/23.27 (succ(s95, s96)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[10, 9])).
% 35.43/23.27 tff(12,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s95, s96)) | trans(s95, s96))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s95, s96)) | trans(s95, s96))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(13,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s95, s96)) | trans(s95, s96))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(14,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s95, s96)) | trans(s95, s96)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[13, 12])).
% 35.43/23.27 tff(15,plain,
% 35.43/23.27 (trans(s95, s96)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[14, 11, 8])).
% 35.43/23.27 tff(16,plain,
% 35.43/23.27 (^[Y: $i, X: $i] : refl(((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ((~always5(X)) | (~trans(X, Y)) | always5(Y)))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(17,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[16])).
% 35.43/23.27 tff(18,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y)) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(19,plain,
% 35.43/23.27 (^[Y: $i, X: $i] : rewrite(((always5(Y) | (~trans(X, Y))) | (~always5(X))) <=> ((~always5(X)) | (~trans(X, Y)) | always5(Y)))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(20,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((always5(Y) | (~trans(X, Y))) | (~always5(X))) <=> ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[19])).
% 35.43/23.27 tff(21,axiom,(![Y: $i, X: $i] : ((always5(Y) | (~trans(X, Y))) | (~always5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty2')).
% 35.43/23.27 tff(22,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[21, 20])).
% 35.43/23.27 tff(23,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[22, 18])).
% 35.43/23.27 tff(24,plain,(
% 35.43/23.27 ![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 35.43/23.27 inference(skolemize,[status(sab)],[23])).
% 35.43/23.27 tff(25,plain,
% 35.43/23.27 (![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[24, 17])).
% 35.43/23.27 tff(26,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s95, s96)) | (~always5(s95)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s95, s96)) | (~always5(s95)) | always5(s96))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(27,plain,
% 35.43/23.27 (((~always5(s95)) | (~trans(s95, s96)) | always5(s96)) <=> ((~trans(s95, s96)) | (~always5(s95)) | always5(s96))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(28,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s95)) | (~trans(s95, s96)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s95, s96)) | (~always5(s95)) | always5(s96)))),
% 35.43/23.27 inference(monotonicity,[status(thm)],[27])).
% 35.43/23.27 tff(29,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s95)) | (~trans(s95, s96)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s95, s96)) | (~always5(s95)) | always5(s96))),
% 35.43/23.27 inference(transitivity,[status(thm)],[28, 26])).
% 35.43/23.27 tff(30,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s95)) | (~trans(s95, s96)) | always5(s96))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(31,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s95, s96)) | (~always5(s95)) | always5(s96)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[30, 29])).
% 35.43/23.27 tff(32,plain,
% 35.43/23.27 ((~always5(s95)) | always5(s96)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[31, 25, 15])).
% 35.43/23.27 tff(33,plain,
% 35.43/23.27 (always5(s96)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[32, 1])).
% 35.43/23.27 tff(34,plain,
% 35.43/23.27 (succ(s96, s97) <=> succ(s96, s97)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(35,axiom,(succ(s96, s97)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound97')).
% 35.43/23.27 tff(36,plain,
% 35.43/23.27 (succ(s96, s97)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[35, 34])).
% 35.43/23.27 tff(37,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s96, s97)) | trans(s96, s97))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s96, s97)) | trans(s96, s97))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(38,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s96, s97)) | trans(s96, s97))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(39,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s96, s97)) | trans(s96, s97)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[38, 37])).
% 35.43/23.27 tff(40,plain,
% 35.43/23.27 (trans(s96, s97)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[39, 36, 8])).
% 35.43/23.27 tff(41,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s96, s97)) | (~always5(s96)) | always5(s97))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s96, s97)) | (~always5(s96)) | always5(s97))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(42,plain,
% 35.43/23.27 (((~always5(s96)) | (~trans(s96, s97)) | always5(s97)) <=> ((~trans(s96, s97)) | (~always5(s96)) | always5(s97))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(43,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s96)) | (~trans(s96, s97)) | always5(s97))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s96, s97)) | (~always5(s96)) | always5(s97)))),
% 35.43/23.27 inference(monotonicity,[status(thm)],[42])).
% 35.43/23.27 tff(44,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s96)) | (~trans(s96, s97)) | always5(s97))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s96, s97)) | (~always5(s96)) | always5(s97))),
% 35.43/23.27 inference(transitivity,[status(thm)],[43, 41])).
% 35.43/23.27 tff(45,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s96)) | (~trans(s96, s97)) | always5(s97))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(46,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s96, s97)) | (~always5(s96)) | always5(s97)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[45, 44])).
% 35.43/23.27 tff(47,plain,
% 35.43/23.27 ((~always5(s96)) | always5(s97)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[46, 25, 40])).
% 35.43/23.27 tff(48,plain,
% 35.43/23.27 (always5(s97)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[47, 33])).
% 35.43/23.27 tff(49,plain,
% 35.43/23.27 (^[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))))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(50,plain,
% 35.43/23.27 (![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)))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[49])).
% 35.43/23.27 tff(51,plain,
% 35.43/23.27 (![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)))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(52,plain,
% 35.43/23.27 (^[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))))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(53,plain,
% 35.43/23.27 (![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)))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[52])).
% 35.43/23.27 tff(54,axiom,(![X: $i] : ((~m_counter_cell_v_carry_out(c_bit2, X)) | (~always5(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty1')).
% 35.43/23.27 tff(55,plain,
% 35.43/23.27 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[54, 53])).
% 35.43/23.27 tff(56,plain,
% 35.43/23.27 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[55, 51])).
% 35.43/23.27 tff(57,plain,(
% 35.43/23.27 ![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 35.43/23.27 inference(skolemize,[status(sab)],[56])).
% 35.43/23.27 tff(58,plain,
% 35.43/23.27 (![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[57, 50])).
% 35.43/23.27 tff(59,plain,
% 35.43/23.27 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s97)) | (~m_counter_cell_v_carry_out(c_bit2, s97)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s97)) | (~m_counter_cell_v_carry_out(c_bit2, s97)))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(60,plain,
% 35.43/23.27 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s97)) | (~m_counter_cell_v_carry_out(c_bit2, s97)))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(61,plain,
% 35.43/23.27 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s97)) | (~m_counter_cell_v_carry_out(c_bit2, s97))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[60, 59])).
% 35.43/23.27 tff(62,plain,
% 35.43/23.27 (~m_counter_cell_v_carry_out(c_bit2, s97)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 35.43/23.27 tff(63,plain,
% 35.43/23.27 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s95)) | (~m_counter_cell_v_carry_out(c_bit2, s95)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s95)) | (~m_counter_cell_v_carry_out(c_bit2, s95)))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(64,plain,
% 35.43/23.27 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s95)) | (~m_counter_cell_v_carry_out(c_bit2, s95)))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(65,plain,
% 35.43/23.27 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s95)) | (~m_counter_cell_v_carry_out(c_bit2, s95))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[64, 63])).
% 35.43/23.27 tff(66,plain,
% 35.43/23.27 (~m_counter_cell_v_carry_out(c_bit2, s95)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[65, 58, 1])).
% 35.43/23.27 tff(67,assumption,(node1(c_bit1, s94)), introduced(assumption)).
% 35.43/23.27 tff(68,plain,
% 35.43/23.27 (succ(s59, s60) <=> succ(s59, s60)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(69,axiom,(succ(s59, s60)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound60')).
% 35.43/23.27 tff(70,plain,
% 35.43/23.27 (succ(s59, s60)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[69, 68])).
% 35.43/23.27 tff(71,plain,
% 35.43/23.27 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s59, s60)) | trans(s59, s60))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s59, s60)) | trans(s59, s60))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(72,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s59, s60)) | trans(s59, s60))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(73,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s59, s60)) | trans(s59, s60)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[72, 71])).
% 35.43/23.27 tff(74,plain,
% 35.43/23.27 (trans(s59, s60)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[73, 70, 8])).
% 35.43/23.27 tff(75,plain,
% 35.43/23.27 (^[Y: $i, I0: $i, X: $i] : refl(((~trans(X, Y)) | node3(I0, X, Y)) <=> ((~trans(X, Y)) | node3(I0, X, Y)))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(76,plain,
% 35.43/23.27 (![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))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[75])).
% 35.43/23.27 tff(77,plain,
% 35.43/23.27 (![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(78,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')).
% 35.43/23.27 tff(79,plain,
% 35.43/23.27 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[78, 77])).
% 35.43/23.27 tff(80,plain,(
% 35.43/23.27 ![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 35.43/23.27 inference(skolemize,[status(sab)],[79])).
% 35.43/23.27 tff(81,plain,
% 35.43/23.27 (![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[80, 76])).
% 35.43/23.27 tff(82,plain,
% 35.43/23.27 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s60)) | node3(c_bit0, s59, s60))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s60)) | node3(c_bit0, s59, s60))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(83,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s60)) | node3(c_bit0, s59, s60))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(84,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s60)) | node3(c_bit0, s59, s60)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[83, 82])).
% 35.43/23.27 tff(85,plain,
% 35.43/23.27 (node3(c_bit0, s59, s60)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[84, 81, 74])).
% 35.43/23.27 tff(86,plain,
% 35.43/23.27 (succ(s5, s6) <=> succ(s5, s6)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(87,axiom,(succ(s5, s6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound6')).
% 35.43/23.27 tff(88,plain,
% 35.43/23.27 (succ(s5, s6)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[87, 86])).
% 35.43/23.27 tff(89,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(90,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s5, s6)) | trans(s5, s6))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(91,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s5, s6)) | trans(s5, s6)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[90, 89])).
% 35.43/23.27 tff(92,plain,
% 35.43/23.27 (trans(s5, s6)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[91, 88, 8])).
% 35.43/23.27 tff(93,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(94,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit0, s5, s6))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(95,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit0, s5, s6)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[94, 93])).
% 35.43/23.27 tff(96,plain,
% 35.43/23.27 (node3(c_bit0, s5, s6)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[95, 81, 92])).
% 35.43/23.27 tff(97,plain,
% 35.43/23.27 (succ(s4, s5) <=> succ(s4, s5)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(98,axiom,(succ(s4, s5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound5')).
% 35.43/23.27 tff(99,plain,
% 35.43/23.27 (succ(s4, s5)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[98, 97])).
% 35.43/23.27 tff(100,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(101,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s4, s5)) | trans(s4, s5))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(102,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s4, s5)) | trans(s4, s5)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[101, 100])).
% 35.43/23.27 tff(103,plain,
% 35.43/23.27 (trans(s4, s5)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[102, 99, 8])).
% 35.43/23.27 tff(104,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(105,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit0, s4, s5))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(106,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit0, s4, s5)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[105, 104])).
% 35.43/23.27 tff(107,plain,
% 35.43/23.27 (node3(c_bit0, s4, s5)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[106, 81, 103])).
% 35.43/23.27 tff(108,plain,
% 35.43/23.27 (succ(s3, s4) <=> succ(s3, s4)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(109,axiom,(succ(s3, s4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound4')).
% 35.43/23.27 tff(110,plain,
% 35.43/23.27 (succ(s3, s4)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[109, 108])).
% 35.43/23.27 tff(111,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(112,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s3, s4)) | trans(s3, s4))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(113,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s3, s4)) | trans(s3, s4)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[112, 111])).
% 35.43/23.27 tff(114,plain,
% 35.43/23.27 (trans(s3, s4)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[113, 110, 8])).
% 35.43/23.27 tff(115,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(116,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit0, s3, s4))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(117,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit0, s3, s4)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[116, 115])).
% 35.43/23.27 tff(118,plain,
% 35.43/23.27 (node3(c_bit0, s3, s4)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[117, 81, 114])).
% 35.43/23.27 tff(119,plain,
% 35.43/23.27 (succ(s2, s3) <=> succ(s2, s3)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(120,axiom,(succ(s2, s3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound3')).
% 35.43/23.27 tff(121,plain,
% 35.43/23.27 (succ(s2, s3)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[120, 119])).
% 35.43/23.27 tff(122,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(123,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s2, s3)) | trans(s2, s3))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(124,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s2, s3)) | trans(s2, s3)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[123, 122])).
% 35.43/23.27 tff(125,plain,
% 35.43/23.27 (trans(s2, s3)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[124, 121, 8])).
% 35.43/23.27 tff(126,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(127,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit0, s2, s3))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(128,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit0, s2, s3)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[127, 126])).
% 35.43/23.27 tff(129,plain,
% 35.43/23.27 (node3(c_bit0, s2, s3)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[128, 81, 125])).
% 35.43/23.27 tff(130,plain,
% 35.43/23.27 (succ(s1, s2) <=> succ(s1, s2)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(131,axiom,(succ(s1, s2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound2')).
% 35.43/23.27 tff(132,plain,
% 35.43/23.27 (succ(s1, s2)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[131, 130])).
% 35.43/23.27 tff(133,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(134,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s1, s2)) | trans(s1, s2))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(135,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s1, s2)) | trans(s1, s2)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[134, 133])).
% 35.43/23.27 tff(136,plain,
% 35.43/23.27 (trans(s1, s2)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[135, 132, 8])).
% 35.43/23.27 tff(137,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(138,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit0, s1, s2))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(139,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit0, s1, s2)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[138, 137])).
% 35.43/23.27 tff(140,plain,
% 35.43/23.27 (node3(c_bit0, s1, s2)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[139, 81, 136])).
% 35.43/23.27 tff(141,assumption,(m_counter_cell_v_value(c_bit0, s0)), introduced(assumption)).
% 35.43/23.27 tff(142,plain,
% 35.43/23.27 (^[I0: $i] : refl((~m_counter_cell_v_value(I0, s0)) <=> (~m_counter_cell_v_value(I0, s0)))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(143,plain,
% 35.43/23.27 (![I0: $i] : (~m_counter_cell_v_value(I0, s0)) <=> ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[142])).
% 35.43/23.27 tff(144,plain,
% 35.43/23.27 (![I0: $i] : (~m_counter_cell_v_value(I0, s0)) <=> ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(145,axiom,(![I0: $i] : (~m_counter_cell_v_value(I0, s0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_counter_cell_1')).
% 35.43/23.27 tff(146,plain,
% 35.43/23.27 (![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[145, 144])).
% 35.43/23.27 tff(147,plain,(
% 35.43/23.27 ![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 35.43/23.27 inference(skolemize,[status(sab)],[146])).
% 35.43/23.27 tff(148,plain,
% 35.43/23.27 (![I0: $i] : (~m_counter_cell_v_value(I0, s0))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[147, 143])).
% 35.43/23.27 tff(149,plain,
% 35.43/23.27 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit0, s0))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(150,plain,
% 35.43/23.27 ($false),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[149, 148, 141])).
% 35.43/23.27 tff(151,plain,(~m_counter_cell_v_value(c_bit0, s0)), inference(lemma,lemma(discharge,[]))).
% 35.43/23.27 tff(152,plain,
% 35.43/23.27 (^[X: $i] : refl(m_counter_cell_v_carry_in(c_bit0, X) <=> m_counter_cell_v_carry_in(c_bit0, X))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(153,plain,
% 35.43/23.27 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X) <=> ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 35.43/23.27 inference(quant_intro,[status(thm)],[152])).
% 35.43/23.27 tff(154,plain,
% 35.43/23.27 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X) <=> ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(155,axiom,(![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m_main_1')).
% 35.43/23.27 tff(156,plain,
% 35.43/23.27 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[155, 154])).
% 35.43/23.27 tff(157,plain,(
% 35.43/23.27 ![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 35.43/23.27 inference(skolemize,[status(sab)],[156])).
% 35.43/23.27 tff(158,plain,
% 35.43/23.27 (![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[157, 153])).
% 35.43/23.27 tff(159,plain,
% 35.43/23.27 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s0)),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(160,plain,
% 35.43/23.27 (m_counter_cell_v_carry_in(c_bit0, s0)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[159, 158])).
% 35.43/23.27 tff(161,plain,
% 35.43/23.27 (^[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)))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(162,plain,
% 35.43/23.27 (![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))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[161])).
% 35.43/23.27 tff(163,plain,
% 35.43/23.27 (![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(164,plain,
% 35.43/23.27 (^[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))))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(165,plain,
% 35.43/23.27 (![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))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[164])).
% 35.43/23.27 tff(166,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')).
% 35.43/23.27 tff(167,plain,
% 35.43/23.27 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[166, 165])).
% 35.43/23.27 tff(168,plain,
% 35.43/23.27 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[167, 163])).
% 35.43/23.27 tff(169,plain,(
% 35.43/23.27 ![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 35.43/23.27 inference(skolemize,[status(sab)],[168])).
% 35.43/23.27 tff(170,plain,
% 35.43/23.27 (![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[169, 162])).
% 35.43/23.27 tff(171,plain,
% 35.43/23.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(172,plain,
% 35.43/23.27 (((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(173,plain,
% 35.43/23.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)))),
% 35.43/23.27 inference(monotonicity,[status(thm)],[172])).
% 35.43/23.27 tff(174,plain,
% 35.43/23.27 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 35.43/23.27 inference(transitivity,[status(thm)],[173, 171])).
% 35.43/23.27 tff(175,plain,
% 35.43/23.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s0)) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(176,plain,
% 35.43/23.27 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s0)) | (~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[175, 174])).
% 35.43/23.27 tff(177,plain,
% 35.43/23.27 ((~node1(c_bit0, s0)) | m_counter_cell_v_value(c_bit0, s0)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[176, 170, 160])).
% 35.43/23.27 tff(178,plain,
% 35.43/23.27 (~node1(c_bit0, s0)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[177, 151])).
% 35.43/23.27 tff(179,plain,
% 35.43/23.27 (succ(s0, s1) <=> succ(s0, s1)),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(180,axiom,(succ(s0, s1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound1')).
% 35.43/23.27 tff(181,plain,
% 35.43/23.27 (succ(s0, s1)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[180, 179])).
% 35.43/23.27 tff(182,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(183,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s0, s1)) | trans(s0, s1))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(184,plain,
% 35.43/23.27 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s0, s1)) | trans(s0, s1)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[183, 182])).
% 35.43/23.27 tff(185,plain,
% 35.43/23.27 (trans(s0, s1)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[184, 181, 8])).
% 35.43/23.27 tff(186,plain,
% 35.43/23.27 (((~![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(187,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit0, s0, s1))),
% 35.43/23.27 inference(quant_inst,[status(thm)],[])).
% 35.43/23.27 tff(188,plain,
% 35.43/23.27 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit0, s0, s1)),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[187, 186])).
% 35.43/23.27 tff(189,plain,
% 35.43/23.27 (node3(c_bit0, s0, s1)),
% 35.43/23.27 inference(unit_resolution,[status(thm)],[188, 81, 185])).
% 35.43/23.27 tff(190,plain,
% 35.43/23.27 (^[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)))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(191,plain,
% 35.43/23.27 (![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))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[190])).
% 35.43/23.27 tff(192,plain,
% 35.43/23.27 (![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))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(193,plain,
% 35.43/23.27 (^[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)))),
% 35.43/23.27 inference(bind,[status(th)],[])).
% 35.43/23.27 tff(194,plain,
% 35.43/23.27 (![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))),
% 35.43/23.27 inference(quant_intro,[status(thm)],[193])).
% 35.43/23.27 tff(195,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')).
% 35.43/23.27 tff(196,plain,
% 35.43/23.27 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[195, 194])).
% 35.43/23.27 tff(197,plain,
% 35.43/23.27 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[196, 192])).
% 35.43/23.27 tff(198,plain,(
% 35.43/23.27 ![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 35.43/23.27 inference(skolemize,[status(sab)],[197])).
% 35.43/23.27 tff(199,plain,
% 35.43/23.27 (![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))),
% 35.43/23.27 inference(modus_ponens,[status(thm)],[198, 191])).
% 35.43/23.27 tff(200,plain,
% 35.43/23.27 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~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))) | m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(201,plain,
% 35.43/23.27 ((node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)) | m_counter_cell_v_value(c_bit0, s1)) <=> (m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)))),
% 35.43/23.27 inference(rewrite,[status(thm)],[])).
% 35.43/23.27 tff(202,plain,
% 35.43/23.27 (((~![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))) | (m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1))))),
% 35.43/23.27 inference(monotonicity,[status(thm)],[201])).
% 35.43/23.27 tff(203,plain,
% 35.43/23.27 (((~![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))) | m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1)))),
% 35.43/23.28 inference(transitivity,[status(thm)],[202, 200])).
% 35.43/23.28 tff(204,plain,
% 35.43/23.28 ((~![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))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(205,plain,
% 35.43/23.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0) | (~node3(c_bit0, s0, s1))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[204, 203])).
% 35.43/23.28 tff(206,plain,
% 35.43/23.28 (m_counter_cell_v_value(c_bit0, s1) | node1(c_bit0, s0)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[205, 199, 189])).
% 35.43/23.28 tff(207,plain,
% 35.43/23.28 (m_counter_cell_v_value(c_bit0, s1)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[206, 178])).
% 35.43/23.28 tff(208,plain,
% 35.43/23.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s1)),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(209,plain,
% 35.43/23.28 (m_counter_cell_v_carry_in(c_bit0, s1)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[208, 158])).
% 35.43/23.28 tff(210,plain,
% 35.43/23.28 (^[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))))),
% 35.43/23.28 inference(bind,[status(th)],[])).
% 35.43/23.28 tff(211,plain,
% 35.43/23.28 (![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)))),
% 35.43/23.28 inference(quant_intro,[status(thm)],[210])).
% 35.43/23.28 tff(212,plain,
% 35.43/23.28 (![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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(213,plain,
% 35.43/23.28 (^[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)))))),
% 35.43/23.28 inference(bind,[status(th)],[])).
% 35.43/23.28 tff(214,plain,
% 35.43/23.28 (![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)))),
% 35.43/23.28 inference(quant_intro,[status(thm)],[213])).
% 35.43/23.28 tff(215,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')).
% 35.43/23.28 tff(216,plain,
% 35.43/23.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[215, 214])).
% 35.43/23.28 tff(217,plain,
% 35.43/23.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[216, 212])).
% 35.43/23.28 tff(218,plain,(
% 35.43/23.28 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 35.43/23.28 inference(skolemize,[status(sab)],[217])).
% 35.43/23.28 tff(219,plain,
% 35.43/23.28 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[218, 211])).
% 35.43/23.28 tff(220,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, 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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(221,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1)))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(222,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s1)) | (~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[221, 220])).
% 35.43/23.28 tff(223,plain,
% 35.43/23.28 ((~m_counter_cell_v_value(c_bit0, s1)) | (~node2(c_bit0, s1))),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[222, 219, 209])).
% 35.43/23.28 tff(224,plain,
% 35.43/23.28 (~node2(c_bit0, s1)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[223, 207])).
% 35.43/23.28 tff(225,plain,
% 35.43/23.28 (^[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))))),
% 35.43/23.28 inference(bind,[status(th)],[])).
% 35.43/23.28 tff(226,plain,
% 35.43/23.28 (![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)))),
% 35.43/23.28 inference(quant_intro,[status(thm)],[225])).
% 35.43/23.28 tff(227,plain,
% 35.43/23.28 (![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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(228,plain,
% 35.43/23.28 (^[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))))),
% 35.43/23.28 inference(bind,[status(th)],[])).
% 35.43/23.28 tff(229,plain,
% 35.43/23.28 (![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)))),
% 35.43/23.28 inference(quant_intro,[status(thm)],[228])).
% 35.43/23.28 tff(230,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')).
% 35.43/23.28 tff(231,plain,
% 35.43/23.28 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[230, 229])).
% 35.43/23.28 tff(232,plain,
% 35.43/23.28 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[231, 227])).
% 35.43/23.28 tff(233,plain,(
% 35.43/23.28 ![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 35.43/23.28 inference(skolemize,[status(sab)],[232])).
% 35.43/23.28 tff(234,plain,
% 35.43/23.28 (![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[233, 226])).
% 35.43/23.28 tff(235,plain,
% 35.43/23.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, 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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(236,plain,
% 35.43/23.28 ((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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(237,plain,
% 35.43/23.28 (((~![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))))),
% 35.43/23.28 inference(monotonicity,[status(thm)],[236])).
% 35.43/23.28 tff(238,plain,
% 35.43/23.28 (((~![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)))),
% 35.43/23.28 inference(transitivity,[status(thm)],[237, 235])).
% 35.43/23.28 tff(239,plain,
% 35.43/23.28 ((~![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)))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(240,plain,
% 35.43/23.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s2)) | node2(c_bit0, s1) | (~node3(c_bit0, s1, s2))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[239, 238])).
% 35.43/23.28 tff(241,plain,
% 35.43/23.28 (~m_counter_cell_v_value(c_bit0, s2)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[240, 234, 224, 140])).
% 35.43/23.28 tff(242,plain,
% 35.43/23.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s2)),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(243,plain,
% 35.43/23.28 (m_counter_cell_v_carry_in(c_bit0, s2)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[242, 158])).
% 35.43/23.28 tff(244,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (m_counter_cell_v_value(c_bit0, s2) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(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) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(245,plain,
% 35.43/23.28 (((~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) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(246,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, 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) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2))))),
% 35.43/23.28 inference(monotonicity,[status(thm)],[245])).
% 35.43/23.28 tff(247,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, 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) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2)))),
% 35.43/23.28 inference(transitivity,[status(thm)],[246, 244])).
% 35.43/23.28 tff(248,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s2)) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | m_counter_cell_v_value(c_bit0, s2))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(249,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | m_counter_cell_v_value(c_bit0, s2) | (~m_counter_cell_v_carry_in(c_bit0, s2)) | (~node1(c_bit0, s2))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[248, 247])).
% 35.43/23.28 tff(250,plain,
% 35.43/23.28 (m_counter_cell_v_value(c_bit0, s2) | (~node1(c_bit0, s2))),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[249, 170, 243])).
% 35.43/23.28 tff(251,plain,
% 35.43/23.28 (~node1(c_bit0, s2)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[250, 241])).
% 35.43/23.28 tff(252,plain,
% 35.43/23.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~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))) | node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(253,plain,
% 35.43/23.28 ((node1(c_bit0, s2) | (~node3(c_bit0, s2, s3)) | m_counter_cell_v_value(c_bit0, s3)) <=> (node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(254,plain,
% 35.43/23.28 (((~![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))) | (node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3))))),
% 35.43/23.28 inference(monotonicity,[status(thm)],[253])).
% 35.43/23.28 tff(255,plain,
% 35.43/23.28 (((~![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))) | node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3)))),
% 35.43/23.28 inference(transitivity,[status(thm)],[254, 252])).
% 35.43/23.28 tff(256,plain,
% 35.43/23.28 ((~![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))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(257,plain,
% 35.43/23.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s2) | m_counter_cell_v_value(c_bit0, s3) | (~node3(c_bit0, s2, s3))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[256, 255])).
% 35.43/23.28 tff(258,plain,
% 35.43/23.28 (m_counter_cell_v_value(c_bit0, s3)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[257, 199, 251, 129])).
% 35.43/23.28 tff(259,plain,
% 35.43/23.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s3)),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(260,plain,
% 35.43/23.28 (m_counter_cell_v_carry_in(c_bit0, s3)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[259, 158])).
% 35.43/23.28 tff(261,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, 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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(262,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3)))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(263,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s3)) | (~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[262, 261])).
% 35.43/23.28 tff(264,plain,
% 35.43/23.28 ((~m_counter_cell_v_value(c_bit0, s3)) | (~node2(c_bit0, s3))),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[263, 219, 260])).
% 35.43/23.28 tff(265,plain,
% 35.43/23.28 (~node2(c_bit0, s3)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[264, 258])).
% 35.43/23.28 tff(266,plain,
% 35.43/23.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, 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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(267,plain,
% 35.43/23.28 ((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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(268,plain,
% 35.43/23.28 (((~![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))))),
% 35.43/23.28 inference(monotonicity,[status(thm)],[267])).
% 35.43/23.28 tff(269,plain,
% 35.43/23.28 (((~![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)))),
% 35.43/23.28 inference(transitivity,[status(thm)],[268, 266])).
% 35.43/23.28 tff(270,plain,
% 35.43/23.28 ((~![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)))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(271,plain,
% 35.43/23.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s4)) | node2(c_bit0, s3) | (~node3(c_bit0, s3, s4))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[270, 269])).
% 35.43/23.28 tff(272,plain,
% 35.43/23.28 (~m_counter_cell_v_value(c_bit0, s4)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[271, 234, 265, 118])).
% 35.43/23.28 tff(273,plain,
% 35.43/23.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s4)),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(274,plain,
% 35.43/23.28 (m_counter_cell_v_carry_in(c_bit0, s4)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[273, 158])).
% 35.43/23.28 tff(275,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, 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))) | (~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(276,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(277,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~node1(c_bit0, s4)) | (~m_counter_cell_v_carry_in(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4)),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[276, 275])).
% 35.43/23.28 tff(278,plain,
% 35.43/23.28 ((~node1(c_bit0, s4)) | m_counter_cell_v_value(c_bit0, s4)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[277, 170, 274])).
% 35.43/23.28 tff(279,plain,
% 35.43/23.28 (~node1(c_bit0, s4)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[278, 272])).
% 35.43/23.28 tff(280,plain,
% 35.43/23.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(281,plain,
% 35.43/23.28 ((node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5)) <=> (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(282,plain,
% 35.43/23.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5))))),
% 35.43/23.28 inference(monotonicity,[status(thm)],[281])).
% 35.43/23.28 tff(283,plain,
% 35.43/23.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)) | m_counter_cell_v_value(c_bit0, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5)))),
% 35.43/23.28 inference(transitivity,[status(thm)],[282, 280])).
% 35.43/23.28 tff(284,plain,
% 35.43/23.28 ((~![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))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(285,plain,
% 35.43/23.28 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s5) | node1(c_bit0, s4) | (~node3(c_bit0, s4, s5))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[284, 283])).
% 35.43/23.28 tff(286,plain,
% 35.43/23.28 (m_counter_cell_v_value(c_bit0, s5)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[285, 199, 279, 107])).
% 35.43/23.28 tff(287,assumption,(~m_counter_cell_v_carry_in(c_bit0, s5)), introduced(assumption)).
% 35.43/23.28 tff(288,plain,
% 35.43/23.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s5)),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(289,plain,
% 35.43/23.28 ($false),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[288, 158, 287])).
% 35.43/23.28 tff(290,plain,(m_counter_cell_v_carry_in(c_bit0, s5)), inference(lemma,lemma(discharge,[]))).
% 35.43/23.28 tff(291,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, 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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(292,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5)))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(293,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s5)) | (~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[292, 291])).
% 35.43/23.28 tff(294,plain,
% 35.43/23.28 ((~m_counter_cell_v_value(c_bit0, s5)) | (~node2(c_bit0, s5))),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[293, 219, 290])).
% 35.43/23.28 tff(295,plain,
% 35.43/23.28 (~node2(c_bit0, s5)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[294, 286])).
% 35.43/23.28 tff(296,plain,
% 35.43/23.28 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, 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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(297,plain,
% 35.43/23.28 ((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)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(298,plain,
% 35.43/23.28 (((~![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))))),
% 35.43/23.28 inference(monotonicity,[status(thm)],[297])).
% 35.43/23.28 tff(299,plain,
% 35.43/23.28 (((~![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)))),
% 35.43/23.28 inference(transitivity,[status(thm)],[298, 296])).
% 35.43/23.28 tff(300,plain,
% 35.43/23.28 ((~![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)))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(301,plain,
% 35.43/23.28 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s6)) | node2(c_bit0, s5) | (~node3(c_bit0, s5, s6))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[300, 299])).
% 35.43/23.28 tff(302,plain,
% 35.43/23.28 (~m_counter_cell_v_value(c_bit0, s6)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[301, 234, 295, 96])).
% 35.43/23.28 tff(303,assumption,(~m_counter_cell_v_carry_in(c_bit0, s6)), introduced(assumption)).
% 35.43/23.28 tff(304,plain,
% 35.43/23.28 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s6)),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(305,plain,
% 35.43/23.28 ($false),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[304, 158, 303])).
% 35.43/23.28 tff(306,plain,(m_counter_cell_v_carry_in(c_bit0, s6)), inference(lemma,lemma(discharge,[]))).
% 35.43/23.28 tff(307,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(308,plain,
% 35.43/23.28 (((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(309,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))))),
% 35.43/23.28 inference(monotonicity,[status(thm)],[308])).
% 35.43/23.28 tff(310,plain,
% 35.43/23.28 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6)))),
% 35.43/23.28 inference(transitivity,[status(thm)],[309, 307])).
% 35.43/23.28 tff(311,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s6)) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(312,plain,
% 35.43/23.28 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s6)) | m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[311, 310])).
% 35.43/23.28 tff(313,plain,
% 35.43/23.28 (m_counter_cell_v_value(c_bit0, s6) | (~node1(c_bit0, s6))),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[312, 170, 306])).
% 35.43/23.28 tff(314,plain,
% 35.43/23.28 (~node1(c_bit0, s6)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[313, 302])).
% 35.43/23.28 tff(315,plain,
% 35.43/23.28 (succ(s6, s7) <=> succ(s6, s7)),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(316,axiom,(succ(s6, s7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound7')).
% 35.43/23.28 tff(317,plain,
% 35.43/23.28 (succ(s6, s7)),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[316, 315])).
% 35.43/23.28 tff(318,plain,
% 35.43/23.28 (((~![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))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(319,plain,
% 35.43/23.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s6, s7)) | trans(s6, s7))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(320,plain,
% 35.43/23.28 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s6, s7)) | trans(s6, s7)),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[319, 318])).
% 35.43/23.28 tff(321,plain,
% 35.43/23.28 (trans(s6, s7)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[320, 317, 8])).
% 35.43/23.28 tff(322,plain,
% 35.43/23.28 (((~![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))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(323,plain,
% 35.43/23.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit0, s6, s7))),
% 35.43/23.28 inference(quant_inst,[status(thm)],[])).
% 35.43/23.28 tff(324,plain,
% 35.43/23.28 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit0, s6, s7)),
% 35.43/23.28 inference(modus_ponens,[status(thm)],[323, 322])).
% 35.43/23.28 tff(325,plain,
% 35.43/23.28 (node3(c_bit0, s6, s7)),
% 35.43/23.28 inference(unit_resolution,[status(thm)],[324, 81, 321])).
% 35.43/23.28 tff(326,plain,
% 35.43/23.28 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~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))) | m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(327,plain,
% 35.43/23.28 ((node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)) | m_counter_cell_v_value(c_bit0, s7)) <=> (m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)))),
% 35.43/23.28 inference(rewrite,[status(thm)],[])).
% 35.43/23.28 tff(328,plain,
% 35.43/23.28 (((~![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))) | (m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7))))),
% 35.43/23.28 inference(monotonicity,[status(thm)],[327])).
% 35.43/23.28 tff(329,plain,
% 35.43/23.28 (((~![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))) | m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7)))),
% 35.43/23.29 inference(transitivity,[status(thm)],[328, 326])).
% 35.43/23.29 tff(330,plain,
% 35.43/23.29 ((~![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))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(331,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6) | (~node3(c_bit0, s6, s7))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[330, 329])).
% 35.43/23.29 tff(332,plain,
% 35.43/23.29 (m_counter_cell_v_value(c_bit0, s7) | node1(c_bit0, s6)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[331, 199, 325])).
% 35.43/23.29 tff(333,plain,
% 35.43/23.29 (m_counter_cell_v_value(c_bit0, s7)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[332, 314])).
% 35.43/23.29 tff(334,assumption,(~m_counter_cell_v_carry_in(c_bit0, s7)), introduced(assumption)).
% 35.43/23.29 tff(335,plain,
% 35.43/23.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s7)),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(336,plain,
% 35.43/23.29 ($false),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[335, 158, 334])).
% 35.43/23.29 tff(337,plain,(m_counter_cell_v_carry_in(c_bit0, s7)), inference(lemma,lemma(discharge,[]))).
% 35.43/23.29 tff(338,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(339,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7)))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(340,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s7)) | (~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[339, 338])).
% 35.43/23.29 tff(341,plain,
% 35.43/23.29 ((~m_counter_cell_v_value(c_bit0, s7)) | (~node2(c_bit0, s7))),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[340, 219, 337])).
% 35.43/23.29 tff(342,plain,
% 35.43/23.29 (~node2(c_bit0, s7)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[341, 333])).
% 35.43/23.29 tff(343,plain,
% 35.43/23.29 (succ(s7, s8) <=> succ(s7, s8)),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(344,axiom,(succ(s7, s8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound8')).
% 35.43/23.29 tff(345,plain,
% 35.43/23.29 (succ(s7, s8)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[344, 343])).
% 35.43/23.29 tff(346,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(347,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s7, s8)) | trans(s7, s8))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(348,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s7, s8)) | trans(s7, s8)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[347, 346])).
% 35.43/23.29 tff(349,plain,
% 35.43/23.29 (trans(s7, s8)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[348, 345, 8])).
% 35.43/23.29 tff(350,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(351,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit0, s7, s8))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(352,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit0, s7, s8)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[351, 350])).
% 35.43/23.29 tff(353,plain,
% 35.43/23.29 (node3(c_bit0, s7, s8)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[352, 81, 349])).
% 35.43/23.29 tff(354,plain,
% 35.43/23.29 (((~![Y: $i, I0: $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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(355,plain,
% 35.43/23.29 ((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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(356,plain,
% 35.43/23.29 (((~![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))))),
% 35.43/23.29 inference(monotonicity,[status(thm)],[355])).
% 35.43/23.29 tff(357,plain,
% 35.43/23.29 (((~![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)))),
% 35.43/23.29 inference(transitivity,[status(thm)],[356, 354])).
% 35.43/23.29 tff(358,plain,
% 35.43/23.29 ((~![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)))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(359,plain,
% 35.43/23.29 ((~![Y: $i, I0: $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))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[358, 357])).
% 35.43/23.29 tff(360,plain,
% 35.43/23.29 ((~m_counter_cell_v_value(c_bit0, s8)) | node2(c_bit0, s7)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[359, 234, 353])).
% 35.43/23.29 tff(361,plain,
% 35.43/23.29 (~m_counter_cell_v_value(c_bit0, s8)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[360, 342])).
% 35.43/23.29 tff(362,plain,
% 35.43/23.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s8)),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(363,plain,
% 35.43/23.29 (m_counter_cell_v_carry_in(c_bit0, s8)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[362, 158])).
% 35.43/23.29 tff(364,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(365,plain,
% 35.43/23.29 (((~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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(366,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.43/23.29 inference(monotonicity,[status(thm)],[365])).
% 35.43/23.29 tff(367,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.43/23.29 inference(transitivity,[status(thm)],[366, 364])).
% 35.43/23.29 tff(368,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s8)) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(369,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s8)) | m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[368, 367])).
% 35.43/23.29 tff(370,plain,
% 35.43/23.29 (m_counter_cell_v_value(c_bit0, s8) | (~node1(c_bit0, s8))),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[369, 170, 363])).
% 35.43/23.29 tff(371,plain,
% 35.43/23.29 (~node1(c_bit0, s8)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[370, 361])).
% 35.43/23.29 tff(372,plain,
% 35.43/23.29 (succ(s8, s9) <=> succ(s8, s9)),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(373,axiom,(succ(s8, s9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound9')).
% 35.43/23.29 tff(374,plain,
% 35.43/23.29 (succ(s8, s9)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[373, 372])).
% 35.43/23.29 tff(375,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(376,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s8, s9)) | trans(s8, s9))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(377,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s8, s9)) | trans(s8, s9)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[376, 375])).
% 35.43/23.29 tff(378,plain,
% 35.43/23.29 (trans(s8, s9)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[377, 374, 8])).
% 35.43/23.29 tff(379,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(380,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit0, s8, s9))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(381,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit0, s8, s9)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[380, 379])).
% 35.43/23.29 tff(382,plain,
% 35.43/23.29 (node3(c_bit0, s8, s9)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[381, 81, 378])).
% 35.43/23.29 tff(383,plain,
% 35.43/23.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(384,plain,
% 35.43/23.29 ((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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(385,plain,
% 35.43/23.29 (((~![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))))),
% 35.43/23.29 inference(monotonicity,[status(thm)],[384])).
% 35.43/23.29 tff(386,plain,
% 35.43/23.29 (((~![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)))),
% 35.43/23.29 inference(transitivity,[status(thm)],[385, 383])).
% 35.43/23.29 tff(387,plain,
% 35.43/23.29 ((~![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))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(388,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8) | (~node3(c_bit0, s8, s9))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[387, 386])).
% 35.43/23.29 tff(389,plain,
% 35.43/23.29 (m_counter_cell_v_value(c_bit0, s9) | node1(c_bit0, s8)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[388, 199, 382])).
% 35.43/23.29 tff(390,plain,
% 35.43/23.29 (m_counter_cell_v_value(c_bit0, s9)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[389, 371])).
% 35.43/23.29 tff(391,plain,
% 35.43/23.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s9)),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(392,plain,
% 35.43/23.29 (m_counter_cell_v_carry_in(c_bit0, s9)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[391, 158])).
% 35.43/23.29 tff(393,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(394,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9)))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(395,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s9)) | (~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[394, 393])).
% 35.43/23.29 tff(396,plain,
% 35.43/23.29 ((~m_counter_cell_v_value(c_bit0, s9)) | (~node2(c_bit0, s9))),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[395, 219, 392])).
% 35.43/23.29 tff(397,plain,
% 35.43/23.29 (~node2(c_bit0, s9)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[396, 390])).
% 35.43/23.29 tff(398,plain,
% 35.43/23.29 (succ(s9, s10) <=> succ(s9, s10)),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(399,axiom,(succ(s9, s10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound10')).
% 35.43/23.29 tff(400,plain,
% 35.43/23.29 (succ(s9, s10)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[399, 398])).
% 35.43/23.29 tff(401,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(402,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s9, s10)) | trans(s9, s10))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(403,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s9, s10)) | trans(s9, s10)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[402, 401])).
% 35.43/23.29 tff(404,plain,
% 35.43/23.29 (trans(s9, s10)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[403, 400, 8])).
% 35.43/23.29 tff(405,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(406,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit0, s9, s10))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(407,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit0, s9, s10)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[406, 405])).
% 35.43/23.29 tff(408,plain,
% 35.43/23.29 (node3(c_bit0, s9, s10)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[407, 81, 404])).
% 35.43/23.29 tff(409,plain,
% 35.43/23.29 (((~![Y: $i, I0: $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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(410,plain,
% 35.43/23.29 ((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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(411,plain,
% 35.43/23.29 (((~![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))))),
% 35.43/23.29 inference(monotonicity,[status(thm)],[410])).
% 35.43/23.29 tff(412,plain,
% 35.43/23.29 (((~![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)))),
% 35.43/23.29 inference(transitivity,[status(thm)],[411, 409])).
% 35.43/23.29 tff(413,plain,
% 35.43/23.29 ((~![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)))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(414,plain,
% 35.43/23.29 ((~![Y: $i, I0: $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))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[413, 412])).
% 35.43/23.29 tff(415,plain,
% 35.43/23.29 ((~m_counter_cell_v_value(c_bit0, s10)) | node2(c_bit0, s9)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[414, 234, 408])).
% 35.43/23.29 tff(416,plain,
% 35.43/23.29 (~m_counter_cell_v_value(c_bit0, s10)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[415, 397])).
% 35.43/23.29 tff(417,assumption,(~m_counter_cell_v_carry_in(c_bit0, s10)), introduced(assumption)).
% 35.43/23.29 tff(418,plain,
% 35.43/23.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s10)),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(419,plain,
% 35.43/23.29 ($false),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[418, 158, 417])).
% 35.43/23.29 tff(420,plain,(m_counter_cell_v_carry_in(c_bit0, s10)), inference(lemma,lemma(discharge,[]))).
% 35.43/23.29 tff(421,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(422,plain,
% 35.43/23.29 (((~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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(423,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.43/23.29 inference(monotonicity,[status(thm)],[422])).
% 35.43/23.29 tff(424,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.43/23.29 inference(transitivity,[status(thm)],[423, 421])).
% 35.43/23.29 tff(425,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s10)) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(426,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s10)) | m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[425, 424])).
% 35.43/23.29 tff(427,plain,
% 35.43/23.29 (m_counter_cell_v_value(c_bit0, s10) | (~node1(c_bit0, s10))),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[426, 170, 420])).
% 35.43/23.29 tff(428,plain,
% 35.43/23.29 (~node1(c_bit0, s10)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[427, 416])).
% 35.43/23.29 tff(429,plain,
% 35.43/23.29 (succ(s10, s11) <=> succ(s10, s11)),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(430,axiom,(succ(s10, s11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound11')).
% 35.43/23.29 tff(431,plain,
% 35.43/23.29 (succ(s10, s11)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[430, 429])).
% 35.43/23.29 tff(432,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(433,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s10, s11)) | trans(s10, s11))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(434,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s10, s11)) | trans(s10, s11)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[433, 432])).
% 35.43/23.29 tff(435,plain,
% 35.43/23.29 (trans(s10, s11)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[434, 431, 8])).
% 35.43/23.29 tff(436,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(437,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit0, s10, s11))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(438,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit0, s10, s11)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[437, 436])).
% 35.43/23.29 tff(439,plain,
% 35.43/23.29 (node3(c_bit0, s10, s11)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[438, 81, 435])).
% 35.43/23.29 tff(440,plain,
% 35.43/23.29 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(441,plain,
% 35.43/23.29 ((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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(442,plain,
% 35.43/23.29 (((~![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))))),
% 35.43/23.29 inference(monotonicity,[status(thm)],[441])).
% 35.43/23.29 tff(443,plain,
% 35.43/23.29 (((~![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)))),
% 35.43/23.29 inference(transitivity,[status(thm)],[442, 440])).
% 35.43/23.29 tff(444,plain,
% 35.43/23.29 ((~![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))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(445,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10) | (~node3(c_bit0, s10, s11))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[444, 443])).
% 35.43/23.29 tff(446,plain,
% 35.43/23.29 (m_counter_cell_v_value(c_bit0, s11) | node1(c_bit0, s10)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[445, 199, 439])).
% 35.43/23.29 tff(447,plain,
% 35.43/23.29 (m_counter_cell_v_value(c_bit0, s11)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[446, 428])).
% 35.43/23.29 tff(448,assumption,(~m_counter_cell_v_carry_in(c_bit0, s11)), introduced(assumption)).
% 35.43/23.29 tff(449,plain,
% 35.43/23.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s11)),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(450,plain,
% 35.43/23.29 ($false),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[449, 158, 448])).
% 35.43/23.29 tff(451,plain,(m_counter_cell_v_carry_in(c_bit0, s11)), inference(lemma,lemma(discharge,[]))).
% 35.43/23.29 tff(452,plain,
% 35.43/23.29 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(453,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11)))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(454,plain,
% 35.43/23.29 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s11)) | (~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[453, 452])).
% 35.43/23.29 tff(455,plain,
% 35.43/23.29 ((~m_counter_cell_v_value(c_bit0, s11)) | (~node2(c_bit0, s11))),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[454, 219, 451])).
% 35.43/23.29 tff(456,plain,
% 35.43/23.29 (~node2(c_bit0, s11)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[455, 447])).
% 35.43/23.29 tff(457,plain,
% 35.43/23.29 (succ(s11, s12) <=> succ(s11, s12)),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(458,axiom,(succ(s11, s12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound12')).
% 35.43/23.29 tff(459,plain,
% 35.43/23.29 (succ(s11, s12)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[458, 457])).
% 35.43/23.29 tff(460,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(461,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s11, s12)) | trans(s11, s12))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(462,plain,
% 35.43/23.29 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s11, s12)) | trans(s11, s12)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[461, 460])).
% 35.43/23.29 tff(463,plain,
% 35.43/23.29 (trans(s11, s12)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[462, 459, 8])).
% 35.43/23.29 tff(464,plain,
% 35.43/23.29 (((~![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))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(465,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit0, s11, s12))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(466,plain,
% 35.43/23.29 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit0, s11, s12)),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[465, 464])).
% 35.43/23.29 tff(467,plain,
% 35.43/23.29 (node3(c_bit0, s11, s12)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[466, 81, 463])).
% 35.43/23.29 tff(468,plain,
% 35.43/23.29 (((~![Y: $i, I0: $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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(469,plain,
% 35.43/23.29 ((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)))),
% 35.43/23.29 inference(rewrite,[status(thm)],[])).
% 35.43/23.29 tff(470,plain,
% 35.43/23.29 (((~![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))))),
% 35.43/23.29 inference(monotonicity,[status(thm)],[469])).
% 35.43/23.29 tff(471,plain,
% 35.43/23.29 (((~![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)))),
% 35.43/23.29 inference(transitivity,[status(thm)],[470, 468])).
% 35.43/23.29 tff(472,plain,
% 35.43/23.29 ((~![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)))),
% 35.43/23.29 inference(quant_inst,[status(thm)],[])).
% 35.43/23.29 tff(473,plain,
% 35.43/23.29 ((~![Y: $i, I0: $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))),
% 35.43/23.29 inference(modus_ponens,[status(thm)],[472, 471])).
% 35.43/23.29 tff(474,plain,
% 35.43/23.29 ((~m_counter_cell_v_value(c_bit0, s12)) | node2(c_bit0, s11)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[473, 234, 467])).
% 35.43/23.29 tff(475,plain,
% 35.43/23.29 (~m_counter_cell_v_value(c_bit0, s12)),
% 35.43/23.29 inference(unit_resolution,[status(thm)],[474, 456])).
% 35.43/23.29 tff(476,assumption,(~m_counter_cell_v_carry_in(c_bit0, s12)), introduced(assumption)).
% 35.43/23.29 tff(477,plain,
% 35.43/23.29 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s12)),
% 35.43/23.30 inference(quant_inst,[status(thm)],[])).
% 35.43/23.30 tff(478,plain,
% 35.43/23.30 ($false),
% 35.43/23.30 inference(unit_resolution,[status(thm)],[477, 158, 476])).
% 35.43/23.30 tff(479,plain,(m_counter_cell_v_carry_in(c_bit0, s12)), inference(lemma,lemma(discharge,[]))).
% 35.43/23.30 tff(480,plain,
% 35.43/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.43/23.30 inference(rewrite,[status(thm)],[])).
% 35.43/23.30 tff(481,plain,
% 35.43/23.30 (((~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)))),
% 35.43/23.30 inference(rewrite,[status(thm)],[])).
% 35.43/23.30 tff(482,plain,
% 35.43/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.43/23.30 inference(monotonicity,[status(thm)],[481])).
% 35.43/23.30 tff(483,plain,
% 35.43/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.43/23.30 inference(transitivity,[status(thm)],[482, 480])).
% 35.43/23.30 tff(484,plain,
% 35.43/23.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s12)) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12))),
% 35.43/23.30 inference(quant_inst,[status(thm)],[])).
% 35.43/23.30 tff(485,plain,
% 35.43/23.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s12)) | m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))),
% 35.43/23.30 inference(modus_ponens,[status(thm)],[484, 483])).
% 35.43/23.30 tff(486,plain,
% 35.43/23.30 (m_counter_cell_v_value(c_bit0, s12) | (~node1(c_bit0, s12))),
% 35.43/23.30 inference(unit_resolution,[status(thm)],[485, 170, 479])).
% 35.43/23.30 tff(487,plain,
% 35.43/23.30 (~node1(c_bit0, s12)),
% 35.43/23.30 inference(unit_resolution,[status(thm)],[486, 475])).
% 35.43/23.30 tff(488,plain,
% 35.43/23.30 (succ(s12, s13) <=> succ(s12, s13)),
% 35.43/23.30 inference(rewrite,[status(thm)],[])).
% 35.43/23.30 tff(489,axiom,(succ(s12, s13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound13')).
% 35.43/23.30 tff(490,plain,
% 35.43/23.30 (succ(s12, s13)),
% 35.43/23.30 inference(modus_ponens,[status(thm)],[489, 488])).
% 35.43/23.30 tff(491,plain,
% 35.43/23.30 (((~![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))),
% 35.43/23.30 inference(rewrite,[status(thm)],[])).
% 35.43/23.30 tff(492,plain,
% 35.43/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s12, s13)) | trans(s12, s13))),
% 35.43/23.30 inference(quant_inst,[status(thm)],[])).
% 35.43/23.30 tff(493,plain,
% 35.43/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s12, s13)) | trans(s12, s13)),
% 35.43/23.30 inference(modus_ponens,[status(thm)],[492, 491])).
% 35.43/23.30 tff(494,plain,
% 35.43/23.30 (trans(s12, s13)),
% 35.43/23.30 inference(unit_resolution,[status(thm)],[493, 490, 8])).
% 35.43/23.30 tff(495,plain,
% 35.43/23.30 (((~![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))),
% 35.43/23.30 inference(rewrite,[status(thm)],[])).
% 35.43/23.30 tff(496,plain,
% 35.43/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit0, s12, s13))),
% 35.43/23.30 inference(quant_inst,[status(thm)],[])).
% 35.43/23.30 tff(497,plain,
% 35.43/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit0, s12, s13)),
% 35.43/23.30 inference(modus_ponens,[status(thm)],[496, 495])).
% 35.43/23.30 tff(498,plain,
% 35.43/23.30 (node3(c_bit0, s12, s13)),
% 35.43/23.30 inference(unit_resolution,[status(thm)],[497, 81, 494])).
% 35.43/23.30 tff(499,plain,
% 35.43/23.30 (((~![Y: $i, I0: $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)))),
% 35.43/23.30 inference(rewrite,[status(thm)],[])).
% 35.43/23.30 tff(500,plain,
% 35.43/23.30 ((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)))),
% 35.43/23.30 inference(rewrite,[status(thm)],[])).
% 35.43/23.30 tff(501,plain,
% 35.43/23.30 (((~![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))))),
% 35.43/23.30 inference(monotonicity,[status(thm)],[500])).
% 35.43/23.30 tff(502,plain,
% 35.43/23.30 (((~![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)))),
% 35.43/23.30 inference(transitivity,[status(thm)],[501, 499])).
% 35.43/23.30 tff(503,plain,
% 35.43/23.30 ((~![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))),
% 35.43/23.30 inference(quant_inst,[status(thm)],[])).
% 35.43/23.30 tff(504,plain,
% 35.43/23.30 ((~![Y: $i, I0: $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))),
% 35.43/23.30 inference(modus_ponens,[status(thm)],[503, 502])).
% 35.43/23.30 tff(505,plain,
% 35.43/23.30 (m_counter_cell_v_value(c_bit0, s13) | node1(c_bit0, s12)),
% 35.43/23.30 inference(unit_resolution,[status(thm)],[504, 199, 498])).
% 35.43/23.30 tff(506,plain,
% 35.43/23.30 (m_counter_cell_v_value(c_bit0, s13)),
% 35.43/23.30 inference(unit_resolution,[status(thm)],[505, 487])).
% 35.43/23.30 tff(507,assumption,(~m_counter_cell_v_carry_in(c_bit0, s13)), introduced(assumption)).
% 35.43/23.30 tff(508,plain,
% 35.43/23.30 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s13)),
% 35.43/23.30 inference(quant_inst,[status(thm)],[])).
% 35.43/23.30 tff(509,plain,
% 35.43/23.30 ($false),
% 35.43/23.30 inference(unit_resolution,[status(thm)],[508, 158, 507])).
% 35.43/23.30 tff(510,plain,(m_counter_cell_v_carry_in(c_bit0, s13)), inference(lemma,lemma(discharge,[]))).
% 35.43/23.30 tff(511,plain,
% 35.43/23.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.43/23.30 inference(rewrite,[status(thm)],[])).
% 35.43/23.30 tff(512,plain,
% 35.43/23.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13)))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(513,plain,
% 35.49/23.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s13)) | (~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13))),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[512, 511])).
% 35.49/23.30 tff(514,plain,
% 35.49/23.30 ((~m_counter_cell_v_value(c_bit0, s13)) | (~node2(c_bit0, s13))),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[513, 219, 510])).
% 35.49/23.30 tff(515,plain,
% 35.49/23.30 (~node2(c_bit0, s13)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[514, 506])).
% 35.49/23.30 tff(516,plain,
% 35.49/23.30 (succ(s13, s14) <=> succ(s13, s14)),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(517,axiom,(succ(s13, s14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound14')).
% 35.49/23.30 tff(518,plain,
% 35.49/23.30 (succ(s13, s14)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[517, 516])).
% 35.49/23.30 tff(519,plain,
% 35.49/23.30 (((~![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))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(520,plain,
% 35.49/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s13, s14)) | trans(s13, s14))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(521,plain,
% 35.49/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s13, s14)) | trans(s13, s14)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[520, 519])).
% 35.49/23.30 tff(522,plain,
% 35.49/23.30 (trans(s13, s14)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[521, 518, 8])).
% 35.49/23.30 tff(523,plain,
% 35.49/23.30 (((~![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))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(524,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit0, s13, s14))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(525,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit0, s13, s14)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[524, 523])).
% 35.49/23.30 tff(526,plain,
% 35.49/23.30 (node3(c_bit0, s13, s14)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[525, 81, 522])).
% 35.49/23.30 tff(527,plain,
% 35.49/23.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(528,plain,
% 35.49/23.30 ((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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(529,plain,
% 35.49/23.30 (((~![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))))),
% 35.49/23.30 inference(monotonicity,[status(thm)],[528])).
% 35.49/23.30 tff(530,plain,
% 35.49/23.30 (((~![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)))),
% 35.49/23.30 inference(transitivity,[status(thm)],[529, 527])).
% 35.49/23.30 tff(531,plain,
% 35.49/23.30 ((~![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)))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(532,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13) | (~node3(c_bit0, s13, s14))),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[531, 530])).
% 35.49/23.30 tff(533,plain,
% 35.49/23.30 ((~m_counter_cell_v_value(c_bit0, s14)) | node2(c_bit0, s13)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[532, 234, 526])).
% 35.49/23.30 tff(534,plain,
% 35.49/23.30 (~m_counter_cell_v_value(c_bit0, s14)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[533, 515])).
% 35.49/23.30 tff(535,assumption,(~m_counter_cell_v_carry_in(c_bit0, s14)), introduced(assumption)).
% 35.49/23.30 tff(536,plain,
% 35.49/23.30 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s14)),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(537,plain,
% 35.49/23.30 ($false),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[536, 158, 535])).
% 35.49/23.30 tff(538,plain,(m_counter_cell_v_carry_in(c_bit0, s14)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.30 tff(539,plain,
% 35.49/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(540,plain,
% 35.49/23.30 (((~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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(541,plain,
% 35.49/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.30 inference(monotonicity,[status(thm)],[540])).
% 35.49/23.30 tff(542,plain,
% 35.49/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.30 inference(transitivity,[status(thm)],[541, 539])).
% 35.49/23.30 tff(543,plain,
% 35.49/23.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s14)) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(544,plain,
% 35.49/23.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s14)) | m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[543, 542])).
% 35.49/23.30 tff(545,plain,
% 35.49/23.30 (m_counter_cell_v_value(c_bit0, s14) | (~node1(c_bit0, s14))),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[544, 170, 538])).
% 35.49/23.30 tff(546,plain,
% 35.49/23.30 (~node1(c_bit0, s14)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[545, 534])).
% 35.49/23.30 tff(547,plain,
% 35.49/23.30 (succ(s14, s15) <=> succ(s14, s15)),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(548,axiom,(succ(s14, s15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound15')).
% 35.49/23.30 tff(549,plain,
% 35.49/23.30 (succ(s14, s15)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[548, 547])).
% 35.49/23.30 tff(550,plain,
% 35.49/23.30 (((~![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))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(551,plain,
% 35.49/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s14, s15)) | trans(s14, s15))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(552,plain,
% 35.49/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s14, s15)) | trans(s14, s15)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[551, 550])).
% 35.49/23.30 tff(553,plain,
% 35.49/23.30 (trans(s14, s15)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[552, 549, 8])).
% 35.49/23.30 tff(554,plain,
% 35.49/23.30 (((~![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))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(555,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit0, s14, s15))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(556,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit0, s14, s15)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[555, 554])).
% 35.49/23.30 tff(557,plain,
% 35.49/23.30 (node3(c_bit0, s14, s15)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[556, 81, 553])).
% 35.49/23.30 tff(558,plain,
% 35.49/23.30 (((~![Y: $i, I0: $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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(559,plain,
% 35.49/23.30 ((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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(560,plain,
% 35.49/23.30 (((~![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))))),
% 35.49/23.30 inference(monotonicity,[status(thm)],[559])).
% 35.49/23.30 tff(561,plain,
% 35.49/23.30 (((~![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)))),
% 35.49/23.30 inference(transitivity,[status(thm)],[560, 558])).
% 35.49/23.30 tff(562,plain,
% 35.49/23.30 ((~![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))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(563,plain,
% 35.49/23.30 ((~![Y: $i, I0: $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))),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[562, 561])).
% 35.49/23.30 tff(564,plain,
% 35.49/23.30 (m_counter_cell_v_value(c_bit0, s15) | node1(c_bit0, s14)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[563, 199, 557])).
% 35.49/23.30 tff(565,plain,
% 35.49/23.30 (m_counter_cell_v_value(c_bit0, s15)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[564, 546])).
% 35.49/23.30 tff(566,assumption,(~m_counter_cell_v_carry_in(c_bit0, s15)), introduced(assumption)).
% 35.49/23.30 tff(567,plain,
% 35.49/23.30 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s15)),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(568,plain,
% 35.49/23.30 ($false),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[567, 158, 566])).
% 35.49/23.30 tff(569,plain,(m_counter_cell_v_carry_in(c_bit0, s15)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.30 tff(570,plain,
% 35.49/23.30 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(571,plain,
% 35.49/23.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15)))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(572,plain,
% 35.49/23.30 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | (~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15))),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[571, 570])).
% 35.49/23.30 tff(573,plain,
% 35.49/23.30 ((~m_counter_cell_v_value(c_bit0, s15)) | (~node2(c_bit0, s15))),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[572, 219, 569])).
% 35.49/23.30 tff(574,plain,
% 35.49/23.30 (~node2(c_bit0, s15)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[573, 565])).
% 35.49/23.30 tff(575,plain,
% 35.49/23.30 (succ(s15, s16) <=> succ(s15, s16)),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(576,axiom,(succ(s15, s16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound16')).
% 35.49/23.30 tff(577,plain,
% 35.49/23.30 (succ(s15, s16)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[576, 575])).
% 35.49/23.30 tff(578,plain,
% 35.49/23.30 (((~![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))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(579,plain,
% 35.49/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s15, s16)) | trans(s15, s16))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(580,plain,
% 35.49/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s15, s16)) | trans(s15, s16)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[579, 578])).
% 35.49/23.30 tff(581,plain,
% 35.49/23.30 (trans(s15, s16)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[580, 577, 8])).
% 35.49/23.30 tff(582,plain,
% 35.49/23.30 (((~![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))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(583,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit0, s15, s16))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(584,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit0, s15, s16)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[583, 582])).
% 35.49/23.30 tff(585,plain,
% 35.49/23.30 (node3(c_bit0, s15, s16)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[584, 81, 581])).
% 35.49/23.30 tff(586,plain,
% 35.49/23.30 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(587,plain,
% 35.49/23.30 ((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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(588,plain,
% 35.49/23.30 (((~![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))))),
% 35.49/23.30 inference(monotonicity,[status(thm)],[587])).
% 35.49/23.30 tff(589,plain,
% 35.49/23.30 (((~![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)))),
% 35.49/23.30 inference(transitivity,[status(thm)],[588, 586])).
% 35.49/23.30 tff(590,plain,
% 35.49/23.30 ((~![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)))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(591,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15) | (~node3(c_bit0, s15, s16))),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[590, 589])).
% 35.49/23.30 tff(592,plain,
% 35.49/23.30 ((~m_counter_cell_v_value(c_bit0, s16)) | node2(c_bit0, s15)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[591, 234, 585])).
% 35.49/23.30 tff(593,plain,
% 35.49/23.30 (~m_counter_cell_v_value(c_bit0, s16)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[592, 574])).
% 35.49/23.30 tff(594,plain,
% 35.49/23.30 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s16)),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(595,plain,
% 35.49/23.30 (m_counter_cell_v_carry_in(c_bit0, s16)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[594, 158])).
% 35.49/23.30 tff(596,plain,
% 35.49/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(597,plain,
% 35.49/23.30 (((~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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(598,plain,
% 35.49/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.30 inference(monotonicity,[status(thm)],[597])).
% 35.49/23.30 tff(599,plain,
% 35.49/23.30 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.30 inference(transitivity,[status(thm)],[598, 596])).
% 35.49/23.30 tff(600,plain,
% 35.49/23.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s16)) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(601,plain,
% 35.49/23.30 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s16)) | m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[600, 599])).
% 35.49/23.30 tff(602,plain,
% 35.49/23.30 (m_counter_cell_v_value(c_bit0, s16) | (~node1(c_bit0, s16))),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[601, 170, 595])).
% 35.49/23.30 tff(603,plain,
% 35.49/23.30 (~node1(c_bit0, s16)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[602, 593])).
% 35.49/23.30 tff(604,plain,
% 35.49/23.30 (succ(s16, s17) <=> succ(s16, s17)),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(605,axiom,(succ(s16, s17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound17')).
% 35.49/23.30 tff(606,plain,
% 35.49/23.30 (succ(s16, s17)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[605, 604])).
% 35.49/23.30 tff(607,plain,
% 35.49/23.30 (((~![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))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(608,plain,
% 35.49/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s16, s17)) | trans(s16, s17))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(609,plain,
% 35.49/23.30 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s16, s17)) | trans(s16, s17)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[608, 607])).
% 35.49/23.30 tff(610,plain,
% 35.49/23.30 (trans(s16, s17)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[609, 606, 8])).
% 35.49/23.30 tff(611,plain,
% 35.49/23.30 (((~![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))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(612,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit0, s16, s17))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(613,plain,
% 35.49/23.30 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit0, s16, s17)),
% 35.49/23.30 inference(modus_ponens,[status(thm)],[612, 611])).
% 35.49/23.30 tff(614,plain,
% 35.49/23.30 (node3(c_bit0, s16, s17)),
% 35.49/23.30 inference(unit_resolution,[status(thm)],[613, 81, 610])).
% 35.49/23.30 tff(615,plain,
% 35.49/23.30 (((~![Y: $i, I0: $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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(616,plain,
% 35.49/23.30 ((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)))),
% 35.49/23.30 inference(rewrite,[status(thm)],[])).
% 35.49/23.30 tff(617,plain,
% 35.49/23.30 (((~![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))))),
% 35.49/23.30 inference(monotonicity,[status(thm)],[616])).
% 35.49/23.30 tff(618,plain,
% 35.49/23.30 (((~![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)))),
% 35.49/23.30 inference(transitivity,[status(thm)],[617, 615])).
% 35.49/23.30 tff(619,plain,
% 35.49/23.30 ((~![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))),
% 35.49/23.30 inference(quant_inst,[status(thm)],[])).
% 35.49/23.30 tff(620,plain,
% 35.49/23.30 ((~![Y: $i, I0: $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))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[619, 618])).
% 35.49/23.31 tff(621,plain,
% 35.49/23.31 (m_counter_cell_v_value(c_bit0, s17) | node1(c_bit0, s16)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[620, 199, 614])).
% 35.49/23.31 tff(622,plain,
% 35.49/23.31 (m_counter_cell_v_value(c_bit0, s17)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[621, 603])).
% 35.49/23.31 tff(623,assumption,(~m_counter_cell_v_carry_in(c_bit0, s17)), introduced(assumption)).
% 35.49/23.31 tff(624,plain,
% 35.49/23.31 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s17)),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(625,plain,
% 35.49/23.31 ($false),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[624, 158, 623])).
% 35.49/23.31 tff(626,plain,(m_counter_cell_v_carry_in(c_bit0, s17)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.31 tff(627,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(628,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17)))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(629,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[628, 627])).
% 35.49/23.31 tff(630,plain,
% 35.49/23.31 ((~m_counter_cell_v_value(c_bit0, s17)) | (~node2(c_bit0, s17))),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[629, 219, 626])).
% 35.49/23.31 tff(631,plain,
% 35.49/23.31 (~node2(c_bit0, s17)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[630, 622])).
% 35.49/23.31 tff(632,plain,
% 35.49/23.31 (succ(s17, s18) <=> succ(s17, s18)),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(633,axiom,(succ(s17, s18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound18')).
% 35.49/23.31 tff(634,plain,
% 35.49/23.31 (succ(s17, s18)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[633, 632])).
% 35.49/23.31 tff(635,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(636,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s17, s18)) | trans(s17, s18))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(637,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s17, s18)) | trans(s17, s18)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[636, 635])).
% 35.49/23.31 tff(638,plain,
% 35.49/23.31 (trans(s17, s18)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[637, 634, 8])).
% 35.49/23.31 tff(639,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(640,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit0, s17, s18))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(641,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit0, s17, s18)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[640, 639])).
% 35.49/23.31 tff(642,plain,
% 35.49/23.31 (node3(c_bit0, s17, s18)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[641, 81, 638])).
% 35.49/23.31 tff(643,plain,
% 35.49/23.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(644,plain,
% 35.49/23.31 ((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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(645,plain,
% 35.49/23.31 (((~![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))))),
% 35.49/23.31 inference(monotonicity,[status(thm)],[644])).
% 35.49/23.31 tff(646,plain,
% 35.49/23.31 (((~![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)))),
% 35.49/23.31 inference(transitivity,[status(thm)],[645, 643])).
% 35.49/23.31 tff(647,plain,
% 35.49/23.31 ((~![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)))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(648,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17) | (~node3(c_bit0, s17, s18))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[647, 646])).
% 35.49/23.31 tff(649,plain,
% 35.49/23.31 ((~m_counter_cell_v_value(c_bit0, s18)) | node2(c_bit0, s17)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[648, 234, 642])).
% 35.49/23.31 tff(650,plain,
% 35.49/23.31 (~m_counter_cell_v_value(c_bit0, s18)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[649, 631])).
% 35.49/23.31 tff(651,assumption,(~m_counter_cell_v_carry_in(c_bit0, s18)), introduced(assumption)).
% 35.49/23.31 tff(652,plain,
% 35.49/23.31 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s18)),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(653,plain,
% 35.49/23.31 ($false),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[652, 158, 651])).
% 35.49/23.31 tff(654,plain,(m_counter_cell_v_carry_in(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.31 tff(655,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(656,plain,
% 35.49/23.31 (((~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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(657,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.31 inference(monotonicity,[status(thm)],[656])).
% 35.49/23.31 tff(658,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.31 inference(transitivity,[status(thm)],[657, 655])).
% 35.49/23.31 tff(659,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s18)) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(660,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s18)) | m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[659, 658])).
% 35.49/23.31 tff(661,plain,
% 35.49/23.31 (m_counter_cell_v_value(c_bit0, s18) | (~node1(c_bit0, s18))),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[660, 170, 654])).
% 35.49/23.31 tff(662,plain,
% 35.49/23.31 (~node1(c_bit0, s18)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[661, 650])).
% 35.49/23.31 tff(663,plain,
% 35.49/23.31 (succ(s18, s19) <=> succ(s18, s19)),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(664,axiom,(succ(s18, s19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound19')).
% 35.49/23.31 tff(665,plain,
% 35.49/23.31 (succ(s18, s19)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[664, 663])).
% 35.49/23.31 tff(666,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(667,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s18, s19)) | trans(s18, s19))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(668,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s18, s19)) | trans(s18, s19)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[667, 666])).
% 35.49/23.31 tff(669,plain,
% 35.49/23.31 (trans(s18, s19)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[668, 665, 8])).
% 35.49/23.31 tff(670,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(671,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit0, s18, s19))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(672,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit0, s18, s19)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[671, 670])).
% 35.49/23.31 tff(673,plain,
% 35.49/23.31 (node3(c_bit0, s18, s19)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[672, 81, 669])).
% 35.49/23.31 tff(674,plain,
% 35.49/23.31 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(675,plain,
% 35.49/23.31 ((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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(676,plain,
% 35.49/23.31 (((~![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))))),
% 35.49/23.31 inference(monotonicity,[status(thm)],[675])).
% 35.49/23.31 tff(677,plain,
% 35.49/23.31 (((~![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)))),
% 35.49/23.31 inference(transitivity,[status(thm)],[676, 674])).
% 35.49/23.31 tff(678,plain,
% 35.49/23.31 ((~![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))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(679,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18) | (~node3(c_bit0, s18, s19))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[678, 677])).
% 35.49/23.31 tff(680,plain,
% 35.49/23.31 (m_counter_cell_v_value(c_bit0, s19) | node1(c_bit0, s18)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[679, 199, 673])).
% 35.49/23.31 tff(681,plain,
% 35.49/23.31 (m_counter_cell_v_value(c_bit0, s19)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[680, 662])).
% 35.49/23.31 tff(682,assumption,(~m_counter_cell_v_carry_in(c_bit0, s19)), introduced(assumption)).
% 35.49/23.31 tff(683,plain,
% 35.49/23.31 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s19)),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(684,plain,
% 35.49/23.31 ($false),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[683, 158, 682])).
% 35.49/23.31 tff(685,plain,(m_counter_cell_v_carry_in(c_bit0, s19)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.31 tff(686,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(687,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19)))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(688,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s19)) | (~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[687, 686])).
% 35.49/23.31 tff(689,plain,
% 35.49/23.31 ((~m_counter_cell_v_value(c_bit0, s19)) | (~node2(c_bit0, s19))),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[688, 219, 685])).
% 35.49/23.31 tff(690,plain,
% 35.49/23.31 (~node2(c_bit0, s19)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[689, 681])).
% 35.49/23.31 tff(691,plain,
% 35.49/23.31 (succ(s19, s20) <=> succ(s19, s20)),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(692,axiom,(succ(s19, s20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound20')).
% 35.49/23.31 tff(693,plain,
% 35.49/23.31 (succ(s19, s20)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[692, 691])).
% 35.49/23.31 tff(694,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(695,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s19, s20)) | trans(s19, s20))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(696,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s19, s20)) | trans(s19, s20)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[695, 694])).
% 35.49/23.31 tff(697,plain,
% 35.49/23.31 (trans(s19, s20)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[696, 693, 8])).
% 35.49/23.31 tff(698,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(699,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit0, s19, s20))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(700,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit0, s19, s20)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[699, 698])).
% 35.49/23.31 tff(701,plain,
% 35.49/23.31 (node3(c_bit0, s19, s20)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[700, 81, 697])).
% 35.49/23.31 tff(702,plain,
% 35.49/23.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(703,plain,
% 35.49/23.31 ((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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(704,plain,
% 35.49/23.31 (((~![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))))),
% 35.49/23.31 inference(monotonicity,[status(thm)],[703])).
% 35.49/23.31 tff(705,plain,
% 35.49/23.31 (((~![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)))),
% 35.49/23.31 inference(transitivity,[status(thm)],[704, 702])).
% 35.49/23.31 tff(706,plain,
% 35.49/23.31 ((~![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)))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(707,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19) | (~node3(c_bit0, s19, s20))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[706, 705])).
% 35.49/23.31 tff(708,plain,
% 35.49/23.31 ((~m_counter_cell_v_value(c_bit0, s20)) | node2(c_bit0, s19)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[707, 234, 701])).
% 35.49/23.31 tff(709,plain,
% 35.49/23.31 (~m_counter_cell_v_value(c_bit0, s20)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[708, 690])).
% 35.49/23.31 tff(710,plain,
% 35.49/23.31 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s20)),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(711,plain,
% 35.49/23.31 (m_counter_cell_v_carry_in(c_bit0, s20)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[710, 158])).
% 35.49/23.31 tff(712,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(713,plain,
% 35.49/23.31 (((~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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(714,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.31 inference(monotonicity,[status(thm)],[713])).
% 35.49/23.31 tff(715,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.31 inference(transitivity,[status(thm)],[714, 712])).
% 35.49/23.31 tff(716,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s20)) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(717,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s20)) | m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[716, 715])).
% 35.49/23.31 tff(718,plain,
% 35.49/23.31 (m_counter_cell_v_value(c_bit0, s20) | (~node1(c_bit0, s20))),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[717, 170, 711])).
% 35.49/23.31 tff(719,plain,
% 35.49/23.31 (~node1(c_bit0, s20)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[718, 709])).
% 35.49/23.31 tff(720,plain,
% 35.49/23.31 (succ(s20, s21) <=> succ(s20, s21)),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(721,axiom,(succ(s20, s21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound21')).
% 35.49/23.31 tff(722,plain,
% 35.49/23.31 (succ(s20, s21)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[721, 720])).
% 35.49/23.31 tff(723,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(724,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s20, s21)) | trans(s20, s21))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(725,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s20, s21)) | trans(s20, s21)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[724, 723])).
% 35.49/23.31 tff(726,plain,
% 35.49/23.31 (trans(s20, s21)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[725, 722, 8])).
% 35.49/23.31 tff(727,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(728,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit0, s20, s21))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(729,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit0, s20, s21)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[728, 727])).
% 35.49/23.31 tff(730,plain,
% 35.49/23.31 (node3(c_bit0, s20, s21)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[729, 81, 726])).
% 35.49/23.31 tff(731,plain,
% 35.49/23.31 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(732,plain,
% 35.49/23.31 ((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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(733,plain,
% 35.49/23.31 (((~![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))))),
% 35.49/23.31 inference(monotonicity,[status(thm)],[732])).
% 35.49/23.31 tff(734,plain,
% 35.49/23.31 (((~![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)))),
% 35.49/23.31 inference(transitivity,[status(thm)],[733, 731])).
% 35.49/23.31 tff(735,plain,
% 35.49/23.31 ((~![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))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(736,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20) | (~node3(c_bit0, s20, s21))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[735, 734])).
% 35.49/23.31 tff(737,plain,
% 35.49/23.31 (m_counter_cell_v_value(c_bit0, s21) | node1(c_bit0, s20)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[736, 199, 730])).
% 35.49/23.31 tff(738,plain,
% 35.49/23.31 (m_counter_cell_v_value(c_bit0, s21)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[737, 719])).
% 35.49/23.31 tff(739,assumption,(~m_counter_cell_v_carry_in(c_bit0, s21)), introduced(assumption)).
% 35.49/23.31 tff(740,plain,
% 35.49/23.31 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s21)),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(741,plain,
% 35.49/23.31 ($false),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[740, 158, 739])).
% 35.49/23.31 tff(742,plain,(m_counter_cell_v_carry_in(c_bit0, s21)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.31 tff(743,plain,
% 35.49/23.31 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(744,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21)))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(745,plain,
% 35.49/23.31 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s21)) | (~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[744, 743])).
% 35.49/23.31 tff(746,plain,
% 35.49/23.31 ((~m_counter_cell_v_value(c_bit0, s21)) | (~node2(c_bit0, s21))),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[745, 219, 742])).
% 35.49/23.31 tff(747,plain,
% 35.49/23.31 (~node2(c_bit0, s21)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[746, 738])).
% 35.49/23.31 tff(748,plain,
% 35.49/23.31 (succ(s21, s22) <=> succ(s21, s22)),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(749,axiom,(succ(s21, s22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound22')).
% 35.49/23.31 tff(750,plain,
% 35.49/23.31 (succ(s21, s22)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[749, 748])).
% 35.49/23.31 tff(751,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(752,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s21, s22)) | trans(s21, s22))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(753,plain,
% 35.49/23.31 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s21, s22)) | trans(s21, s22)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[752, 751])).
% 35.49/23.31 tff(754,plain,
% 35.49/23.31 (trans(s21, s22)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[753, 750, 8])).
% 35.49/23.31 tff(755,plain,
% 35.49/23.31 (((~![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))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(756,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit0, s21, s22))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(757,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit0, s21, s22)),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[756, 755])).
% 35.49/23.31 tff(758,plain,
% 35.49/23.31 (node3(c_bit0, s21, s22)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[757, 81, 754])).
% 35.49/23.31 tff(759,plain,
% 35.49/23.31 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(760,plain,
% 35.49/23.31 ((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)))),
% 35.49/23.31 inference(rewrite,[status(thm)],[])).
% 35.49/23.31 tff(761,plain,
% 35.49/23.31 (((~![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))))),
% 35.49/23.31 inference(monotonicity,[status(thm)],[760])).
% 35.49/23.31 tff(762,plain,
% 35.49/23.31 (((~![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)))),
% 35.49/23.31 inference(transitivity,[status(thm)],[761, 759])).
% 35.49/23.31 tff(763,plain,
% 35.49/23.31 ((~![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)))),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.31 tff(764,plain,
% 35.49/23.31 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21) | (~node3(c_bit0, s21, s22))),
% 35.49/23.31 inference(modus_ponens,[status(thm)],[763, 762])).
% 35.49/23.31 tff(765,plain,
% 35.49/23.31 ((~m_counter_cell_v_value(c_bit0, s22)) | node2(c_bit0, s21)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[764, 234, 758])).
% 35.49/23.31 tff(766,plain,
% 35.49/23.31 (~m_counter_cell_v_value(c_bit0, s22)),
% 35.49/23.31 inference(unit_resolution,[status(thm)],[765, 747])).
% 35.49/23.31 tff(767,assumption,(~m_counter_cell_v_carry_in(c_bit0, s22)), introduced(assumption)).
% 35.49/23.31 tff(768,plain,
% 35.49/23.31 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s22)),
% 35.49/23.31 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(769,plain,
% 35.49/23.32 ($false),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[768, 158, 767])).
% 35.49/23.32 tff(770,plain,(m_counter_cell_v_carry_in(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.32 tff(771,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(772,plain,
% 35.49/23.32 (((~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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(773,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.32 inference(monotonicity,[status(thm)],[772])).
% 35.49/23.32 tff(774,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.32 inference(transitivity,[status(thm)],[773, 771])).
% 35.49/23.32 tff(775,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s22)) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(776,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s22)) | m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[775, 774])).
% 35.49/23.32 tff(777,plain,
% 35.49/23.32 (m_counter_cell_v_value(c_bit0, s22) | (~node1(c_bit0, s22))),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[776, 170, 770])).
% 35.49/23.32 tff(778,plain,
% 35.49/23.32 (~node1(c_bit0, s22)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[777, 766])).
% 35.49/23.32 tff(779,plain,
% 35.49/23.32 (succ(s22, s23) <=> succ(s22, s23)),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(780,axiom,(succ(s22, s23)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound23')).
% 35.49/23.32 tff(781,plain,
% 35.49/23.32 (succ(s22, s23)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[780, 779])).
% 35.49/23.32 tff(782,plain,
% 35.49/23.32 (((~![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))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(783,plain,
% 35.49/23.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s22, s23)) | trans(s22, s23))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(784,plain,
% 35.49/23.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s22, s23)) | trans(s22, s23)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[783, 782])).
% 35.49/23.32 tff(785,plain,
% 35.49/23.32 (trans(s22, s23)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[784, 781, 8])).
% 35.49/23.32 tff(786,plain,
% 35.49/23.32 (((~![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))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(787,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit0, s22, s23))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(788,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit0, s22, s23)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[787, 786])).
% 35.49/23.32 tff(789,plain,
% 35.49/23.32 (node3(c_bit0, s22, s23)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[788, 81, 785])).
% 35.49/23.32 tff(790,plain,
% 35.49/23.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(791,plain,
% 35.49/23.32 ((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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(792,plain,
% 35.49/23.32 (((~![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))))),
% 35.49/23.32 inference(monotonicity,[status(thm)],[791])).
% 35.49/23.32 tff(793,plain,
% 35.49/23.32 (((~![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)))),
% 35.49/23.32 inference(transitivity,[status(thm)],[792, 790])).
% 35.49/23.32 tff(794,plain,
% 35.49/23.32 ((~![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))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(795,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22) | (~node3(c_bit0, s22, s23))),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[794, 793])).
% 35.49/23.32 tff(796,plain,
% 35.49/23.32 (m_counter_cell_v_value(c_bit0, s23) | node1(c_bit0, s22)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[795, 199, 789])).
% 35.49/23.32 tff(797,plain,
% 35.49/23.32 (m_counter_cell_v_value(c_bit0, s23)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[796, 778])).
% 35.49/23.32 tff(798,assumption,(~m_counter_cell_v_carry_in(c_bit0, s23)), introduced(assumption)).
% 35.49/23.32 tff(799,plain,
% 35.49/23.32 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s23)),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(800,plain,
% 35.49/23.32 ($false),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[799, 158, 798])).
% 35.49/23.32 tff(801,plain,(m_counter_cell_v_carry_in(c_bit0, s23)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.32 tff(802,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(803,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23)))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(804,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s23)) | (~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23))),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[803, 802])).
% 35.49/23.32 tff(805,plain,
% 35.49/23.32 ((~m_counter_cell_v_value(c_bit0, s23)) | (~node2(c_bit0, s23))),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[804, 219, 801])).
% 35.49/23.32 tff(806,plain,
% 35.49/23.32 (~node2(c_bit0, s23)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[805, 797])).
% 35.49/23.32 tff(807,plain,
% 35.49/23.32 (succ(s23, s24) <=> succ(s23, s24)),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(808,axiom,(succ(s23, s24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound24')).
% 35.49/23.32 tff(809,plain,
% 35.49/23.32 (succ(s23, s24)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[808, 807])).
% 35.49/23.32 tff(810,plain,
% 35.49/23.32 (((~![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))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(811,plain,
% 35.49/23.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s23, s24)) | trans(s23, s24))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(812,plain,
% 35.49/23.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s23, s24)) | trans(s23, s24)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[811, 810])).
% 35.49/23.32 tff(813,plain,
% 35.49/23.32 (trans(s23, s24)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[812, 809, 8])).
% 35.49/23.32 tff(814,plain,
% 35.49/23.32 (((~![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))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(815,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit0, s23, s24))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(816,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit0, s23, s24)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[815, 814])).
% 35.49/23.32 tff(817,plain,
% 35.49/23.32 (node3(c_bit0, s23, s24)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[816, 81, 813])).
% 35.49/23.32 tff(818,plain,
% 35.49/23.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(819,plain,
% 35.49/23.32 ((node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24))) <=> ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(820,plain,
% 35.49/23.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24))))),
% 35.49/23.32 inference(monotonicity,[status(thm)],[819])).
% 35.49/23.32 tff(821,plain,
% 35.49/23.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)) | (~m_counter_cell_v_value(c_bit0, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24)))),
% 35.49/23.32 inference(transitivity,[status(thm)],[820, 818])).
% 35.49/23.32 tff(822,plain,
% 35.49/23.32 ((~![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)))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(823,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23) | (~node3(c_bit0, s23, s24))),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[822, 821])).
% 35.49/23.32 tff(824,plain,
% 35.49/23.32 ((~m_counter_cell_v_value(c_bit0, s24)) | node2(c_bit0, s23)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[823, 234, 817])).
% 35.49/23.32 tff(825,plain,
% 35.49/23.32 (~m_counter_cell_v_value(c_bit0, s24)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[824, 806])).
% 35.49/23.32 tff(826,assumption,(~m_counter_cell_v_carry_in(c_bit0, s24)), introduced(assumption)).
% 35.49/23.32 tff(827,plain,
% 35.49/23.32 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s24)),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(828,plain,
% 35.49/23.32 ($false),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[827, 158, 826])).
% 35.49/23.32 tff(829,plain,(m_counter_cell_v_carry_in(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.32 tff(830,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(831,plain,
% 35.49/23.32 (((~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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(832,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.32 inference(monotonicity,[status(thm)],[831])).
% 35.49/23.32 tff(833,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.32 inference(transitivity,[status(thm)],[832, 830])).
% 35.49/23.32 tff(834,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s24)) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(835,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s24)) | m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[834, 833])).
% 35.49/23.32 tff(836,plain,
% 35.49/23.32 (m_counter_cell_v_value(c_bit0, s24) | (~node1(c_bit0, s24))),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[835, 170, 829])).
% 35.49/23.32 tff(837,plain,
% 35.49/23.32 (~node1(c_bit0, s24)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[836, 825])).
% 35.49/23.32 tff(838,plain,
% 35.49/23.32 (succ(s24, s25) <=> succ(s24, s25)),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(839,axiom,(succ(s24, s25)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound25')).
% 35.49/23.32 tff(840,plain,
% 35.49/23.32 (succ(s24, s25)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[839, 838])).
% 35.49/23.32 tff(841,plain,
% 35.49/23.32 (((~![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))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(842,plain,
% 35.49/23.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s24, s25)) | trans(s24, s25))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(843,plain,
% 35.49/23.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s24, s25)) | trans(s24, s25)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[842, 841])).
% 35.49/23.32 tff(844,plain,
% 35.49/23.32 (trans(s24, s25)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[843, 840, 8])).
% 35.49/23.32 tff(845,plain,
% 35.49/23.32 (((~![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))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(846,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit0, s24, s25))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(847,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit0, s24, s25)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[846, 845])).
% 35.49/23.32 tff(848,plain,
% 35.49/23.32 (node3(c_bit0, s24, s25)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[847, 81, 844])).
% 35.49/23.32 tff(849,plain,
% 35.49/23.32 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(850,plain,
% 35.49/23.32 ((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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(851,plain,
% 35.49/23.32 (((~![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))))),
% 35.49/23.32 inference(monotonicity,[status(thm)],[850])).
% 35.49/23.32 tff(852,plain,
% 35.49/23.32 (((~![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)))),
% 35.49/23.32 inference(transitivity,[status(thm)],[851, 849])).
% 35.49/23.32 tff(853,plain,
% 35.49/23.32 ((~![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))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(854,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24) | (~node3(c_bit0, s24, s25))),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[853, 852])).
% 35.49/23.32 tff(855,plain,
% 35.49/23.32 (m_counter_cell_v_value(c_bit0, s25) | node1(c_bit0, s24)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[854, 199, 848])).
% 35.49/23.32 tff(856,plain,
% 35.49/23.32 (m_counter_cell_v_value(c_bit0, s25)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[855, 837])).
% 35.49/23.32 tff(857,plain,
% 35.49/23.32 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s25)),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(858,plain,
% 35.49/23.32 (m_counter_cell_v_carry_in(c_bit0, s25)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[857, 158])).
% 35.49/23.32 tff(859,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(860,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25)))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(861,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | (~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25))),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[860, 859])).
% 35.49/23.32 tff(862,plain,
% 35.49/23.32 ((~m_counter_cell_v_value(c_bit0, s25)) | (~node2(c_bit0, s25))),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[861, 219, 858])).
% 35.49/23.32 tff(863,plain,
% 35.49/23.32 (~node2(c_bit0, s25)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[862, 856])).
% 35.49/23.32 tff(864,plain,
% 35.49/23.32 (succ(s25, s26) <=> succ(s25, s26)),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(865,axiom,(succ(s25, s26)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound26')).
% 35.49/23.32 tff(866,plain,
% 35.49/23.32 (succ(s25, s26)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[865, 864])).
% 35.49/23.32 tff(867,plain,
% 35.49/23.32 (((~![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))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(868,plain,
% 35.49/23.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s25, s26)) | trans(s25, s26))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(869,plain,
% 35.49/23.32 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s25, s26)) | trans(s25, s26)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[868, 867])).
% 35.49/23.32 tff(870,plain,
% 35.49/23.32 (trans(s25, s26)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[869, 866, 8])).
% 35.49/23.32 tff(871,plain,
% 35.49/23.32 (((~![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))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(872,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit0, s25, s26))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(873,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit0, s25, s26)),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[872, 871])).
% 35.49/23.32 tff(874,plain,
% 35.49/23.32 (node3(c_bit0, s25, s26)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[873, 81, 870])).
% 35.49/23.32 tff(875,plain,
% 35.49/23.32 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(876,plain,
% 35.49/23.32 ((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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(877,plain,
% 35.49/23.32 (((~![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))))),
% 35.49/23.32 inference(monotonicity,[status(thm)],[876])).
% 35.49/23.32 tff(878,plain,
% 35.49/23.32 (((~![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)))),
% 35.49/23.32 inference(transitivity,[status(thm)],[877, 875])).
% 35.49/23.32 tff(879,plain,
% 35.49/23.32 ((~![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)))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(880,plain,
% 35.49/23.32 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25) | (~node3(c_bit0, s25, s26))),
% 35.49/23.32 inference(modus_ponens,[status(thm)],[879, 878])).
% 35.49/23.32 tff(881,plain,
% 35.49/23.32 ((~m_counter_cell_v_value(c_bit0, s26)) | node2(c_bit0, s25)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[880, 234, 874])).
% 35.49/23.32 tff(882,plain,
% 35.49/23.32 (~m_counter_cell_v_value(c_bit0, s26)),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[881, 863])).
% 35.49/23.32 tff(883,assumption,(~m_counter_cell_v_carry_in(c_bit0, s26)), introduced(assumption)).
% 35.49/23.32 tff(884,plain,
% 35.49/23.32 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s26)),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(885,plain,
% 35.49/23.32 ($false),
% 35.49/23.32 inference(unit_resolution,[status(thm)],[884, 158, 883])).
% 35.49/23.32 tff(886,plain,(m_counter_cell_v_carry_in(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.32 tff(887,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(888,plain,
% 35.49/23.32 (((~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)))),
% 35.49/23.32 inference(rewrite,[status(thm)],[])).
% 35.49/23.32 tff(889,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.32 inference(monotonicity,[status(thm)],[888])).
% 35.49/23.32 tff(890,plain,
% 35.49/23.32 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.32 inference(transitivity,[status(thm)],[889, 887])).
% 35.49/23.32 tff(891,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s26)) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26))),
% 35.49/23.32 inference(quant_inst,[status(thm)],[])).
% 35.49/23.32 tff(892,plain,
% 35.49/23.32 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s26)) | m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[891, 890])).
% 35.49/23.33 tff(893,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s26) | (~node1(c_bit0, s26))),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[892, 170, 886])).
% 35.49/23.33 tff(894,plain,
% 35.49/23.33 (~node1(c_bit0, s26)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[893, 882])).
% 35.49/23.33 tff(895,plain,
% 35.49/23.33 (succ(s26, s27) <=> succ(s26, s27)),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(896,axiom,(succ(s26, s27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound27')).
% 35.49/23.33 tff(897,plain,
% 35.49/23.33 (succ(s26, s27)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[896, 895])).
% 35.49/23.33 tff(898,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(899,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s26, s27)) | trans(s26, s27))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(900,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s26, s27)) | trans(s26, s27)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[899, 898])).
% 35.49/23.33 tff(901,plain,
% 35.49/23.33 (trans(s26, s27)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[900, 897, 8])).
% 35.49/23.33 tff(902,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(903,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit0, s26, s27))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(904,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit0, s26, s27)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[903, 902])).
% 35.49/23.33 tff(905,plain,
% 35.49/23.33 (node3(c_bit0, s26, s27)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[904, 81, 901])).
% 35.49/23.33 tff(906,plain,
% 35.49/23.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(907,plain,
% 35.49/23.33 ((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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(908,plain,
% 35.49/23.33 (((~![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))))),
% 35.49/23.33 inference(monotonicity,[status(thm)],[907])).
% 35.49/23.33 tff(909,plain,
% 35.49/23.33 (((~![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)))),
% 35.49/23.33 inference(transitivity,[status(thm)],[908, 906])).
% 35.49/23.33 tff(910,plain,
% 35.49/23.33 ((~![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))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(911,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26) | (~node3(c_bit0, s26, s27))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[910, 909])).
% 35.49/23.33 tff(912,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s27) | node1(c_bit0, s26)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[911, 199, 905])).
% 35.49/23.33 tff(913,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s27)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[912, 894])).
% 35.49/23.33 tff(914,assumption,(~m_counter_cell_v_carry_in(c_bit0, s27)), introduced(assumption)).
% 35.49/23.33 tff(915,plain,
% 35.49/23.33 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s27)),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(916,plain,
% 35.49/23.33 ($false),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[915, 158, 914])).
% 35.49/23.33 tff(917,plain,(m_counter_cell_v_carry_in(c_bit0, s27)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.33 tff(918,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(919,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27)))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(920,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s27)) | (~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[919, 918])).
% 35.49/23.33 tff(921,plain,
% 35.49/23.33 ((~m_counter_cell_v_value(c_bit0, s27)) | (~node2(c_bit0, s27))),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[920, 219, 917])).
% 35.49/23.33 tff(922,plain,
% 35.49/23.33 (~node2(c_bit0, s27)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[921, 913])).
% 35.49/23.33 tff(923,plain,
% 35.49/23.33 (succ(s27, s28) <=> succ(s27, s28)),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(924,axiom,(succ(s27, s28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound28')).
% 35.49/23.33 tff(925,plain,
% 35.49/23.33 (succ(s27, s28)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[924, 923])).
% 35.49/23.33 tff(926,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(927,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s27, s28)) | trans(s27, s28))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(928,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s27, s28)) | trans(s27, s28)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[927, 926])).
% 35.49/23.33 tff(929,plain,
% 35.49/23.33 (trans(s27, s28)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[928, 925, 8])).
% 35.49/23.33 tff(930,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(931,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit0, s27, s28))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(932,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit0, s27, s28)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[931, 930])).
% 35.49/23.33 tff(933,plain,
% 35.49/23.33 (node3(c_bit0, s27, s28)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[932, 81, 929])).
% 35.49/23.33 tff(934,plain,
% 35.49/23.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(935,plain,
% 35.49/23.33 ((node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28))) <=> ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(936,plain,
% 35.49/23.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28))))),
% 35.49/23.33 inference(monotonicity,[status(thm)],[935])).
% 35.49/23.33 tff(937,plain,
% 35.49/23.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)) | (~m_counter_cell_v_value(c_bit0, s28)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28)))),
% 35.49/23.33 inference(transitivity,[status(thm)],[936, 934])).
% 35.49/23.33 tff(938,plain,
% 35.49/23.33 ((~![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)))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(939,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27) | (~node3(c_bit0, s27, s28))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[938, 937])).
% 35.49/23.33 tff(940,plain,
% 35.49/23.33 ((~m_counter_cell_v_value(c_bit0, s28)) | node2(c_bit0, s27)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[939, 234, 933])).
% 35.49/23.33 tff(941,plain,
% 35.49/23.33 (~m_counter_cell_v_value(c_bit0, s28)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[940, 922])).
% 35.49/23.33 tff(942,plain,
% 35.49/23.33 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s28)),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(943,plain,
% 35.49/23.33 (m_counter_cell_v_carry_in(c_bit0, s28)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[942, 158])).
% 35.49/23.33 tff(944,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(945,plain,
% 35.49/23.33 (((~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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(946,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.33 inference(monotonicity,[status(thm)],[945])).
% 35.49/23.33 tff(947,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.33 inference(transitivity,[status(thm)],[946, 944])).
% 35.49/23.33 tff(948,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s28)) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(949,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s28)) | m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[948, 947])).
% 35.49/23.33 tff(950,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s28) | (~node1(c_bit0, s28))),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[949, 170, 943])).
% 35.49/23.33 tff(951,plain,
% 35.49/23.33 (~node1(c_bit0, s28)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[950, 941])).
% 35.49/23.33 tff(952,plain,
% 35.49/23.33 (succ(s28, s29) <=> succ(s28, s29)),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(953,axiom,(succ(s28, s29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound29')).
% 35.49/23.33 tff(954,plain,
% 35.49/23.33 (succ(s28, s29)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[953, 952])).
% 35.49/23.33 tff(955,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(956,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s28, s29)) | trans(s28, s29))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(957,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s28, s29)) | trans(s28, s29)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[956, 955])).
% 35.49/23.33 tff(958,plain,
% 35.49/23.33 (trans(s28, s29)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[957, 954, 8])).
% 35.49/23.33 tff(959,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(960,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit0, s28, s29))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(961,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit0, s28, s29)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[960, 959])).
% 35.49/23.33 tff(962,plain,
% 35.49/23.33 (node3(c_bit0, s28, s29)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[961, 81, 958])).
% 35.49/23.33 tff(963,plain,
% 35.49/23.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(964,plain,
% 35.49/23.33 ((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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(965,plain,
% 35.49/23.33 (((~![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))))),
% 35.49/23.33 inference(monotonicity,[status(thm)],[964])).
% 35.49/23.33 tff(966,plain,
% 35.49/23.33 (((~![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)))),
% 35.49/23.33 inference(transitivity,[status(thm)],[965, 963])).
% 35.49/23.33 tff(967,plain,
% 35.49/23.33 ((~![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))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(968,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28) | (~node3(c_bit0, s28, s29))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[967, 966])).
% 35.49/23.33 tff(969,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s29) | node1(c_bit0, s28)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[968, 199, 962])).
% 35.49/23.33 tff(970,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s29)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[969, 951])).
% 35.49/23.33 tff(971,assumption,(~m_counter_cell_v_carry_in(c_bit0, s29)), introduced(assumption)).
% 35.49/23.33 tff(972,plain,
% 35.49/23.33 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s29)),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(973,plain,
% 35.49/23.33 ($false),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[972, 158, 971])).
% 35.49/23.33 tff(974,plain,(m_counter_cell_v_carry_in(c_bit0, s29)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.33 tff(975,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(976,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29)))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(977,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s29)) | (~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[976, 975])).
% 35.49/23.33 tff(978,plain,
% 35.49/23.33 ((~m_counter_cell_v_value(c_bit0, s29)) | (~node2(c_bit0, s29))),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[977, 219, 974])).
% 35.49/23.33 tff(979,plain,
% 35.49/23.33 (~node2(c_bit0, s29)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[978, 970])).
% 35.49/23.33 tff(980,plain,
% 35.49/23.33 (succ(s29, s30) <=> succ(s29, s30)),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(981,axiom,(succ(s29, s30)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound30')).
% 35.49/23.33 tff(982,plain,
% 35.49/23.33 (succ(s29, s30)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[981, 980])).
% 35.49/23.33 tff(983,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(984,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s29, s30)) | trans(s29, s30))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(985,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s29, s30)) | trans(s29, s30)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[984, 983])).
% 35.49/23.33 tff(986,plain,
% 35.49/23.33 (trans(s29, s30)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[985, 982, 8])).
% 35.49/23.33 tff(987,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(988,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit0, s29, s30))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(989,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit0, s29, s30)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[988, 987])).
% 35.49/23.33 tff(990,plain,
% 35.49/23.33 (node3(c_bit0, s29, s30)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[989, 81, 986])).
% 35.49/23.33 tff(991,plain,
% 35.49/23.33 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(992,plain,
% 35.49/23.33 ((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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(993,plain,
% 35.49/23.33 (((~![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))))),
% 35.49/23.33 inference(monotonicity,[status(thm)],[992])).
% 35.49/23.33 tff(994,plain,
% 35.49/23.33 (((~![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)))),
% 35.49/23.33 inference(transitivity,[status(thm)],[993, 991])).
% 35.49/23.33 tff(995,plain,
% 35.49/23.33 ((~![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)))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(996,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29) | (~node3(c_bit0, s29, s30))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[995, 994])).
% 35.49/23.33 tff(997,plain,
% 35.49/23.33 ((~m_counter_cell_v_value(c_bit0, s30)) | node2(c_bit0, s29)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[996, 234, 990])).
% 35.49/23.33 tff(998,plain,
% 35.49/23.33 (~m_counter_cell_v_value(c_bit0, s30)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[997, 979])).
% 35.49/23.33 tff(999,assumption,(~m_counter_cell_v_carry_in(c_bit0, s30)), introduced(assumption)).
% 35.49/23.33 tff(1000,plain,
% 35.49/23.33 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s30)),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(1001,plain,
% 35.49/23.33 ($false),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1000, 158, 999])).
% 35.49/23.33 tff(1002,plain,(m_counter_cell_v_carry_in(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.33 tff(1003,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1004,plain,
% 35.49/23.33 (((~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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1005,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.33 inference(monotonicity,[status(thm)],[1004])).
% 35.49/23.33 tff(1006,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.33 inference(transitivity,[status(thm)],[1005, 1003])).
% 35.49/23.33 tff(1007,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s30)) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(1008,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s30)) | m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 35.49/23.33 tff(1009,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s30) | (~node1(c_bit0, s30))),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1008, 170, 1002])).
% 35.49/23.33 tff(1010,plain,
% 35.49/23.33 (~node1(c_bit0, s30)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1009, 998])).
% 35.49/23.33 tff(1011,plain,
% 35.49/23.33 (succ(s30, s31) <=> succ(s30, s31)),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1012,axiom,(succ(s30, s31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound31')).
% 35.49/23.33 tff(1013,plain,
% 35.49/23.33 (succ(s30, s31)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[1012, 1011])).
% 35.49/23.33 tff(1014,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1015,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s30, s31)) | trans(s30, s31))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(1016,plain,
% 35.49/23.33 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s30, s31)) | trans(s30, s31)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 35.49/23.33 tff(1017,plain,
% 35.49/23.33 (trans(s30, s31)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1016, 1013, 8])).
% 35.49/23.33 tff(1018,plain,
% 35.49/23.33 (((~![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))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1019,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit0, s30, s31))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(1020,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit0, s30, s31)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[1019, 1018])).
% 35.49/23.33 tff(1021,plain,
% 35.49/23.33 (node3(c_bit0, s30, s31)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1020, 81, 1017])).
% 35.49/23.33 tff(1022,plain,
% 35.49/23.33 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1023,plain,
% 35.49/23.33 ((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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1024,plain,
% 35.49/23.33 (((~![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))))),
% 35.49/23.33 inference(monotonicity,[status(thm)],[1023])).
% 35.49/23.33 tff(1025,plain,
% 35.49/23.33 (((~![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)))),
% 35.49/23.33 inference(transitivity,[status(thm)],[1024, 1022])).
% 35.49/23.33 tff(1026,plain,
% 35.49/23.33 ((~![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))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(1027,plain,
% 35.49/23.33 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30) | (~node3(c_bit0, s30, s31))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 35.49/23.33 tff(1028,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s31) | node1(c_bit0, s30)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1027, 199, 1021])).
% 35.49/23.33 tff(1029,plain,
% 35.49/23.33 (m_counter_cell_v_value(c_bit0, s31)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1028, 1010])).
% 35.49/23.33 tff(1030,assumption,(~m_counter_cell_v_carry_in(c_bit0, s31)), introduced(assumption)).
% 35.49/23.33 tff(1031,plain,
% 35.49/23.33 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s31)),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(1032,plain,
% 35.49/23.33 ($false),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1031, 158, 1030])).
% 35.49/23.33 tff(1033,plain,(m_counter_cell_v_carry_in(c_bit0, s31)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.33 tff(1034,plain,
% 35.49/23.33 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1035,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31)))),
% 35.49/23.33 inference(quant_inst,[status(thm)],[])).
% 35.49/23.33 tff(1036,plain,
% 35.49/23.33 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31))),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[1035, 1034])).
% 35.49/23.33 tff(1037,plain,
% 35.49/23.33 ((~m_counter_cell_v_value(c_bit0, s31)) | (~node2(c_bit0, s31))),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1036, 219, 1033])).
% 35.49/23.33 tff(1038,plain,
% 35.49/23.33 (~node2(c_bit0, s31)),
% 35.49/23.33 inference(unit_resolution,[status(thm)],[1037, 1029])).
% 35.49/23.33 tff(1039,plain,
% 35.49/23.33 (succ(s31, s32) <=> succ(s31, s32)),
% 35.49/23.33 inference(rewrite,[status(thm)],[])).
% 35.49/23.33 tff(1040,axiom,(succ(s31, s32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound32')).
% 35.49/23.33 tff(1041,plain,
% 35.49/23.33 (succ(s31, s32)),
% 35.49/23.33 inference(modus_ponens,[status(thm)],[1040, 1039])).
% 35.49/23.33 tff(1042,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1043,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s31, s32)) | trans(s31, s32))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1044,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s31, s32)) | trans(s31, s32)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 35.49/23.34 tff(1045,plain,
% 35.49/23.34 (trans(s31, s32)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1044, 1041, 8])).
% 35.49/23.34 tff(1046,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1047,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit0, s31, s32))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1048,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit0, s31, s32)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1047, 1046])).
% 35.49/23.34 tff(1049,plain,
% 35.49/23.34 (node3(c_bit0, s31, s32)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1048, 81, 1045])).
% 35.49/23.34 tff(1050,plain,
% 35.49/23.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1051,plain,
% 35.49/23.34 ((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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1052,plain,
% 35.49/23.34 (((~![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))))),
% 35.49/23.34 inference(monotonicity,[status(thm)],[1051])).
% 35.49/23.34 tff(1053,plain,
% 35.49/23.34 (((~![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)))),
% 35.49/23.34 inference(transitivity,[status(thm)],[1052, 1050])).
% 35.49/23.34 tff(1054,plain,
% 35.49/23.34 ((~![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)))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1055,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31) | (~node3(c_bit0, s31, s32))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1054, 1053])).
% 35.49/23.34 tff(1056,plain,
% 35.49/23.34 ((~m_counter_cell_v_value(c_bit0, s32)) | node2(c_bit0, s31)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1055, 234, 1049])).
% 35.49/23.34 tff(1057,plain,
% 35.49/23.34 (~m_counter_cell_v_value(c_bit0, s32)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1056, 1038])).
% 35.49/23.34 tff(1058,assumption,(~m_counter_cell_v_carry_in(c_bit0, s32)), introduced(assumption)).
% 35.49/23.34 tff(1059,plain,
% 35.49/23.34 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s32)),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1060,plain,
% 35.49/23.34 ($false),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1059, 158, 1058])).
% 35.49/23.34 tff(1061,plain,(m_counter_cell_v_carry_in(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.34 tff(1062,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1063,plain,
% 35.49/23.34 (((~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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1064,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.34 inference(monotonicity,[status(thm)],[1063])).
% 35.49/23.34 tff(1065,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.34 inference(transitivity,[status(thm)],[1064, 1062])).
% 35.49/23.34 tff(1066,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s32)) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1067,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s32)) | m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 35.49/23.34 tff(1068,plain,
% 35.49/23.34 (m_counter_cell_v_value(c_bit0, s32) | (~node1(c_bit0, s32))),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1067, 170, 1061])).
% 35.49/23.34 tff(1069,plain,
% 35.49/23.34 (~node1(c_bit0, s32)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1068, 1057])).
% 35.49/23.34 tff(1070,plain,
% 35.49/23.34 (succ(s32, s33) <=> succ(s32, s33)),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1071,axiom,(succ(s32, s33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound33')).
% 35.49/23.34 tff(1072,plain,
% 35.49/23.34 (succ(s32, s33)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 35.49/23.34 tff(1073,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1074,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s32, s33)) | trans(s32, s33))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1075,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s32, s33)) | trans(s32, s33)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 35.49/23.34 tff(1076,plain,
% 35.49/23.34 (trans(s32, s33)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1075, 1072, 8])).
% 35.49/23.34 tff(1077,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1078,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit0, s32, s33))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1079,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit0, s32, s33)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1078, 1077])).
% 35.49/23.34 tff(1080,plain,
% 35.49/23.34 (node3(c_bit0, s32, s33)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1079, 81, 1076])).
% 35.49/23.34 tff(1081,plain,
% 35.49/23.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1082,plain,
% 35.49/23.34 ((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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1083,plain,
% 35.49/23.34 (((~![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))))),
% 35.49/23.34 inference(monotonicity,[status(thm)],[1082])).
% 35.49/23.34 tff(1084,plain,
% 35.49/23.34 (((~![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)))),
% 35.49/23.34 inference(transitivity,[status(thm)],[1083, 1081])).
% 35.49/23.34 tff(1085,plain,
% 35.49/23.34 ((~![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))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1086,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32) | (~node3(c_bit0, s32, s33))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1085, 1084])).
% 35.49/23.34 tff(1087,plain,
% 35.49/23.34 (m_counter_cell_v_value(c_bit0, s33) | node1(c_bit0, s32)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1086, 199, 1080])).
% 35.49/23.34 tff(1088,plain,
% 35.49/23.34 (m_counter_cell_v_value(c_bit0, s33)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1087, 1069])).
% 35.49/23.34 tff(1089,assumption,(~m_counter_cell_v_carry_in(c_bit0, s33)), introduced(assumption)).
% 35.49/23.34 tff(1090,plain,
% 35.49/23.34 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s33)),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1091,plain,
% 35.49/23.34 ($false),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1090, 158, 1089])).
% 35.49/23.34 tff(1092,plain,(m_counter_cell_v_carry_in(c_bit0, s33)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.34 tff(1093,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1094,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33)))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1095,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s33)) | (~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1094, 1093])).
% 35.49/23.34 tff(1096,plain,
% 35.49/23.34 ((~m_counter_cell_v_value(c_bit0, s33)) | (~node2(c_bit0, s33))),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1095, 219, 1092])).
% 35.49/23.34 tff(1097,plain,
% 35.49/23.34 (~node2(c_bit0, s33)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1096, 1088])).
% 35.49/23.34 tff(1098,plain,
% 35.49/23.34 (succ(s33, s34) <=> succ(s33, s34)),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1099,axiom,(succ(s33, s34)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound34')).
% 35.49/23.34 tff(1100,plain,
% 35.49/23.34 (succ(s33, s34)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1099, 1098])).
% 35.49/23.34 tff(1101,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1102,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s33, s34)) | trans(s33, s34))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1103,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s33, s34)) | trans(s33, s34)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 35.49/23.34 tff(1104,plain,
% 35.49/23.34 (trans(s33, s34)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1103, 1100, 8])).
% 35.49/23.34 tff(1105,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1106,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit0, s33, s34))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1107,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit0, s33, s34)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 35.49/23.34 tff(1108,plain,
% 35.49/23.34 (node3(c_bit0, s33, s34)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1107, 81, 1104])).
% 35.49/23.34 tff(1109,plain,
% 35.49/23.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1110,plain,
% 35.49/23.34 ((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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1111,plain,
% 35.49/23.34 (((~![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))))),
% 35.49/23.34 inference(monotonicity,[status(thm)],[1110])).
% 35.49/23.34 tff(1112,plain,
% 35.49/23.34 (((~![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)))),
% 35.49/23.34 inference(transitivity,[status(thm)],[1111, 1109])).
% 35.49/23.34 tff(1113,plain,
% 35.49/23.34 ((~![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)))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1114,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33) | (~node3(c_bit0, s33, s34))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 35.49/23.34 tff(1115,plain,
% 35.49/23.34 ((~m_counter_cell_v_value(c_bit0, s34)) | node2(c_bit0, s33)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1114, 234, 1108])).
% 35.49/23.34 tff(1116,plain,
% 35.49/23.34 (~m_counter_cell_v_value(c_bit0, s34)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1115, 1097])).
% 35.49/23.34 tff(1117,assumption,(~m_counter_cell_v_carry_in(c_bit0, s34)), introduced(assumption)).
% 35.49/23.34 tff(1118,plain,
% 35.49/23.34 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s34)),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1119,plain,
% 35.49/23.34 ($false),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1118, 158, 1117])).
% 35.49/23.34 tff(1120,plain,(m_counter_cell_v_carry_in(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.34 tff(1121,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1122,plain,
% 35.49/23.34 (((~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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1123,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.34 inference(monotonicity,[status(thm)],[1122])).
% 35.49/23.34 tff(1124,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.34 inference(transitivity,[status(thm)],[1123, 1121])).
% 35.49/23.34 tff(1125,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s34)) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1126,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s34)) | m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1125, 1124])).
% 35.49/23.34 tff(1127,plain,
% 35.49/23.34 (m_counter_cell_v_value(c_bit0, s34) | (~node1(c_bit0, s34))),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1126, 170, 1120])).
% 35.49/23.34 tff(1128,plain,
% 35.49/23.34 (~node1(c_bit0, s34)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1127, 1116])).
% 35.49/23.34 tff(1129,plain,
% 35.49/23.34 (succ(s34, s35) <=> succ(s34, s35)),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1130,axiom,(succ(s34, s35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound35')).
% 35.49/23.34 tff(1131,plain,
% 35.49/23.34 (succ(s34, s35)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 35.49/23.34 tff(1132,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1133,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s34, s35)) | trans(s34, s35))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1134,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s34, s35)) | trans(s34, s35)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1133, 1132])).
% 35.49/23.34 tff(1135,plain,
% 35.49/23.34 (trans(s34, s35)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1134, 1131, 8])).
% 35.49/23.34 tff(1136,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1137,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit0, s34, s35))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1138,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit0, s34, s35)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 35.49/23.34 tff(1139,plain,
% 35.49/23.34 (node3(c_bit0, s34, s35)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1138, 81, 1135])).
% 35.49/23.34 tff(1140,plain,
% 35.49/23.34 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1141,plain,
% 35.49/23.34 ((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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1142,plain,
% 35.49/23.34 (((~![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))))),
% 35.49/23.34 inference(monotonicity,[status(thm)],[1141])).
% 35.49/23.34 tff(1143,plain,
% 35.49/23.34 (((~![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)))),
% 35.49/23.34 inference(transitivity,[status(thm)],[1142, 1140])).
% 35.49/23.34 tff(1144,plain,
% 35.49/23.34 ((~![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))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1145,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34) | (~node3(c_bit0, s34, s35))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 35.49/23.34 tff(1146,plain,
% 35.49/23.34 (m_counter_cell_v_value(c_bit0, s35) | node1(c_bit0, s34)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1145, 199, 1139])).
% 35.49/23.34 tff(1147,plain,
% 35.49/23.34 (m_counter_cell_v_value(c_bit0, s35)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1146, 1128])).
% 35.49/23.34 tff(1148,assumption,(~m_counter_cell_v_carry_in(c_bit0, s35)), introduced(assumption)).
% 35.49/23.34 tff(1149,plain,
% 35.49/23.34 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s35)),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1150,plain,
% 35.49/23.34 ($false),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1149, 158, 1148])).
% 35.49/23.34 tff(1151,plain,(m_counter_cell_v_carry_in(c_bit0, s35)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.34 tff(1152,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1153,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35)))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1154,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s35)) | (~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 35.49/23.34 tff(1155,plain,
% 35.49/23.34 ((~m_counter_cell_v_value(c_bit0, s35)) | (~node2(c_bit0, s35))),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1154, 219, 1151])).
% 35.49/23.34 tff(1156,plain,
% 35.49/23.34 (~node2(c_bit0, s35)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1155, 1147])).
% 35.49/23.34 tff(1157,plain,
% 35.49/23.34 (succ(s35, s36) <=> succ(s35, s36)),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1158,axiom,(succ(s35, s36)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound36')).
% 35.49/23.34 tff(1159,plain,
% 35.49/23.34 (succ(s35, s36)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 35.49/23.34 tff(1160,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1161,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s35, s36)) | trans(s35, s36))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1162,plain,
% 35.49/23.34 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s35, s36)) | trans(s35, s36)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1161, 1160])).
% 35.49/23.34 tff(1163,plain,
% 35.49/23.34 (trans(s35, s36)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1162, 1159, 8])).
% 35.49/23.34 tff(1164,plain,
% 35.49/23.34 (((~![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))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1165,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit0, s35, s36))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1166,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit0, s35, s36)),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 35.49/23.34 tff(1167,plain,
% 35.49/23.34 (node3(c_bit0, s35, s36)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1166, 81, 1163])).
% 35.49/23.34 tff(1168,plain,
% 35.49/23.34 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1169,plain,
% 35.49/23.34 ((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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1170,plain,
% 35.49/23.34 (((~![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))))),
% 35.49/23.34 inference(monotonicity,[status(thm)],[1169])).
% 35.49/23.34 tff(1171,plain,
% 35.49/23.34 (((~![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)))),
% 35.49/23.34 inference(transitivity,[status(thm)],[1170, 1168])).
% 35.49/23.34 tff(1172,plain,
% 35.49/23.34 ((~![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)))),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1173,plain,
% 35.49/23.34 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35) | (~node3(c_bit0, s35, s36))),
% 35.49/23.34 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 35.49/23.34 tff(1174,plain,
% 35.49/23.34 ((~m_counter_cell_v_value(c_bit0, s36)) | node2(c_bit0, s35)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1173, 234, 1167])).
% 35.49/23.34 tff(1175,plain,
% 35.49/23.34 (~m_counter_cell_v_value(c_bit0, s36)),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1174, 1156])).
% 35.49/23.34 tff(1176,assumption,(~m_counter_cell_v_carry_in(c_bit0, s36)), introduced(assumption)).
% 35.49/23.34 tff(1177,plain,
% 35.49/23.34 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s36)),
% 35.49/23.34 inference(quant_inst,[status(thm)],[])).
% 35.49/23.34 tff(1178,plain,
% 35.49/23.34 ($false),
% 35.49/23.34 inference(unit_resolution,[status(thm)],[1177, 158, 1176])).
% 35.49/23.34 tff(1179,plain,(m_counter_cell_v_carry_in(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.34 tff(1180,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1181,plain,
% 35.49/23.34 (((~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)))),
% 35.49/23.34 inference(rewrite,[status(thm)],[])).
% 35.49/23.34 tff(1182,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.34 inference(monotonicity,[status(thm)],[1181])).
% 35.49/23.34 tff(1183,plain,
% 35.49/23.34 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.34 inference(transitivity,[status(thm)],[1182, 1180])).
% 35.49/23.34 tff(1184,plain,
% 35.49/23.34 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s36)) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1185,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s36)) | m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1184, 1183])).
% 35.49/23.35 tff(1186,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s36) | (~node1(c_bit0, s36))),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1185, 170, 1179])).
% 35.49/23.35 tff(1187,plain,
% 35.49/23.35 (~node1(c_bit0, s36)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1186, 1175])).
% 35.49/23.35 tff(1188,plain,
% 35.49/23.35 (succ(s36, s37) <=> succ(s36, s37)),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1189,axiom,(succ(s36, s37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound37')).
% 35.49/23.35 tff(1190,plain,
% 35.49/23.35 (succ(s36, s37)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1189, 1188])).
% 35.49/23.35 tff(1191,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1192,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s36, s37)) | trans(s36, s37))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1193,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s36, s37)) | trans(s36, s37)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1192, 1191])).
% 35.49/23.35 tff(1194,plain,
% 35.49/23.35 (trans(s36, s37)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1193, 1190, 8])).
% 35.49/23.35 tff(1195,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1196,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit0, s36, s37))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1197,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit0, s36, s37)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 35.49/23.35 tff(1198,plain,
% 35.49/23.35 (node3(c_bit0, s36, s37)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1197, 81, 1194])).
% 35.49/23.35 tff(1199,plain,
% 35.49/23.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1200,plain,
% 35.49/23.35 ((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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1201,plain,
% 35.49/23.35 (((~![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))))),
% 35.49/23.35 inference(monotonicity,[status(thm)],[1200])).
% 35.49/23.35 tff(1202,plain,
% 35.49/23.35 (((~![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)))),
% 35.49/23.35 inference(transitivity,[status(thm)],[1201, 1199])).
% 35.49/23.35 tff(1203,plain,
% 35.49/23.35 ((~![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))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1204,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36) | (~node3(c_bit0, s36, s37))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1203, 1202])).
% 35.49/23.35 tff(1205,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s37) | node1(c_bit0, s36)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1204, 199, 1198])).
% 35.49/23.35 tff(1206,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s37)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1205, 1187])).
% 35.49/23.35 tff(1207,assumption,(~m_counter_cell_v_carry_in(c_bit0, s37)), introduced(assumption)).
% 35.49/23.35 tff(1208,plain,
% 35.49/23.35 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s37)),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1209,plain,
% 35.49/23.35 ($false),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1208, 158, 1207])).
% 35.49/23.35 tff(1210,plain,(m_counter_cell_v_carry_in(c_bit0, s37)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.35 tff(1211,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1212,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37)))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1213,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s37)) | (~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 35.49/23.35 tff(1214,plain,
% 35.49/23.35 ((~m_counter_cell_v_value(c_bit0, s37)) | (~node2(c_bit0, s37))),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1213, 219, 1210])).
% 35.49/23.35 tff(1215,plain,
% 35.49/23.35 (~node2(c_bit0, s37)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1214, 1206])).
% 35.49/23.35 tff(1216,plain,
% 35.49/23.35 (succ(s37, s38) <=> succ(s37, s38)),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1217,axiom,(succ(s37, s38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound38')).
% 35.49/23.35 tff(1218,plain,
% 35.49/23.35 (succ(s37, s38)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1217, 1216])).
% 35.49/23.35 tff(1219,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1220,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s37, s38)) | trans(s37, s38))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1221,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s37, s38)) | trans(s37, s38)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1220, 1219])).
% 35.49/23.35 tff(1222,plain,
% 35.49/23.35 (trans(s37, s38)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1221, 1218, 8])).
% 35.49/23.35 tff(1223,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1224,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit0, s37, s38))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1225,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit0, s37, s38)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 35.49/23.35 tff(1226,plain,
% 35.49/23.35 (node3(c_bit0, s37, s38)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1225, 81, 1222])).
% 35.49/23.35 tff(1227,plain,
% 35.49/23.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1228,plain,
% 35.49/23.35 ((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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1229,plain,
% 35.49/23.35 (((~![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))))),
% 35.49/23.35 inference(monotonicity,[status(thm)],[1228])).
% 35.49/23.35 tff(1230,plain,
% 35.49/23.35 (((~![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)))),
% 35.49/23.35 inference(transitivity,[status(thm)],[1229, 1227])).
% 35.49/23.35 tff(1231,plain,
% 35.49/23.35 ((~![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)))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1232,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37) | (~node3(c_bit0, s37, s38))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 35.49/23.35 tff(1233,plain,
% 35.49/23.35 ((~m_counter_cell_v_value(c_bit0, s38)) | node2(c_bit0, s37)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1232, 234, 1226])).
% 35.49/23.35 tff(1234,plain,
% 35.49/23.35 (~m_counter_cell_v_value(c_bit0, s38)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1233, 1215])).
% 35.49/23.35 tff(1235,assumption,(~m_counter_cell_v_carry_in(c_bit0, s38)), introduced(assumption)).
% 35.49/23.35 tff(1236,plain,
% 35.49/23.35 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s38)),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1237,plain,
% 35.49/23.35 ($false),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1236, 158, 1235])).
% 35.49/23.35 tff(1238,plain,(m_counter_cell_v_carry_in(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.35 tff(1239,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1240,plain,
% 35.49/23.35 (((~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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1241,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.35 inference(monotonicity,[status(thm)],[1240])).
% 35.49/23.35 tff(1242,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.35 inference(transitivity,[status(thm)],[1241, 1239])).
% 35.49/23.35 tff(1243,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s38)) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1244,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s38)) | m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 35.49/23.35 tff(1245,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s38) | (~node1(c_bit0, s38))),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1244, 170, 1238])).
% 35.49/23.35 tff(1246,plain,
% 35.49/23.35 (~node1(c_bit0, s38)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1245, 1234])).
% 35.49/23.35 tff(1247,plain,
% 35.49/23.35 (succ(s38, s39) <=> succ(s38, s39)),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1248,axiom,(succ(s38, s39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound39')).
% 35.49/23.35 tff(1249,plain,
% 35.49/23.35 (succ(s38, s39)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1248, 1247])).
% 35.49/23.35 tff(1250,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1251,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s38, s39)) | trans(s38, s39))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1252,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s38, s39)) | trans(s38, s39)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 35.49/23.35 tff(1253,plain,
% 35.49/23.35 (trans(s38, s39)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1252, 1249, 8])).
% 35.49/23.35 tff(1254,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1255,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit0, s38, s39))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1256,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit0, s38, s39)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 35.49/23.35 tff(1257,plain,
% 35.49/23.35 (node3(c_bit0, s38, s39)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1256, 81, 1253])).
% 35.49/23.35 tff(1258,plain,
% 35.49/23.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1259,plain,
% 35.49/23.35 ((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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1260,plain,
% 35.49/23.35 (((~![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))))),
% 35.49/23.35 inference(monotonicity,[status(thm)],[1259])).
% 35.49/23.35 tff(1261,plain,
% 35.49/23.35 (((~![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)))),
% 35.49/23.35 inference(transitivity,[status(thm)],[1260, 1258])).
% 35.49/23.35 tff(1262,plain,
% 35.49/23.35 ((~![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))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1263,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38) | (~node3(c_bit0, s38, s39))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 35.49/23.35 tff(1264,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s39) | node1(c_bit0, s38)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1263, 199, 1257])).
% 35.49/23.35 tff(1265,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s39)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1264, 1246])).
% 35.49/23.35 tff(1266,assumption,(~m_counter_cell_v_carry_in(c_bit0, s39)), introduced(assumption)).
% 35.49/23.35 tff(1267,plain,
% 35.49/23.35 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s39)),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1268,plain,
% 35.49/23.35 ($false),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1267, 158, 1266])).
% 35.49/23.35 tff(1269,plain,(m_counter_cell_v_carry_in(c_bit0, s39)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.35 tff(1270,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1271,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39)))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1272,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s39)) | (~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1271, 1270])).
% 35.49/23.35 tff(1273,plain,
% 35.49/23.35 ((~m_counter_cell_v_value(c_bit0, s39)) | (~node2(c_bit0, s39))),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1272, 219, 1269])).
% 35.49/23.35 tff(1274,plain,
% 35.49/23.35 (~node2(c_bit0, s39)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1273, 1265])).
% 35.49/23.35 tff(1275,plain,
% 35.49/23.35 (succ(s39, s40) <=> succ(s39, s40)),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1276,axiom,(succ(s39, s40)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound40')).
% 35.49/23.35 tff(1277,plain,
% 35.49/23.35 (succ(s39, s40)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1276, 1275])).
% 35.49/23.35 tff(1278,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1279,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s39, s40)) | trans(s39, s40))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1280,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s39, s40)) | trans(s39, s40)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1279, 1278])).
% 35.49/23.35 tff(1281,plain,
% 35.49/23.35 (trans(s39, s40)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1280, 1277, 8])).
% 35.49/23.35 tff(1282,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1283,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit0, s39, s40))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1284,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit0, s39, s40)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 35.49/23.35 tff(1285,plain,
% 35.49/23.35 (node3(c_bit0, s39, s40)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1284, 81, 1281])).
% 35.49/23.35 tff(1286,plain,
% 35.49/23.35 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1287,plain,
% 35.49/23.35 ((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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1288,plain,
% 35.49/23.35 (((~![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))))),
% 35.49/23.35 inference(monotonicity,[status(thm)],[1287])).
% 35.49/23.35 tff(1289,plain,
% 35.49/23.35 (((~![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)))),
% 35.49/23.35 inference(transitivity,[status(thm)],[1288, 1286])).
% 35.49/23.35 tff(1290,plain,
% 35.49/23.35 ((~![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)))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1291,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39) | (~node3(c_bit0, s39, s40))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1290, 1289])).
% 35.49/23.35 tff(1292,plain,
% 35.49/23.35 ((~m_counter_cell_v_value(c_bit0, s40)) | node2(c_bit0, s39)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1291, 234, 1285])).
% 35.49/23.35 tff(1293,plain,
% 35.49/23.35 (~m_counter_cell_v_value(c_bit0, s40)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1292, 1274])).
% 35.49/23.35 tff(1294,assumption,(~m_counter_cell_v_carry_in(c_bit0, s40)), introduced(assumption)).
% 35.49/23.35 tff(1295,plain,
% 35.49/23.35 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s40)),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1296,plain,
% 35.49/23.35 ($false),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1295, 158, 1294])).
% 35.49/23.35 tff(1297,plain,(m_counter_cell_v_carry_in(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.35 tff(1298,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1299,plain,
% 35.49/23.35 (((~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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1300,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.35 inference(monotonicity,[status(thm)],[1299])).
% 35.49/23.35 tff(1301,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.35 inference(transitivity,[status(thm)],[1300, 1298])).
% 35.49/23.35 tff(1302,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s40)) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1303,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s40)) | m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 35.49/23.35 tff(1304,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s40) | (~node1(c_bit0, s40))),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1303, 170, 1297])).
% 35.49/23.35 tff(1305,plain,
% 35.49/23.35 (~node1(c_bit0, s40)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1304, 1293])).
% 35.49/23.35 tff(1306,plain,
% 35.49/23.35 (succ(s40, s41) <=> succ(s40, s41)),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1307,axiom,(succ(s40, s41)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound41')).
% 35.49/23.35 tff(1308,plain,
% 35.49/23.35 (succ(s40, s41)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 35.49/23.35 tff(1309,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1310,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s40, s41)) | trans(s40, s41))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1311,plain,
% 35.49/23.35 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s40, s41)) | trans(s40, s41)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1310, 1309])).
% 35.49/23.35 tff(1312,plain,
% 35.49/23.35 (trans(s40, s41)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1311, 1308, 8])).
% 35.49/23.35 tff(1313,plain,
% 35.49/23.35 (((~![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))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1314,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit0, s40, s41))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1315,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit0, s40, s41)),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1314, 1313])).
% 35.49/23.35 tff(1316,plain,
% 35.49/23.35 (node3(c_bit0, s40, s41)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1315, 81, 1312])).
% 35.49/23.35 tff(1317,plain,
% 35.49/23.35 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1318,plain,
% 35.49/23.35 ((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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1319,plain,
% 35.49/23.35 (((~![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))))),
% 35.49/23.35 inference(monotonicity,[status(thm)],[1318])).
% 35.49/23.35 tff(1320,plain,
% 35.49/23.35 (((~![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)))),
% 35.49/23.35 inference(transitivity,[status(thm)],[1319, 1317])).
% 35.49/23.35 tff(1321,plain,
% 35.49/23.35 ((~![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))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1322,plain,
% 35.49/23.35 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40) | (~node3(c_bit0, s40, s41))),
% 35.49/23.35 inference(modus_ponens,[status(thm)],[1321, 1320])).
% 35.49/23.35 tff(1323,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s41) | node1(c_bit0, s40)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1322, 199, 1316])).
% 35.49/23.35 tff(1324,plain,
% 35.49/23.35 (m_counter_cell_v_value(c_bit0, s41)),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1323, 1305])).
% 35.49/23.35 tff(1325,assumption,(~m_counter_cell_v_carry_in(c_bit0, s41)), introduced(assumption)).
% 35.49/23.35 tff(1326,plain,
% 35.49/23.35 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s41)),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1327,plain,
% 35.49/23.35 ($false),
% 35.49/23.35 inference(unit_resolution,[status(thm)],[1326, 158, 1325])).
% 35.49/23.35 tff(1328,plain,(m_counter_cell_v_carry_in(c_bit0, s41)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.35 tff(1329,plain,
% 35.49/23.35 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.35 inference(rewrite,[status(thm)],[])).
% 35.49/23.35 tff(1330,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41)))),
% 35.49/23.35 inference(quant_inst,[status(thm)],[])).
% 35.49/23.35 tff(1331,plain,
% 35.49/23.35 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s41)) | (~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41))),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1330, 1329])).
% 35.49/23.36 tff(1332,plain,
% 35.49/23.36 ((~m_counter_cell_v_value(c_bit0, s41)) | (~node2(c_bit0, s41))),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1331, 219, 1328])).
% 35.49/23.36 tff(1333,plain,
% 35.49/23.36 (~node2(c_bit0, s41)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1332, 1324])).
% 35.49/23.36 tff(1334,plain,
% 35.49/23.36 (succ(s41, s42) <=> succ(s41, s42)),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1335,axiom,(succ(s41, s42)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound42')).
% 35.49/23.36 tff(1336,plain,
% 35.49/23.36 (succ(s41, s42)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1335, 1334])).
% 35.49/23.36 tff(1337,plain,
% 35.49/23.36 (((~![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))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1338,plain,
% 35.49/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s41, s42)) | trans(s41, s42))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1339,plain,
% 35.49/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s41, s42)) | trans(s41, s42)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 35.49/23.36 tff(1340,plain,
% 35.49/23.36 (trans(s41, s42)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1339, 1336, 8])).
% 35.49/23.36 tff(1341,plain,
% 35.49/23.36 (((~![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))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1342,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit0, s41, s42))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1343,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit0, s41, s42)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 35.49/23.36 tff(1344,plain,
% 35.49/23.36 (node3(c_bit0, s41, s42)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1343, 81, 1340])).
% 35.49/23.36 tff(1345,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1346,plain,
% 35.49/23.36 ((node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42))) <=> ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1347,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42))))),
% 35.49/23.36 inference(monotonicity,[status(thm)],[1346])).
% 35.49/23.36 tff(1348,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)) | (~m_counter_cell_v_value(c_bit0, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42)))),
% 35.49/23.36 inference(transitivity,[status(thm)],[1347, 1345])).
% 35.49/23.36 tff(1349,plain,
% 35.49/23.36 ((~![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)))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1350,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41) | (~node3(c_bit0, s41, s42))),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1349, 1348])).
% 35.49/23.36 tff(1351,plain,
% 35.49/23.36 ((~m_counter_cell_v_value(c_bit0, s42)) | node2(c_bit0, s41)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1350, 234, 1344])).
% 35.49/23.36 tff(1352,plain,
% 35.49/23.36 (~m_counter_cell_v_value(c_bit0, s42)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1351, 1333])).
% 35.49/23.36 tff(1353,assumption,(~m_counter_cell_v_carry_in(c_bit0, s42)), introduced(assumption)).
% 35.49/23.36 tff(1354,plain,
% 35.49/23.36 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s42)),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1355,plain,
% 35.49/23.36 ($false),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1354, 158, 1353])).
% 35.49/23.36 tff(1356,plain,(m_counter_cell_v_carry_in(c_bit0, s42)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.36 tff(1357,plain,
% 35.49/23.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1358,plain,
% 35.49/23.36 (((~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)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1359,plain,
% 35.49/23.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.36 inference(monotonicity,[status(thm)],[1358])).
% 35.49/23.36 tff(1360,plain,
% 35.49/23.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.36 inference(transitivity,[status(thm)],[1359, 1357])).
% 35.49/23.36 tff(1361,plain,
% 35.49/23.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s42)) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1362,plain,
% 35.49/23.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s42)) | m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 35.49/23.36 tff(1363,plain,
% 35.49/23.36 (m_counter_cell_v_value(c_bit0, s42) | (~node1(c_bit0, s42))),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1362, 170, 1356])).
% 35.49/23.36 tff(1364,plain,
% 35.49/23.36 (~node1(c_bit0, s42)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1363, 1352])).
% 35.49/23.36 tff(1365,plain,
% 35.49/23.36 (succ(s42, s43) <=> succ(s42, s43)),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1366,axiom,(succ(s42, s43)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound43')).
% 35.49/23.36 tff(1367,plain,
% 35.49/23.36 (succ(s42, s43)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 35.49/23.36 tff(1368,plain,
% 35.49/23.36 (((~![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))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1369,plain,
% 35.49/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s42, s43)) | trans(s42, s43))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1370,plain,
% 35.49/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s42, s43)) | trans(s42, s43)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1369, 1368])).
% 35.49/23.36 tff(1371,plain,
% 35.49/23.36 (trans(s42, s43)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1370, 1367, 8])).
% 35.49/23.36 tff(1372,plain,
% 35.49/23.36 (((~![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))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1373,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit0, s42, s43))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1374,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit0, s42, s43)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 35.49/23.36 tff(1375,plain,
% 35.49/23.36 (node3(c_bit0, s42, s43)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1374, 81, 1371])).
% 35.49/23.36 tff(1376,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1377,plain,
% 35.49/23.36 ((node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43)) <=> (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1378,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43))))),
% 35.49/23.36 inference(monotonicity,[status(thm)],[1377])).
% 35.49/23.36 tff(1379,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)) | m_counter_cell_v_value(c_bit0, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43)))),
% 35.49/23.36 inference(transitivity,[status(thm)],[1378, 1376])).
% 35.49/23.36 tff(1380,plain,
% 35.49/23.36 ((~![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))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1381,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42) | (~node3(c_bit0, s42, s43))),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1380, 1379])).
% 35.49/23.36 tff(1382,plain,
% 35.49/23.36 (m_counter_cell_v_value(c_bit0, s43) | node1(c_bit0, s42)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1381, 199, 1375])).
% 35.49/23.36 tff(1383,plain,
% 35.49/23.36 (m_counter_cell_v_value(c_bit0, s43)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1382, 1364])).
% 35.49/23.36 tff(1384,assumption,(~m_counter_cell_v_carry_in(c_bit0, s43)), introduced(assumption)).
% 35.49/23.36 tff(1385,plain,
% 35.49/23.36 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s43)),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1386,plain,
% 35.49/23.36 ($false),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1385, 158, 1384])).
% 35.49/23.36 tff(1387,plain,(m_counter_cell_v_carry_in(c_bit0, s43)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.36 tff(1388,plain,
% 35.49/23.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1389,plain,
% 35.49/23.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43)))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1390,plain,
% 35.49/23.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s43)) | (~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43))),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 35.49/23.36 tff(1391,plain,
% 35.49/23.36 ((~m_counter_cell_v_value(c_bit0, s43)) | (~node2(c_bit0, s43))),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1390, 219, 1387])).
% 35.49/23.36 tff(1392,plain,
% 35.49/23.36 (~node2(c_bit0, s43)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1391, 1383])).
% 35.49/23.36 tff(1393,plain,
% 35.49/23.36 (succ(s43, s44) <=> succ(s43, s44)),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1394,axiom,(succ(s43, s44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound44')).
% 35.49/23.36 tff(1395,plain,
% 35.49/23.36 (succ(s43, s44)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1394, 1393])).
% 35.49/23.36 tff(1396,plain,
% 35.49/23.36 (((~![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))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1397,plain,
% 35.49/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s43, s44)) | trans(s43, s44))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1398,plain,
% 35.49/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s43, s44)) | trans(s43, s44)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1397, 1396])).
% 35.49/23.36 tff(1399,plain,
% 35.49/23.36 (trans(s43, s44)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1398, 1395, 8])).
% 35.49/23.36 tff(1400,plain,
% 35.49/23.36 (((~![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))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1401,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit0, s43, s44))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1402,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit0, s43, s44)),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1401, 1400])).
% 35.49/23.36 tff(1403,plain,
% 35.49/23.36 (node3(c_bit0, s43, s44)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1402, 81, 1399])).
% 35.49/23.36 tff(1404,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1405,plain,
% 35.49/23.36 ((node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44))) <=> ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1406,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44))))),
% 35.49/23.36 inference(monotonicity,[status(thm)],[1405])).
% 35.49/23.36 tff(1407,plain,
% 35.49/23.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)) | (~m_counter_cell_v_value(c_bit0, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44)))),
% 35.49/23.36 inference(transitivity,[status(thm)],[1406, 1404])).
% 35.49/23.36 tff(1408,plain,
% 35.49/23.36 ((~![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)))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1409,plain,
% 35.49/23.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43) | (~node3(c_bit0, s43, s44))),
% 35.49/23.36 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 35.49/23.36 tff(1410,plain,
% 35.49/23.36 ((~m_counter_cell_v_value(c_bit0, s44)) | node2(c_bit0, s43)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1409, 234, 1403])).
% 35.49/23.36 tff(1411,plain,
% 35.49/23.36 (~m_counter_cell_v_value(c_bit0, s44)),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1410, 1392])).
% 35.49/23.36 tff(1412,assumption,(~m_counter_cell_v_carry_in(c_bit0, s44)), introduced(assumption)).
% 35.49/23.36 tff(1413,plain,
% 35.49/23.36 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s44)),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.49/23.36 tff(1414,plain,
% 35.49/23.36 ($false),
% 35.49/23.36 inference(unit_resolution,[status(thm)],[1413, 158, 1412])).
% 35.49/23.36 tff(1415,plain,(m_counter_cell_v_carry_in(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 35.49/23.36 tff(1416,plain,
% 35.49/23.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1417,plain,
% 35.49/23.36 (((~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)))),
% 35.49/23.36 inference(rewrite,[status(thm)],[])).
% 35.49/23.36 tff(1418,plain,
% 35.49/23.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.49/23.36 inference(monotonicity,[status(thm)],[1417])).
% 35.49/23.36 tff(1419,plain,
% 35.49/23.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.49/23.36 inference(transitivity,[status(thm)],[1418, 1416])).
% 35.49/23.36 tff(1420,plain,
% 35.49/23.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s44)) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44))),
% 35.49/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1421,plain,
% 35.56/23.36 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s44)) | m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 35.56/23.36 tff(1422,plain,
% 35.56/23.36 (m_counter_cell_v_value(c_bit0, s44) | (~node1(c_bit0, s44))),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1421, 170, 1415])).
% 35.56/23.36 tff(1423,plain,
% 35.56/23.36 (~node1(c_bit0, s44)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1422, 1411])).
% 35.56/23.36 tff(1424,plain,
% 35.56/23.36 (succ(s44, s45) <=> succ(s44, s45)),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1425,axiom,(succ(s44, s45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound45')).
% 35.56/23.36 tff(1426,plain,
% 35.56/23.36 (succ(s44, s45)),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 35.56/23.36 tff(1427,plain,
% 35.56/23.36 (((~![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))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1428,plain,
% 35.56/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s44, s45)) | trans(s44, s45))),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1429,plain,
% 35.56/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s44, s45)) | trans(s44, s45)),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 35.56/23.36 tff(1430,plain,
% 35.56/23.36 (trans(s44, s45)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1429, 1426, 8])).
% 35.56/23.36 tff(1431,plain,
% 35.56/23.36 (((~![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))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1432,plain,
% 35.56/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit0, s44, s45))),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1433,plain,
% 35.56/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit0, s44, s45)),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1432, 1431])).
% 35.56/23.36 tff(1434,plain,
% 35.56/23.36 (node3(c_bit0, s44, s45)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1433, 81, 1430])).
% 35.56/23.36 tff(1435,plain,
% 35.56/23.36 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1436,plain,
% 35.56/23.36 ((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)))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1437,plain,
% 35.56/23.36 (((~![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))))),
% 35.56/23.36 inference(monotonicity,[status(thm)],[1436])).
% 35.56/23.36 tff(1438,plain,
% 35.56/23.36 (((~![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)))),
% 35.56/23.36 inference(transitivity,[status(thm)],[1437, 1435])).
% 35.56/23.36 tff(1439,plain,
% 35.56/23.36 ((~![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))),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1440,plain,
% 35.56/23.36 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44) | (~node3(c_bit0, s44, s45))),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 35.56/23.36 tff(1441,plain,
% 35.56/23.36 (m_counter_cell_v_value(c_bit0, s45) | node1(c_bit0, s44)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1440, 199, 1434])).
% 35.56/23.36 tff(1442,plain,
% 35.56/23.36 (m_counter_cell_v_value(c_bit0, s45)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1441, 1423])).
% 35.56/23.36 tff(1443,plain,
% 35.56/23.36 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s45)),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1444,plain,
% 35.56/23.36 (m_counter_cell_v_carry_in(c_bit0, s45)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1443, 158])).
% 35.56/23.36 tff(1445,plain,
% 35.56/23.36 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1446,plain,
% 35.56/23.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45)))),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1447,plain,
% 35.56/23.36 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s45)) | (~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45))),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1446, 1445])).
% 35.56/23.36 tff(1448,plain,
% 35.56/23.36 ((~m_counter_cell_v_value(c_bit0, s45)) | (~node2(c_bit0, s45))),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1447, 219, 1444])).
% 35.56/23.36 tff(1449,plain,
% 35.56/23.36 (~node2(c_bit0, s45)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1448, 1442])).
% 35.56/23.36 tff(1450,plain,
% 35.56/23.36 (succ(s45, s46) <=> succ(s45, s46)),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1451,axiom,(succ(s45, s46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound46')).
% 35.56/23.36 tff(1452,plain,
% 35.56/23.36 (succ(s45, s46)),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 35.56/23.36 tff(1453,plain,
% 35.56/23.36 (((~![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))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1454,plain,
% 35.56/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s45, s46)) | trans(s45, s46))),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1455,plain,
% 35.56/23.36 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s45, s46)) | trans(s45, s46)),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 35.56/23.36 tff(1456,plain,
% 35.56/23.36 (trans(s45, s46)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1455, 1452, 8])).
% 35.56/23.36 tff(1457,plain,
% 35.56/23.36 (((~![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))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1458,plain,
% 35.56/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit0, s45, s46))),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1459,plain,
% 35.56/23.36 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit0, s45, s46)),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1458, 1457])).
% 35.56/23.36 tff(1460,plain,
% 35.56/23.36 (node3(c_bit0, s45, s46)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1459, 81, 1456])).
% 35.56/23.36 tff(1461,plain,
% 35.56/23.36 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1462,plain,
% 35.56/23.36 ((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)))),
% 35.56/23.36 inference(rewrite,[status(thm)],[])).
% 35.56/23.36 tff(1463,plain,
% 35.56/23.36 (((~![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))))),
% 35.56/23.36 inference(monotonicity,[status(thm)],[1462])).
% 35.56/23.36 tff(1464,plain,
% 35.56/23.36 (((~![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)))),
% 35.56/23.36 inference(transitivity,[status(thm)],[1463, 1461])).
% 35.56/23.36 tff(1465,plain,
% 35.56/23.36 ((~![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)))),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1466,plain,
% 35.56/23.36 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45) | (~node3(c_bit0, s45, s46))),
% 35.56/23.36 inference(modus_ponens,[status(thm)],[1465, 1464])).
% 35.56/23.36 tff(1467,plain,
% 35.56/23.36 ((~m_counter_cell_v_value(c_bit0, s46)) | node2(c_bit0, s45)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1466, 234, 1460])).
% 35.56/23.36 tff(1468,plain,
% 35.56/23.36 (~m_counter_cell_v_value(c_bit0, s46)),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1467, 1449])).
% 35.56/23.36 tff(1469,assumption,(~m_counter_cell_v_carry_in(c_bit0, s46)), introduced(assumption)).
% 35.56/23.36 tff(1470,plain,
% 35.56/23.36 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s46)),
% 35.56/23.36 inference(quant_inst,[status(thm)],[])).
% 35.56/23.36 tff(1471,plain,
% 35.56/23.36 ($false),
% 35.56/23.36 inference(unit_resolution,[status(thm)],[1470, 158, 1469])).
% 35.56/23.36 tff(1472,plain,(m_counter_cell_v_carry_in(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.36 tff(1473,plain,
% 35.56/23.36 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1474,plain,
% 35.56/23.37 (((~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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1475,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.56/23.37 inference(monotonicity,[status(thm)],[1474])).
% 35.56/23.37 tff(1476,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.56/23.37 inference(transitivity,[status(thm)],[1475, 1473])).
% 35.56/23.37 tff(1477,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s46)) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1478,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s46)) | m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 35.56/23.37 tff(1479,plain,
% 35.56/23.37 (m_counter_cell_v_value(c_bit0, s46) | (~node1(c_bit0, s46))),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1478, 170, 1472])).
% 35.56/23.37 tff(1480,plain,
% 35.56/23.37 (~node1(c_bit0, s46)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1479, 1468])).
% 35.56/23.37 tff(1481,plain,
% 35.56/23.37 (succ(s46, s47) <=> succ(s46, s47)),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1482,axiom,(succ(s46, s47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound47')).
% 35.56/23.37 tff(1483,plain,
% 35.56/23.37 (succ(s46, s47)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1482, 1481])).
% 35.56/23.37 tff(1484,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1485,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s46, s47)) | trans(s46, s47))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1486,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s46, s47)) | trans(s46, s47)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 35.56/23.37 tff(1487,plain,
% 35.56/23.37 (trans(s46, s47)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1486, 1483, 8])).
% 35.56/23.37 tff(1488,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1489,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit0, s46, s47))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1490,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit0, s46, s47)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1489, 1488])).
% 35.56/23.37 tff(1491,plain,
% 35.56/23.37 (node3(c_bit0, s46, s47)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1490, 81, 1487])).
% 35.56/23.37 tff(1492,plain,
% 35.56/23.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1493,plain,
% 35.56/23.37 ((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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1494,plain,
% 35.56/23.37 (((~![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))))),
% 35.56/23.37 inference(monotonicity,[status(thm)],[1493])).
% 35.56/23.37 tff(1495,plain,
% 35.56/23.37 (((~![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)))),
% 35.56/23.37 inference(transitivity,[status(thm)],[1494, 1492])).
% 35.56/23.37 tff(1496,plain,
% 35.56/23.37 ((~![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))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1497,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46) | (~node3(c_bit0, s46, s47))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1496, 1495])).
% 35.56/23.37 tff(1498,plain,
% 35.56/23.37 (m_counter_cell_v_value(c_bit0, s47) | node1(c_bit0, s46)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1497, 199, 1491])).
% 35.56/23.37 tff(1499,plain,
% 35.56/23.37 (m_counter_cell_v_value(c_bit0, s47)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1498, 1480])).
% 35.56/23.37 tff(1500,assumption,(~m_counter_cell_v_carry_in(c_bit0, s47)), introduced(assumption)).
% 35.56/23.37 tff(1501,plain,
% 35.56/23.37 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s47)),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1502,plain,
% 35.56/23.37 ($false),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1501, 158, 1500])).
% 35.56/23.37 tff(1503,plain,(m_counter_cell_v_carry_in(c_bit0, s47)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.37 tff(1504,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1505,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47)))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1506,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s47)) | (~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 35.56/23.37 tff(1507,plain,
% 35.56/23.37 ((~m_counter_cell_v_value(c_bit0, s47)) | (~node2(c_bit0, s47))),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1506, 219, 1503])).
% 35.56/23.37 tff(1508,plain,
% 35.56/23.37 (~node2(c_bit0, s47)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1507, 1499])).
% 35.56/23.37 tff(1509,plain,
% 35.56/23.37 (succ(s47, s48) <=> succ(s47, s48)),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1510,axiom,(succ(s47, s48)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound48')).
% 35.56/23.37 tff(1511,plain,
% 35.56/23.37 (succ(s47, s48)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1510, 1509])).
% 35.56/23.37 tff(1512,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1513,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s47, s48)) | trans(s47, s48))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1514,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s47, s48)) | trans(s47, s48)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 35.56/23.37 tff(1515,plain,
% 35.56/23.37 (trans(s47, s48)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1514, 1511, 8])).
% 35.56/23.37 tff(1516,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1517,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit0, s47, s48))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1518,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit0, s47, s48)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1517, 1516])).
% 35.56/23.37 tff(1519,plain,
% 35.56/23.37 (node3(c_bit0, s47, s48)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1518, 81, 1515])).
% 35.56/23.37 tff(1520,plain,
% 35.56/23.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1521,plain,
% 35.56/23.37 ((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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1522,plain,
% 35.56/23.37 (((~![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))))),
% 35.56/23.37 inference(monotonicity,[status(thm)],[1521])).
% 35.56/23.37 tff(1523,plain,
% 35.56/23.37 (((~![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)))),
% 35.56/23.37 inference(transitivity,[status(thm)],[1522, 1520])).
% 35.56/23.37 tff(1524,plain,
% 35.56/23.37 ((~![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)))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1525,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47) | (~node3(c_bit0, s47, s48))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1524, 1523])).
% 35.56/23.37 tff(1526,plain,
% 35.56/23.37 ((~m_counter_cell_v_value(c_bit0, s48)) | node2(c_bit0, s47)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1525, 234, 1519])).
% 35.56/23.37 tff(1527,plain,
% 35.56/23.37 (~m_counter_cell_v_value(c_bit0, s48)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1526, 1508])).
% 35.56/23.37 tff(1528,assumption,(~m_counter_cell_v_carry_in(c_bit0, s48)), introduced(assumption)).
% 35.56/23.37 tff(1529,plain,
% 35.56/23.37 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s48)),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1530,plain,
% 35.56/23.37 ($false),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1529, 158, 1528])).
% 35.56/23.37 tff(1531,plain,(m_counter_cell_v_carry_in(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.37 tff(1532,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1533,plain,
% 35.56/23.37 (((~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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1534,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.56/23.37 inference(monotonicity,[status(thm)],[1533])).
% 35.56/23.37 tff(1535,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.56/23.37 inference(transitivity,[status(thm)],[1534, 1532])).
% 35.56/23.37 tff(1536,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s48)) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1537,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s48)) | m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1536, 1535])).
% 35.56/23.37 tff(1538,plain,
% 35.56/23.37 (m_counter_cell_v_value(c_bit0, s48) | (~node1(c_bit0, s48))),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1537, 170, 1531])).
% 35.56/23.37 tff(1539,plain,
% 35.56/23.37 (~node1(c_bit0, s48)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1538, 1527])).
% 35.56/23.37 tff(1540,plain,
% 35.56/23.37 (succ(s48, s49) <=> succ(s48, s49)),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1541,axiom,(succ(s48, s49)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound49')).
% 35.56/23.37 tff(1542,plain,
% 35.56/23.37 (succ(s48, s49)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 35.56/23.37 tff(1543,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1544,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s48, s49)) | trans(s48, s49))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1545,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s48, s49)) | trans(s48, s49)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1544, 1543])).
% 35.56/23.37 tff(1546,plain,
% 35.56/23.37 (trans(s48, s49)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1545, 1542, 8])).
% 35.56/23.37 tff(1547,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1548,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit0, s48, s49))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1549,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit0, s48, s49)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 35.56/23.37 tff(1550,plain,
% 35.56/23.37 (node3(c_bit0, s48, s49)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1549, 81, 1546])).
% 35.56/23.37 tff(1551,plain,
% 35.56/23.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1552,plain,
% 35.56/23.37 ((node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49)) <=> (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1553,plain,
% 35.56/23.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49))))),
% 35.56/23.37 inference(monotonicity,[status(thm)],[1552])).
% 35.56/23.37 tff(1554,plain,
% 35.56/23.37 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)) | m_counter_cell_v_value(c_bit0, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49)))),
% 35.56/23.37 inference(transitivity,[status(thm)],[1553, 1551])).
% 35.56/23.37 tff(1555,plain,
% 35.56/23.37 ((~![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))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1556,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48) | (~node3(c_bit0, s48, s49))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 35.56/23.37 tff(1557,plain,
% 35.56/23.37 (m_counter_cell_v_value(c_bit0, s49) | node1(c_bit0, s48)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1556, 199, 1550])).
% 35.56/23.37 tff(1558,plain,
% 35.56/23.37 (m_counter_cell_v_value(c_bit0, s49)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1557, 1539])).
% 35.56/23.37 tff(1559,assumption,(~m_counter_cell_v_carry_in(c_bit0, s49)), introduced(assumption)).
% 35.56/23.37 tff(1560,plain,
% 35.56/23.37 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s49)),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1561,plain,
% 35.56/23.37 ($false),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1560, 158, 1559])).
% 35.56/23.37 tff(1562,plain,(m_counter_cell_v_carry_in(c_bit0, s49)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.37 tff(1563,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1564,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49)))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1565,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s49)) | (~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 35.56/23.37 tff(1566,plain,
% 35.56/23.37 ((~m_counter_cell_v_value(c_bit0, s49)) | (~node2(c_bit0, s49))),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1565, 219, 1562])).
% 35.56/23.37 tff(1567,plain,
% 35.56/23.37 (~node2(c_bit0, s49)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1566, 1558])).
% 35.56/23.37 tff(1568,plain,
% 35.56/23.37 (succ(s49, s50) <=> succ(s49, s50)),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1569,axiom,(succ(s49, s50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound50')).
% 35.56/23.37 tff(1570,plain,
% 35.56/23.37 (succ(s49, s50)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1569, 1568])).
% 35.56/23.37 tff(1571,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1572,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s49, s50)) | trans(s49, s50))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1573,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s49, s50)) | trans(s49, s50)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 35.56/23.37 tff(1574,plain,
% 35.56/23.37 (trans(s49, s50)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1573, 1570, 8])).
% 35.56/23.37 tff(1575,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1576,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit0, s49, s50))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1577,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit0, s49, s50)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1576, 1575])).
% 35.56/23.37 tff(1578,plain,
% 35.56/23.37 (node3(c_bit0, s49, s50)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1577, 81, 1574])).
% 35.56/23.37 tff(1579,plain,
% 35.56/23.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1580,plain,
% 35.56/23.37 ((node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50))) <=> ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1581,plain,
% 35.56/23.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50))))),
% 35.56/23.37 inference(monotonicity,[status(thm)],[1580])).
% 35.56/23.37 tff(1582,plain,
% 35.56/23.37 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)) | (~m_counter_cell_v_value(c_bit0, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50)))),
% 35.56/23.37 inference(transitivity,[status(thm)],[1581, 1579])).
% 35.56/23.37 tff(1583,plain,
% 35.56/23.37 ((~![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)))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1584,plain,
% 35.56/23.37 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49) | (~node3(c_bit0, s49, s50))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1583, 1582])).
% 35.56/23.37 tff(1585,plain,
% 35.56/23.37 ((~m_counter_cell_v_value(c_bit0, s50)) | node2(c_bit0, s49)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1584, 234, 1578])).
% 35.56/23.37 tff(1586,plain,
% 35.56/23.37 (~m_counter_cell_v_value(c_bit0, s50)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1585, 1567])).
% 35.56/23.37 tff(1587,assumption,(~m_counter_cell_v_carry_in(c_bit0, s50)), introduced(assumption)).
% 35.56/23.37 tff(1588,plain,
% 35.56/23.37 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s50)),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1589,plain,
% 35.56/23.37 ($false),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1588, 158, 1587])).
% 35.56/23.37 tff(1590,plain,(m_counter_cell_v_carry_in(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.37 tff(1591,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1592,plain,
% 35.56/23.37 (((~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)))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1593,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.56/23.37 inference(monotonicity,[status(thm)],[1592])).
% 35.56/23.37 tff(1594,plain,
% 35.56/23.37 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.56/23.37 inference(transitivity,[status(thm)],[1593, 1591])).
% 35.56/23.37 tff(1595,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s50)) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1596,plain,
% 35.56/23.37 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s50)) | m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1595, 1594])).
% 35.56/23.37 tff(1597,plain,
% 35.56/23.37 (m_counter_cell_v_value(c_bit0, s50) | (~node1(c_bit0, s50))),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1596, 170, 1590])).
% 35.56/23.37 tff(1598,plain,
% 35.56/23.37 (~node1(c_bit0, s50)),
% 35.56/23.37 inference(unit_resolution,[status(thm)],[1597, 1586])).
% 35.56/23.37 tff(1599,plain,
% 35.56/23.37 (succ(s50, s51) <=> succ(s50, s51)),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1600,axiom,(succ(s50, s51)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound51')).
% 35.56/23.37 tff(1601,plain,
% 35.56/23.37 (succ(s50, s51)),
% 35.56/23.37 inference(modus_ponens,[status(thm)],[1600, 1599])).
% 35.56/23.37 tff(1602,plain,
% 35.56/23.37 (((~![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))),
% 35.56/23.37 inference(rewrite,[status(thm)],[])).
% 35.56/23.37 tff(1603,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s50, s51)) | trans(s50, s51))),
% 35.56/23.37 inference(quant_inst,[status(thm)],[])).
% 35.56/23.37 tff(1604,plain,
% 35.56/23.37 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s50, s51)) | trans(s50, s51)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 35.56/23.38 tff(1605,plain,
% 35.56/23.38 (trans(s50, s51)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1604, 1601, 8])).
% 35.56/23.38 tff(1606,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1607,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit0, s50, s51))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1608,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit0, s50, s51)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1607, 1606])).
% 35.56/23.38 tff(1609,plain,
% 35.56/23.38 (node3(c_bit0, s50, s51)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1608, 81, 1605])).
% 35.56/23.38 tff(1610,plain,
% 35.56/23.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1611,plain,
% 35.56/23.38 ((node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51)) <=> (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1612,plain,
% 35.56/23.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51))))),
% 35.56/23.38 inference(monotonicity,[status(thm)],[1611])).
% 35.56/23.38 tff(1613,plain,
% 35.56/23.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)) | m_counter_cell_v_value(c_bit0, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51)))),
% 35.56/23.38 inference(transitivity,[status(thm)],[1612, 1610])).
% 35.56/23.38 tff(1614,plain,
% 35.56/23.38 ((~![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))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1615,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50) | (~node3(c_bit0, s50, s51))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1614, 1613])).
% 35.56/23.38 tff(1616,plain,
% 35.56/23.38 (m_counter_cell_v_value(c_bit0, s51) | node1(c_bit0, s50)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1615, 199, 1609])).
% 35.56/23.38 tff(1617,plain,
% 35.56/23.38 (m_counter_cell_v_value(c_bit0, s51)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1616, 1598])).
% 35.56/23.38 tff(1618,assumption,(~m_counter_cell_v_carry_in(c_bit0, s51)), introduced(assumption)).
% 35.56/23.38 tff(1619,plain,
% 35.56/23.38 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s51)),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1620,plain,
% 35.56/23.38 ($false),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1619, 158, 1618])).
% 35.56/23.38 tff(1621,plain,(m_counter_cell_v_carry_in(c_bit0, s51)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.38 tff(1622,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1623,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51)))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1624,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s51)) | (~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1623, 1622])).
% 35.56/23.38 tff(1625,plain,
% 35.56/23.38 ((~m_counter_cell_v_value(c_bit0, s51)) | (~node2(c_bit0, s51))),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1624, 219, 1621])).
% 35.56/23.38 tff(1626,plain,
% 35.56/23.38 (~node2(c_bit0, s51)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1625, 1617])).
% 35.56/23.38 tff(1627,plain,
% 35.56/23.38 (succ(s51, s52) <=> succ(s51, s52)),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1628,axiom,(succ(s51, s52)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound52')).
% 35.56/23.38 tff(1629,plain,
% 35.56/23.38 (succ(s51, s52)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1628, 1627])).
% 35.56/23.38 tff(1630,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1631,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s51, s52)) | trans(s51, s52))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1632,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s51, s52)) | trans(s51, s52)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 35.56/23.38 tff(1633,plain,
% 35.56/23.38 (trans(s51, s52)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1632, 1629, 8])).
% 35.56/23.38 tff(1634,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1635,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit0, s51, s52))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1636,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit0, s51, s52)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 35.56/23.38 tff(1637,plain,
% 35.56/23.38 (node3(c_bit0, s51, s52)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1636, 81, 1633])).
% 35.56/23.38 tff(1638,plain,
% 35.56/23.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1639,plain,
% 35.56/23.38 ((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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1640,plain,
% 35.56/23.38 (((~![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))))),
% 35.56/23.38 inference(monotonicity,[status(thm)],[1639])).
% 35.56/23.38 tff(1641,plain,
% 35.56/23.38 (((~![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)))),
% 35.56/23.38 inference(transitivity,[status(thm)],[1640, 1638])).
% 35.56/23.38 tff(1642,plain,
% 35.56/23.38 ((~![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)))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1643,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51) | (~node3(c_bit0, s51, s52))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1642, 1641])).
% 35.56/23.38 tff(1644,plain,
% 35.56/23.38 ((~m_counter_cell_v_value(c_bit0, s52)) | node2(c_bit0, s51)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1643, 234, 1637])).
% 35.56/23.38 tff(1645,plain,
% 35.56/23.38 (~m_counter_cell_v_value(c_bit0, s52)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1644, 1626])).
% 35.56/23.38 tff(1646,assumption,(~m_counter_cell_v_carry_in(c_bit0, s52)), introduced(assumption)).
% 35.56/23.38 tff(1647,plain,
% 35.56/23.38 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s52)),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1648,plain,
% 35.56/23.38 ($false),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1647, 158, 1646])).
% 35.56/23.38 tff(1649,plain,(m_counter_cell_v_carry_in(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.38 tff(1650,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1651,plain,
% 35.56/23.38 (((~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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1652,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.56/23.38 inference(monotonicity,[status(thm)],[1651])).
% 35.56/23.38 tff(1653,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.56/23.38 inference(transitivity,[status(thm)],[1652, 1650])).
% 35.56/23.38 tff(1654,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s52)) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1655,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s52)) | m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1654, 1653])).
% 35.56/23.38 tff(1656,plain,
% 35.56/23.38 (m_counter_cell_v_value(c_bit0, s52) | (~node1(c_bit0, s52))),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1655, 170, 1649])).
% 35.56/23.38 tff(1657,plain,
% 35.56/23.38 (~node1(c_bit0, s52)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1656, 1645])).
% 35.56/23.38 tff(1658,plain,
% 35.56/23.38 (succ(s52, s53) <=> succ(s52, s53)),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1659,axiom,(succ(s52, s53)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound53')).
% 35.56/23.38 tff(1660,plain,
% 35.56/23.38 (succ(s52, s53)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 35.56/23.38 tff(1661,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1662,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s52, s53)) | trans(s52, s53))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1663,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s52, s53)) | trans(s52, s53)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 35.56/23.38 tff(1664,plain,
% 35.56/23.38 (trans(s52, s53)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1663, 1660, 8])).
% 35.56/23.38 tff(1665,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1666,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit0, s52, s53))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1667,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit0, s52, s53)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1666, 1665])).
% 35.56/23.38 tff(1668,plain,
% 35.56/23.38 (node3(c_bit0, s52, s53)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1667, 81, 1664])).
% 35.56/23.38 tff(1669,plain,
% 35.56/23.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~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))) | node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1670,plain,
% 35.56/23.38 ((node1(c_bit0, s52) | (~node3(c_bit0, s52, s53)) | m_counter_cell_v_value(c_bit0, s53)) <=> (node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1671,plain,
% 35.56/23.38 (((~![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))) | (node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53))))),
% 35.56/23.38 inference(monotonicity,[status(thm)],[1670])).
% 35.56/23.38 tff(1672,plain,
% 35.56/23.38 (((~![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))) | node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53)))),
% 35.56/23.38 inference(transitivity,[status(thm)],[1671, 1669])).
% 35.56/23.38 tff(1673,plain,
% 35.56/23.38 ((~![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))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1674,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53) | (~node3(c_bit0, s52, s53))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 35.56/23.38 tff(1675,plain,
% 35.56/23.38 (node1(c_bit0, s52) | m_counter_cell_v_value(c_bit0, s53)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1674, 199, 1668])).
% 35.56/23.38 tff(1676,plain,
% 35.56/23.38 (m_counter_cell_v_value(c_bit0, s53)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1675, 1657])).
% 35.56/23.38 tff(1677,assumption,(~m_counter_cell_v_carry_in(c_bit0, s53)), introduced(assumption)).
% 35.56/23.38 tff(1678,plain,
% 35.56/23.38 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s53)),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1679,plain,
% 35.56/23.38 ($false),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1678, 158, 1677])).
% 35.56/23.38 tff(1680,plain,(m_counter_cell_v_carry_in(c_bit0, s53)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.38 tff(1681,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1682,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53)))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1683,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s53)) | (~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 35.56/23.38 tff(1684,plain,
% 35.56/23.38 ((~m_counter_cell_v_value(c_bit0, s53)) | (~node2(c_bit0, s53))),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1683, 219, 1680])).
% 35.56/23.38 tff(1685,plain,
% 35.56/23.38 (~node2(c_bit0, s53)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1684, 1676])).
% 35.56/23.38 tff(1686,plain,
% 35.56/23.38 (succ(s53, s54) <=> succ(s53, s54)),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1687,axiom,(succ(s53, s54)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound54')).
% 35.56/23.38 tff(1688,plain,
% 35.56/23.38 (succ(s53, s54)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1687, 1686])).
% 35.56/23.38 tff(1689,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1690,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s53, s54)) | trans(s53, s54))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1691,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s53, s54)) | trans(s53, s54)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 35.56/23.38 tff(1692,plain,
% 35.56/23.38 (trans(s53, s54)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1691, 1688, 8])).
% 35.56/23.38 tff(1693,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1694,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit0, s53, s54))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1695,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit0, s53, s54)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 35.56/23.38 tff(1696,plain,
% 35.56/23.38 (node3(c_bit0, s53, s54)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1695, 81, 1692])).
% 35.56/23.38 tff(1697,plain,
% 35.56/23.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1698,plain,
% 35.56/23.38 ((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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1699,plain,
% 35.56/23.38 (((~![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))))),
% 35.56/23.38 inference(monotonicity,[status(thm)],[1698])).
% 35.56/23.38 tff(1700,plain,
% 35.56/23.38 (((~![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)))),
% 35.56/23.38 inference(transitivity,[status(thm)],[1699, 1697])).
% 35.56/23.38 tff(1701,plain,
% 35.56/23.38 ((~![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)))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1702,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53) | (~node3(c_bit0, s53, s54))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1701, 1700])).
% 35.56/23.38 tff(1703,plain,
% 35.56/23.38 ((~m_counter_cell_v_value(c_bit0, s54)) | node2(c_bit0, s53)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1702, 234, 1696])).
% 35.56/23.38 tff(1704,plain,
% 35.56/23.38 (~m_counter_cell_v_value(c_bit0, s54)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1703, 1685])).
% 35.56/23.38 tff(1705,assumption,(~m_counter_cell_v_carry_in(c_bit0, s54)), introduced(assumption)).
% 35.56/23.38 tff(1706,plain,
% 35.56/23.38 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s54)),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1707,plain,
% 35.56/23.38 ($false),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1706, 158, 1705])).
% 35.56/23.38 tff(1708,plain,(m_counter_cell_v_carry_in(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.38 tff(1709,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1710,plain,
% 35.56/23.38 (((~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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1711,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.56/23.38 inference(monotonicity,[status(thm)],[1710])).
% 35.56/23.38 tff(1712,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.56/23.38 inference(transitivity,[status(thm)],[1711, 1709])).
% 35.56/23.38 tff(1713,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s54)) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1714,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s54)) | m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1713, 1712])).
% 35.56/23.38 tff(1715,plain,
% 35.56/23.38 (m_counter_cell_v_value(c_bit0, s54) | (~node1(c_bit0, s54))),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1714, 170, 1708])).
% 35.56/23.38 tff(1716,plain,
% 35.56/23.38 (~node1(c_bit0, s54)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1715, 1704])).
% 35.56/23.38 tff(1717,plain,
% 35.56/23.38 (succ(s54, s55) <=> succ(s54, s55)),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1718,axiom,(succ(s54, s55)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound55')).
% 35.56/23.38 tff(1719,plain,
% 35.56/23.38 (succ(s54, s55)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1718, 1717])).
% 35.56/23.38 tff(1720,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1721,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s54, s55)) | trans(s54, s55))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1722,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s54, s55)) | trans(s54, s55)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1721, 1720])).
% 35.56/23.38 tff(1723,plain,
% 35.56/23.38 (trans(s54, s55)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1722, 1719, 8])).
% 35.56/23.38 tff(1724,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1725,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit0, s54, s55))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1726,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit0, s54, s55)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 35.56/23.38 tff(1727,plain,
% 35.56/23.38 (node3(c_bit0, s54, s55)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1726, 81, 1723])).
% 35.56/23.38 tff(1728,plain,
% 35.56/23.38 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1729,plain,
% 35.56/23.38 ((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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1730,plain,
% 35.56/23.38 (((~![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))))),
% 35.56/23.38 inference(monotonicity,[status(thm)],[1729])).
% 35.56/23.38 tff(1731,plain,
% 35.56/23.38 (((~![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)))),
% 35.56/23.38 inference(transitivity,[status(thm)],[1730, 1728])).
% 35.56/23.38 tff(1732,plain,
% 35.56/23.38 ((~![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))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1733,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54) | (~node3(c_bit0, s54, s55))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1732, 1731])).
% 35.56/23.38 tff(1734,plain,
% 35.56/23.38 (m_counter_cell_v_value(c_bit0, s55) | node1(c_bit0, s54)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1733, 199, 1727])).
% 35.56/23.38 tff(1735,plain,
% 35.56/23.38 (m_counter_cell_v_value(c_bit0, s55)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1734, 1716])).
% 35.56/23.38 tff(1736,assumption,(~m_counter_cell_v_carry_in(c_bit0, s55)), introduced(assumption)).
% 35.56/23.38 tff(1737,plain,
% 35.56/23.38 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s55)),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1738,plain,
% 35.56/23.38 ($false),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1737, 158, 1736])).
% 35.56/23.38 tff(1739,plain,(m_counter_cell_v_carry_in(c_bit0, s55)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.38 tff(1740,plain,
% 35.56/23.38 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1741,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55)))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1742,plain,
% 35.56/23.38 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s55)) | (~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55))),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 35.56/23.38 tff(1743,plain,
% 35.56/23.38 ((~m_counter_cell_v_value(c_bit0, s55)) | (~node2(c_bit0, s55))),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1742, 219, 1739])).
% 35.56/23.38 tff(1744,plain,
% 35.56/23.38 (~node2(c_bit0, s55)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1743, 1735])).
% 35.56/23.38 tff(1745,plain,
% 35.56/23.38 (succ(s55, s56) <=> succ(s55, s56)),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1746,axiom,(succ(s55, s56)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound56')).
% 35.56/23.38 tff(1747,plain,
% 35.56/23.38 (succ(s55, s56)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1746, 1745])).
% 35.56/23.38 tff(1748,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1749,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s55, s56)) | trans(s55, s56))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1750,plain,
% 35.56/23.38 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s55, s56)) | trans(s55, s56)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 35.56/23.38 tff(1751,plain,
% 35.56/23.38 (trans(s55, s56)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1750, 1747, 8])).
% 35.56/23.38 tff(1752,plain,
% 35.56/23.38 (((~![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))),
% 35.56/23.38 inference(rewrite,[status(thm)],[])).
% 35.56/23.38 tff(1753,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit0, s55, s56))),
% 35.56/23.38 inference(quant_inst,[status(thm)],[])).
% 35.56/23.38 tff(1754,plain,
% 35.56/23.38 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit0, s55, s56)),
% 35.56/23.38 inference(modus_ponens,[status(thm)],[1753, 1752])).
% 35.56/23.38 tff(1755,plain,
% 35.56/23.38 (node3(c_bit0, s55, s56)),
% 35.56/23.38 inference(unit_resolution,[status(thm)],[1754, 81, 1751])).
% 35.56/23.38 tff(1756,plain,
% 35.56/23.38 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s56)) | (~node3(c_bit0, s55, s56)) | node2(c_bit0, s55))) <=> ((~![Y: $i, I0: $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)) | (~node3(c_bit0, s55, s56)) | node2(c_bit0, s55))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1757,plain,
% 35.56/23.39 ((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)) | (~node3(c_bit0, s55, s56)) | node2(c_bit0, s55))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1758,plain,
% 35.56/23.39 (((~![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)) | (~node3(c_bit0, s55, s56)) | node2(c_bit0, s55)))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1757])).
% 35.56/23.39 tff(1759,plain,
% 35.56/23.39 (((~![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)) | (~node3(c_bit0, s55, s56)) | node2(c_bit0, s55))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1758, 1756])).
% 35.56/23.39 tff(1760,plain,
% 35.56/23.39 ((~![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)))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1761,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s56)) | (~node3(c_bit0, s55, s56)) | node2(c_bit0, s55)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 35.56/23.39 tff(1762,plain,
% 35.56/23.39 ((~m_counter_cell_v_value(c_bit0, s56)) | node2(c_bit0, s55)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1761, 234, 1755])).
% 35.56/23.39 tff(1763,plain,
% 35.56/23.39 (~m_counter_cell_v_value(c_bit0, s56)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1762, 1744])).
% 35.56/23.39 tff(1764,assumption,(~m_counter_cell_v_carry_in(c_bit0, s56)), introduced(assumption)).
% 35.56/23.39 tff(1765,plain,
% 35.56/23.39 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s56)),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1766,plain,
% 35.56/23.39 ($false),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1765, 158, 1764])).
% 35.56/23.39 tff(1767,plain,(m_counter_cell_v_carry_in(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.39 tff(1768,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1769,plain,
% 35.56/23.39 (((~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)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1770,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1769])).
% 35.56/23.39 tff(1771,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1770, 1768])).
% 35.56/23.39 tff(1772,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s56)) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1773,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s56)) | m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1772, 1771])).
% 35.56/23.39 tff(1774,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s56) | (~node1(c_bit0, s56))),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1773, 170, 1767])).
% 35.56/23.39 tff(1775,plain,
% 35.56/23.39 (~node1(c_bit0, s56)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1774, 1763])).
% 35.56/23.39 tff(1776,plain,
% 35.56/23.39 (succ(s56, s57) <=> succ(s56, s57)),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1777,axiom,(succ(s56, s57)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound57')).
% 35.56/23.39 tff(1778,plain,
% 35.56/23.39 (succ(s56, s57)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1777, 1776])).
% 35.56/23.39 tff(1779,plain,
% 35.56/23.39 (((~![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))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1780,plain,
% 35.56/23.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s56, s57)) | trans(s56, s57))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1781,plain,
% 35.56/23.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s56, s57)) | trans(s56, s57)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 35.56/23.39 tff(1782,plain,
% 35.56/23.39 (trans(s56, s57)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1781, 1778, 8])).
% 35.56/23.39 tff(1783,plain,
% 35.56/23.39 (((~![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))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1784,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit0, s56, s57))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1785,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit0, s56, s57)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1784, 1783])).
% 35.56/23.39 tff(1786,plain,
% 35.56/23.39 (node3(c_bit0, s56, s57)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1785, 81, 1782])).
% 35.56/23.39 tff(1787,plain,
% 35.56/23.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1788,plain,
% 35.56/23.39 ((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))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1789,plain,
% 35.56/23.39 (((~![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)))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1788])).
% 35.56/23.39 tff(1790,plain,
% 35.56/23.39 (((~![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))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1789, 1787])).
% 35.56/23.39 tff(1791,plain,
% 35.56/23.39 ((~![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))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1792,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s57) | (~node3(c_bit0, s56, s57)) | node1(c_bit0, s56)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 35.56/23.39 tff(1793,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s57) | node1(c_bit0, s56)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1792, 199, 1786])).
% 35.56/23.39 tff(1794,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s57)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1793, 1775])).
% 35.56/23.39 tff(1795,assumption,(~m_counter_cell_v_carry_in(c_bit0, s57)), introduced(assumption)).
% 35.56/23.39 tff(1796,plain,
% 35.56/23.39 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s57)),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1797,plain,
% 35.56/23.39 ($false),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1796, 158, 1795])).
% 35.56/23.39 tff(1798,plain,(m_counter_cell_v_carry_in(c_bit0, s57)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.39 tff(1799,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1800,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57)))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1801,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s57)) | (~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1800, 1799])).
% 35.56/23.39 tff(1802,plain,
% 35.56/23.39 ((~m_counter_cell_v_value(c_bit0, s57)) | (~node2(c_bit0, s57))),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1801, 219, 1798])).
% 35.56/23.39 tff(1803,plain,
% 35.56/23.39 (~node2(c_bit0, s57)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1802, 1794])).
% 35.56/23.39 tff(1804,plain,
% 35.56/23.39 (succ(s57, s58) <=> succ(s57, s58)),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1805,axiom,(succ(s57, s58)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound58')).
% 35.56/23.39 tff(1806,plain,
% 35.56/23.39 (succ(s57, s58)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1805, 1804])).
% 35.56/23.39 tff(1807,plain,
% 35.56/23.39 (((~![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))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1808,plain,
% 35.56/23.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s57, s58)) | trans(s57, s58))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1809,plain,
% 35.56/23.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s57, s58)) | trans(s57, s58)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 35.56/23.39 tff(1810,plain,
% 35.56/23.39 (trans(s57, s58)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1809, 1806, 8])).
% 35.56/23.39 tff(1811,plain,
% 35.56/23.39 (((~![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))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1812,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit0, s57, s58))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1813,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit0, s57, s58)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1812, 1811])).
% 35.56/23.39 tff(1814,plain,
% 35.56/23.39 (node3(c_bit0, s57, s58)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1813, 81, 1810])).
% 35.56/23.39 tff(1815,plain,
% 35.56/23.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~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)))) | node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1816,plain,
% 35.56/23.39 ((node2(c_bit0, s57) | (~node3(c_bit0, s57, s58)) | (~m_counter_cell_v_value(c_bit0, s58))) <=> (node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1817,plain,
% 35.56/23.39 (((~![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)))) | (node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58))))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1816])).
% 35.56/23.39 tff(1818,plain,
% 35.56/23.39 (((~![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)))) | node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58)))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1817, 1815])).
% 35.56/23.39 tff(1819,plain,
% 35.56/23.39 ((~![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)))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1820,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58)) | (~node3(c_bit0, s57, s58))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1819, 1818])).
% 35.56/23.39 tff(1821,plain,
% 35.56/23.39 (node2(c_bit0, s57) | (~m_counter_cell_v_value(c_bit0, s58))),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1820, 234, 1814])).
% 35.56/23.39 tff(1822,plain,
% 35.56/23.39 (~m_counter_cell_v_value(c_bit0, s58)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1821, 1803])).
% 35.56/23.39 tff(1823,assumption,(~m_counter_cell_v_carry_in(c_bit0, s58)), introduced(assumption)).
% 35.56/23.39 tff(1824,plain,
% 35.56/23.39 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s58)),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1825,plain,
% 35.56/23.39 ($false),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1824, 158, 1823])).
% 35.56/23.39 tff(1826,plain,(m_counter_cell_v_carry_in(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.39 tff(1827,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1828,plain,
% 35.56/23.39 (((~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)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1829,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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))))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1828])).
% 35.56/23.39 tff(1830,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_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)))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1829, 1827])).
% 35.56/23.39 tff(1831,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s58)) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1832,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s58)) | m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1831, 1830])).
% 35.56/23.39 tff(1833,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s58) | (~node1(c_bit0, s58))),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1832, 170, 1826])).
% 35.56/23.39 tff(1834,plain,
% 35.56/23.39 (~node1(c_bit0, s58)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1833, 1822])).
% 35.56/23.39 tff(1835,plain,
% 35.56/23.39 (succ(s58, s59) <=> succ(s58, s59)),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1836,axiom,(succ(s58, s59)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound59')).
% 35.56/23.39 tff(1837,plain,
% 35.56/23.39 (succ(s58, s59)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 35.56/23.39 tff(1838,plain,
% 35.56/23.39 (((~![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))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1839,plain,
% 35.56/23.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s58, s59)) | trans(s58, s59))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1840,plain,
% 35.56/23.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s58, s59)) | trans(s58, s59)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 35.56/23.39 tff(1841,plain,
% 35.56/23.39 (trans(s58, s59)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1840, 1837, 8])).
% 35.56/23.39 tff(1842,plain,
% 35.56/23.39 (((~![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))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1843,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit0, s58, s59))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1844,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit0, s58, s59)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1843, 1842])).
% 35.56/23.39 tff(1845,plain,
% 35.56/23.39 (node3(c_bit0, s58, s59)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1844, 81, 1841])).
% 35.56/23.39 tff(1846,plain,
% 35.56/23.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_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)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1847,plain,
% 35.56/23.39 ((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)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1848,plain,
% 35.56/23.39 (((~![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))))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1847])).
% 35.56/23.39 tff(1849,plain,
% 35.56/23.39 (((~![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)))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1848, 1846])).
% 35.56/23.39 tff(1850,plain,
% 35.56/23.39 ((~![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))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1851,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58) | (~node3(c_bit0, s58, s59))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1850, 1849])).
% 35.56/23.39 tff(1852,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s59) | node1(c_bit0, s58)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1851, 199, 1845])).
% 35.56/23.39 tff(1853,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s59)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1852, 1834])).
% 35.56/23.39 tff(1854,assumption,(~m_counter_cell_v_carry_in(c_bit0, s59)), introduced(assumption)).
% 35.56/23.39 tff(1855,plain,
% 35.56/23.39 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s59)),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1856,plain,
% 35.56/23.39 ($false),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1855, 158, 1854])).
% 35.56/23.39 tff(1857,plain,(m_counter_cell_v_carry_in(c_bit0, s59)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.39 tff(1858,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_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)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1859,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59)))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1860,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s59)) | (~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 35.56/23.39 tff(1861,plain,
% 35.56/23.39 ((~m_counter_cell_v_value(c_bit0, s59)) | (~node2(c_bit0, s59))),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1860, 219, 1857])).
% 35.56/23.39 tff(1862,plain,
% 35.56/23.39 (~node2(c_bit0, s59)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1861, 1853])).
% 35.56/23.39 tff(1863,plain,
% 35.56/23.39 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1864,plain,
% 35.56/23.39 ((node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)) | (~m_counter_cell_v_value(c_bit0, s60))) <=> ((~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1865,plain,
% 35.56/23.39 (((~![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, s60)) | (~m_counter_cell_v_value(c_bit0, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60))))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1864])).
% 35.56/23.39 tff(1866,plain,
% 35.56/23.39 (((~![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, s60)) | (~m_counter_cell_v_value(c_bit0, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60)))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1865, 1863])).
% 35.56/23.39 tff(1867,plain,
% 35.56/23.39 ((~![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, s60)) | (~m_counter_cell_v_value(c_bit0, s60)))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1868,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s60)) | node2(c_bit0, s59) | (~node3(c_bit0, s59, s60))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 35.56/23.39 tff(1869,plain,
% 35.56/23.39 (~m_counter_cell_v_value(c_bit0, s60)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1868, 234, 1862, 85])).
% 35.56/23.39 tff(1870,assumption,(~m_counter_cell_v_carry_in(c_bit0, s60)), introduced(assumption)).
% 35.56/23.39 tff(1871,plain,
% 35.56/23.39 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s60)),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1872,plain,
% 35.56/23.39 ($false),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1871, 158, 1870])).
% 35.56/23.39 tff(1873,plain,(m_counter_cell_v_carry_in(c_bit0, s60)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.39 tff(1874,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1875,plain,
% 35.56/23.39 (((~node1(c_bit0, s60)) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1876,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s60)) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60))))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1875])).
% 35.56/23.39 tff(1877,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s60)) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60)))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1876, 1874])).
% 35.56/23.39 tff(1878,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s60)) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1879,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s60)) | m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 35.56/23.39 tff(1880,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s60) | (~node1(c_bit0, s60))),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1879, 170, 1873])).
% 35.56/23.39 tff(1881,plain,
% 35.56/23.39 (~node1(c_bit0, s60)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1880, 1869])).
% 35.56/23.39 tff(1882,plain,
% 35.56/23.39 (succ(s60, s61) <=> succ(s60, s61)),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1883,axiom,(succ(s60, s61)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound61')).
% 35.56/23.39 tff(1884,plain,
% 35.56/23.39 (succ(s60, s61)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 35.56/23.39 tff(1885,plain,
% 35.56/23.39 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s60, s61)) | trans(s60, s61))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s60, s61)) | trans(s60, s61))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1886,plain,
% 35.56/23.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s60, s61)) | trans(s60, s61))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1887,plain,
% 35.56/23.39 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s60, s61)) | trans(s60, s61)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1886, 1885])).
% 35.56/23.39 tff(1888,plain,
% 35.56/23.39 (trans(s60, s61)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1887, 1884, 8])).
% 35.56/23.39 tff(1889,plain,
% 35.56/23.39 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s60, s61)) | node3(c_bit0, s60, s61))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s60, s61)) | node3(c_bit0, s60, s61))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1890,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s60, s61)) | node3(c_bit0, s60, s61))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1891,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s60, s61)) | node3(c_bit0, s60, s61)),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1890, 1889])).
% 35.56/23.39 tff(1892,plain,
% 35.56/23.39 (node3(c_bit0, s60, s61)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1891, 81, 1888])).
% 35.56/23.39 tff(1893,plain,
% 35.56/23.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1894,plain,
% 35.56/23.39 ((node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)) | m_counter_cell_v_value(c_bit0, s61)) <=> (m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1895,plain,
% 35.56/23.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)) | m_counter_cell_v_value(c_bit0, s61))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61))))),
% 35.56/23.39 inference(monotonicity,[status(thm)],[1894])).
% 35.56/23.39 tff(1896,plain,
% 35.56/23.39 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)) | m_counter_cell_v_value(c_bit0, s61))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)))),
% 35.56/23.39 inference(transitivity,[status(thm)],[1895, 1893])).
% 35.56/23.39 tff(1897,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s60) | (~node3(c_bit0, s60, s61)) | m_counter_cell_v_value(c_bit0, s61))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1898,plain,
% 35.56/23.39 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60) | (~node3(c_bit0, s60, s61))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1897, 1896])).
% 35.56/23.39 tff(1899,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s61) | node1(c_bit0, s60)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1898, 199, 1892])).
% 35.56/23.39 tff(1900,plain,
% 35.56/23.39 (m_counter_cell_v_value(c_bit0, s61)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1899, 1881])).
% 35.56/23.39 tff(1901,assumption,(~m_counter_cell_v_carry_in(c_bit0, s61)), introduced(assumption)).
% 35.56/23.39 tff(1902,plain,
% 35.56/23.39 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s61)),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1903,plain,
% 35.56/23.39 ($false),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1902, 158, 1901])).
% 35.56/23.39 tff(1904,plain,(m_counter_cell_v_carry_in(c_bit0, s61)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.39 tff(1905,plain,
% 35.56/23.39 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61)))),
% 35.56/23.39 inference(rewrite,[status(thm)],[])).
% 35.56/23.39 tff(1906,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61)))),
% 35.56/23.39 inference(quant_inst,[status(thm)],[])).
% 35.56/23.39 tff(1907,plain,
% 35.56/23.39 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61))),
% 35.56/23.39 inference(modus_ponens,[status(thm)],[1906, 1905])).
% 35.56/23.39 tff(1908,plain,
% 35.56/23.39 ((~m_counter_cell_v_value(c_bit0, s61)) | (~node2(c_bit0, s61))),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1907, 219, 1904])).
% 35.56/23.39 tff(1909,plain,
% 35.56/23.39 (~node2(c_bit0, s61)),
% 35.56/23.39 inference(unit_resolution,[status(thm)],[1908, 1900])).
% 35.56/23.40 tff(1910,plain,
% 35.56/23.40 (succ(s61, s62) <=> succ(s61, s62)),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1911,axiom,(succ(s61, s62)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound62')).
% 35.56/23.40 tff(1912,plain,
% 35.56/23.40 (succ(s61, s62)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1911, 1910])).
% 35.56/23.40 tff(1913,plain,
% 35.56/23.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s61, s62)) | trans(s61, s62))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s61, s62)) | trans(s61, s62))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1914,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s61, s62)) | trans(s61, s62))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1915,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s61, s62)) | trans(s61, s62)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 35.56/23.40 tff(1916,plain,
% 35.56/23.40 (trans(s61, s62)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1915, 1912, 8])).
% 35.56/23.40 tff(1917,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s61, s62)) | node3(c_bit0, s61, s62))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s61, s62)) | node3(c_bit0, s61, s62))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1918,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s61, s62)) | node3(c_bit0, s61, s62))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1919,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s61, s62)) | node3(c_bit0, s61, s62)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 35.56/23.40 tff(1920,plain,
% 35.56/23.40 (node3(c_bit0, s61, s62)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1919, 81, 1916])).
% 35.56/23.40 tff(1921,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1922,plain,
% 35.56/23.40 ((node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)) | (~m_counter_cell_v_value(c_bit0, s62))) <=> ((~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1923,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)) | (~m_counter_cell_v_value(c_bit0, s62)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62))))),
% 35.56/23.40 inference(monotonicity,[status(thm)],[1922])).
% 35.56/23.40 tff(1924,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)) | (~m_counter_cell_v_value(c_bit0, s62)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)))),
% 35.56/23.40 inference(transitivity,[status(thm)],[1923, 1921])).
% 35.56/23.40 tff(1925,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s61) | (~node3(c_bit0, s61, s62)) | (~m_counter_cell_v_value(c_bit0, s62)))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1926,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61) | (~node3(c_bit0, s61, s62))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 35.56/23.40 tff(1927,plain,
% 35.56/23.40 ((~m_counter_cell_v_value(c_bit0, s62)) | node2(c_bit0, s61)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1926, 234, 1920])).
% 35.56/23.40 tff(1928,plain,
% 35.56/23.40 (~m_counter_cell_v_value(c_bit0, s62)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1927, 1909])).
% 35.56/23.40 tff(1929,assumption,(~m_counter_cell_v_carry_in(c_bit0, s62)), introduced(assumption)).
% 35.56/23.40 tff(1930,plain,
% 35.56/23.40 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s62)),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1931,plain,
% 35.56/23.40 ($false),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1930, 158, 1929])).
% 35.56/23.40 tff(1932,plain,(m_counter_cell_v_carry_in(c_bit0, s62)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.40 tff(1933,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1934,plain,
% 35.56/23.40 (((~node1(c_bit0, s62)) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1935,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s62)) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62))))),
% 35.56/23.40 inference(monotonicity,[status(thm)],[1934])).
% 35.56/23.40 tff(1936,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s62)) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62)))),
% 35.56/23.40 inference(transitivity,[status(thm)],[1935, 1933])).
% 35.56/23.40 tff(1937,plain,
% 35.56/23.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s62)) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1938,plain,
% 35.56/23.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s62)) | m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 35.56/23.40 tff(1939,plain,
% 35.56/23.40 (m_counter_cell_v_value(c_bit0, s62) | (~node1(c_bit0, s62))),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1938, 170, 1932])).
% 35.56/23.40 tff(1940,plain,
% 35.56/23.40 (~node1(c_bit0, s62)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1939, 1928])).
% 35.56/23.40 tff(1941,plain,
% 35.56/23.40 (succ(s62, s63) <=> succ(s62, s63)),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1942,axiom,(succ(s62, s63)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound63')).
% 35.56/23.40 tff(1943,plain,
% 35.56/23.40 (succ(s62, s63)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1942, 1941])).
% 35.56/23.40 tff(1944,plain,
% 35.56/23.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s62, s63)) | trans(s62, s63))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s62, s63)) | trans(s62, s63))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1945,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s62, s63)) | trans(s62, s63))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1946,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s62, s63)) | trans(s62, s63)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1945, 1944])).
% 35.56/23.40 tff(1947,plain,
% 35.56/23.40 (trans(s62, s63)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1946, 1943, 8])).
% 35.56/23.40 tff(1948,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s62, s63)) | node3(c_bit0, s62, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s62, s63)) | node3(c_bit0, s62, s63))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1949,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s62, s63)) | node3(c_bit0, s62, s63))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1950,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s62, s63)) | node3(c_bit0, s62, s63)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1949, 1948])).
% 35.56/23.40 tff(1951,plain,
% 35.56/23.40 (node3(c_bit0, s62, s63)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1950, 81, 1947])).
% 35.56/23.40 tff(1952,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1953,plain,
% 35.56/23.40 ((node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)) | m_counter_cell_v_value(c_bit0, s63)) <=> (m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1954,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)) | m_counter_cell_v_value(c_bit0, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63))))),
% 35.56/23.40 inference(monotonicity,[status(thm)],[1953])).
% 35.56/23.40 tff(1955,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)) | m_counter_cell_v_value(c_bit0, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)))),
% 35.56/23.40 inference(transitivity,[status(thm)],[1954, 1952])).
% 35.56/23.40 tff(1956,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s62) | (~node3(c_bit0, s62, s63)) | m_counter_cell_v_value(c_bit0, s63))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1957,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62) | (~node3(c_bit0, s62, s63))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 35.56/23.40 tff(1958,plain,
% 35.56/23.40 (m_counter_cell_v_value(c_bit0, s63) | node1(c_bit0, s62)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1957, 199, 1951])).
% 35.56/23.40 tff(1959,plain,
% 35.56/23.40 (m_counter_cell_v_value(c_bit0, s63)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1958, 1940])).
% 35.56/23.40 tff(1960,assumption,(~m_counter_cell_v_carry_in(c_bit0, s63)), introduced(assumption)).
% 35.56/23.40 tff(1961,plain,
% 35.56/23.40 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s63)),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1962,plain,
% 35.56/23.40 ($false),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1961, 158, 1960])).
% 35.56/23.40 tff(1963,plain,(m_counter_cell_v_carry_in(c_bit0, s63)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.40 tff(1964,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1965,plain,
% 35.56/23.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63)))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1966,plain,
% 35.56/23.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1965, 1964])).
% 35.56/23.40 tff(1967,plain,
% 35.56/23.40 ((~m_counter_cell_v_value(c_bit0, s63)) | (~node2(c_bit0, s63))),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1966, 219, 1963])).
% 35.56/23.40 tff(1968,plain,
% 35.56/23.40 (~node2(c_bit0, s63)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1967, 1959])).
% 35.56/23.40 tff(1969,plain,
% 35.56/23.40 (succ(s63, s64) <=> succ(s63, s64)),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1970,axiom,(succ(s63, s64)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound64')).
% 35.56/23.40 tff(1971,plain,
% 35.56/23.40 (succ(s63, s64)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 35.56/23.40 tff(1972,plain,
% 35.56/23.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s63, s64)) | trans(s63, s64))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s63, s64)) | trans(s63, s64))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1973,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s63, s64)) | trans(s63, s64))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1974,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s63, s64)) | trans(s63, s64)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1973, 1972])).
% 35.56/23.40 tff(1975,plain,
% 35.56/23.40 (trans(s63, s64)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1974, 1971, 8])).
% 35.56/23.40 tff(1976,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s63, s64)) | node3(c_bit0, s63, s64))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s63, s64)) | node3(c_bit0, s63, s64))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1977,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s63, s64)) | node3(c_bit0, s63, s64))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1978,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s63, s64)) | node3(c_bit0, s63, s64)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1977, 1976])).
% 35.56/23.40 tff(1979,plain,
% 35.56/23.40 (node3(c_bit0, s63, s64)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1978, 81, 1975])).
% 35.56/23.40 tff(1980,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1981,plain,
% 35.56/23.40 ((node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)) | (~m_counter_cell_v_value(c_bit0, s64))) <=> ((~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1982,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)) | (~m_counter_cell_v_value(c_bit0, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64))))),
% 35.56/23.40 inference(monotonicity,[status(thm)],[1981])).
% 35.56/23.40 tff(1983,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)) | (~m_counter_cell_v_value(c_bit0, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)))),
% 35.56/23.40 inference(transitivity,[status(thm)],[1982, 1980])).
% 35.56/23.40 tff(1984,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s63) | (~node3(c_bit0, s63, s64)) | (~m_counter_cell_v_value(c_bit0, s64)))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1985,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63) | (~node3(c_bit0, s63, s64))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1984, 1983])).
% 35.56/23.40 tff(1986,plain,
% 35.56/23.40 ((~m_counter_cell_v_value(c_bit0, s64)) | node2(c_bit0, s63)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1985, 234, 1979])).
% 35.56/23.40 tff(1987,plain,
% 35.56/23.40 (~m_counter_cell_v_value(c_bit0, s64)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1986, 1968])).
% 35.56/23.40 tff(1988,assumption,(~m_counter_cell_v_carry_in(c_bit0, s64)), introduced(assumption)).
% 35.56/23.40 tff(1989,plain,
% 35.56/23.40 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s64)),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1990,plain,
% 35.56/23.40 ($false),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1989, 158, 1988])).
% 35.56/23.40 tff(1991,plain,(m_counter_cell_v_carry_in(c_bit0, s64)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.40 tff(1992,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1993,plain,
% 35.56/23.40 (((~node1(c_bit0, s64)) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(1994,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s64)) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64))))),
% 35.56/23.40 inference(monotonicity,[status(thm)],[1993])).
% 35.56/23.40 tff(1995,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s64)) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64)))),
% 35.56/23.40 inference(transitivity,[status(thm)],[1994, 1992])).
% 35.56/23.40 tff(1996,plain,
% 35.56/23.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s64)) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(1997,plain,
% 35.56/23.40 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s64)) | m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[1996, 1995])).
% 35.56/23.40 tff(1998,plain,
% 35.56/23.40 (m_counter_cell_v_value(c_bit0, s64) | (~node1(c_bit0, s64))),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1997, 170, 1991])).
% 35.56/23.40 tff(1999,plain,
% 35.56/23.40 (~node1(c_bit0, s64)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[1998, 1987])).
% 35.56/23.40 tff(2000,plain,
% 35.56/23.40 (succ(s64, s65) <=> succ(s64, s65)),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2001,axiom,(succ(s64, s65)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound65')).
% 35.56/23.40 tff(2002,plain,
% 35.56/23.40 (succ(s64, s65)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2001, 2000])).
% 35.56/23.40 tff(2003,plain,
% 35.56/23.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s64, s65)) | trans(s64, s65))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s64, s65)) | trans(s64, s65))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2004,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s64, s65)) | trans(s64, s65))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2005,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s64, s65)) | trans(s64, s65)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 35.56/23.40 tff(2006,plain,
% 35.56/23.40 (trans(s64, s65)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2005, 2002, 8])).
% 35.56/23.40 tff(2007,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s64, s65)) | node3(c_bit0, s64, s65))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s64, s65)) | node3(c_bit0, s64, s65))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2008,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s64, s65)) | node3(c_bit0, s64, s65))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2009,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s64, s65)) | node3(c_bit0, s64, s65)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 35.56/23.40 tff(2010,plain,
% 35.56/23.40 (node3(c_bit0, s64, s65)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2009, 81, 2006])).
% 35.56/23.40 tff(2011,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2012,plain,
% 35.56/23.40 ((node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)) | m_counter_cell_v_value(c_bit0, s65)) <=> (m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2013,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)) | m_counter_cell_v_value(c_bit0, s65))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65))))),
% 35.56/23.40 inference(monotonicity,[status(thm)],[2012])).
% 35.56/23.40 tff(2014,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)) | m_counter_cell_v_value(c_bit0, s65))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)))),
% 35.56/23.40 inference(transitivity,[status(thm)],[2013, 2011])).
% 35.56/23.40 tff(2015,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s64) | (~node3(c_bit0, s64, s65)) | m_counter_cell_v_value(c_bit0, s65))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2016,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64) | (~node3(c_bit0, s64, s65))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 35.56/23.40 tff(2017,plain,
% 35.56/23.40 (m_counter_cell_v_value(c_bit0, s65) | node1(c_bit0, s64)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2016, 199, 2010])).
% 35.56/23.40 tff(2018,plain,
% 35.56/23.40 (m_counter_cell_v_value(c_bit0, s65)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2017, 1999])).
% 35.56/23.40 tff(2019,assumption,(~m_counter_cell_v_carry_in(c_bit0, s65)), introduced(assumption)).
% 35.56/23.40 tff(2020,plain,
% 35.56/23.40 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s65)),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2021,plain,
% 35.56/23.40 ($false),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2020, 158, 2019])).
% 35.56/23.40 tff(2022,plain,(m_counter_cell_v_carry_in(c_bit0, s65)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.40 tff(2023,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2024,plain,
% 35.56/23.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65)))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2025,plain,
% 35.56/23.40 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2024, 2023])).
% 35.56/23.40 tff(2026,plain,
% 35.56/23.40 ((~m_counter_cell_v_value(c_bit0, s65)) | (~node2(c_bit0, s65))),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2025, 219, 2022])).
% 35.56/23.40 tff(2027,plain,
% 35.56/23.40 (~node2(c_bit0, s65)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2026, 2018])).
% 35.56/23.40 tff(2028,plain,
% 35.56/23.40 (succ(s65, s66) <=> succ(s65, s66)),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2029,axiom,(succ(s65, s66)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound66')).
% 35.56/23.40 tff(2030,plain,
% 35.56/23.40 (succ(s65, s66)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 35.56/23.40 tff(2031,plain,
% 35.56/23.40 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s65, s66)) | trans(s65, s66))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s65, s66)) | trans(s65, s66))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2032,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s65, s66)) | trans(s65, s66))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2033,plain,
% 35.56/23.40 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s65, s66)) | trans(s65, s66)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 35.56/23.40 tff(2034,plain,
% 35.56/23.40 (trans(s65, s66)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2033, 2030, 8])).
% 35.56/23.40 tff(2035,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s65, s66)) | node3(c_bit0, s65, s66))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s65, s66)) | node3(c_bit0, s65, s66))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2036,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s65, s66)) | node3(c_bit0, s65, s66))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2037,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s65, s66)) | node3(c_bit0, s65, s66)),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 35.56/23.40 tff(2038,plain,
% 35.56/23.40 (node3(c_bit0, s65, s66)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2037, 81, 2034])).
% 35.56/23.40 tff(2039,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2040,plain,
% 35.56/23.40 ((node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)) | (~m_counter_cell_v_value(c_bit0, s66))) <=> ((~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2041,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)) | (~m_counter_cell_v_value(c_bit0, s66)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66))))),
% 35.56/23.40 inference(monotonicity,[status(thm)],[2040])).
% 35.56/23.40 tff(2042,plain,
% 35.56/23.40 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)) | (~m_counter_cell_v_value(c_bit0, s66)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)))),
% 35.56/23.40 inference(transitivity,[status(thm)],[2041, 2039])).
% 35.56/23.40 tff(2043,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s65) | (~node3(c_bit0, s65, s66)) | (~m_counter_cell_v_value(c_bit0, s66)))),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2044,plain,
% 35.56/23.40 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65) | (~node3(c_bit0, s65, s66))),
% 35.56/23.40 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 35.56/23.40 tff(2045,plain,
% 35.56/23.40 ((~m_counter_cell_v_value(c_bit0, s66)) | node2(c_bit0, s65)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2044, 234, 2038])).
% 35.56/23.40 tff(2046,plain,
% 35.56/23.40 (~m_counter_cell_v_value(c_bit0, s66)),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2045, 2027])).
% 35.56/23.40 tff(2047,assumption,(~m_counter_cell_v_carry_in(c_bit0, s66)), introduced(assumption)).
% 35.56/23.40 tff(2048,plain,
% 35.56/23.40 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s66)),
% 35.56/23.40 inference(quant_inst,[status(thm)],[])).
% 35.56/23.40 tff(2049,plain,
% 35.56/23.40 ($false),
% 35.56/23.40 inference(unit_resolution,[status(thm)],[2048, 158, 2047])).
% 35.56/23.40 tff(2050,plain,(m_counter_cell_v_carry_in(c_bit0, s66)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.40 tff(2051,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2052,plain,
% 35.56/23.40 (((~node1(c_bit0, s66)) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66)))),
% 35.56/23.40 inference(rewrite,[status(thm)],[])).
% 35.56/23.40 tff(2053,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s66)) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66))))),
% 35.56/23.40 inference(monotonicity,[status(thm)],[2052])).
% 35.56/23.40 tff(2054,plain,
% 35.56/23.40 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s66)) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66)))),
% 35.56/23.41 inference(transitivity,[status(thm)],[2053, 2051])).
% 35.56/23.41 tff(2055,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s66)) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2056,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s66)) | m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 35.56/23.41 tff(2057,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s66) | (~node1(c_bit0, s66))),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2056, 170, 2050])).
% 35.56/23.41 tff(2058,plain,
% 35.56/23.41 (~node1(c_bit0, s66)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2057, 2046])).
% 35.56/23.41 tff(2059,plain,
% 35.56/23.41 (succ(s66, s67) <=> succ(s66, s67)),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2060,axiom,(succ(s66, s67)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound67')).
% 35.56/23.41 tff(2061,plain,
% 35.56/23.41 (succ(s66, s67)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 35.56/23.41 tff(2062,plain,
% 35.56/23.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s66, s67)) | trans(s66, s67))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s66, s67)) | trans(s66, s67))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2063,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s66, s67)) | trans(s66, s67))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2064,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s66, s67)) | trans(s66, s67)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 35.56/23.41 tff(2065,plain,
% 35.56/23.41 (trans(s66, s67)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2064, 2061, 8])).
% 35.56/23.41 tff(2066,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s66, s67)) | node3(c_bit0, s66, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s66, s67)) | node3(c_bit0, s66, s67))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2067,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s66, s67)) | node3(c_bit0, s66, s67))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2068,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s66, s67)) | node3(c_bit0, s66, s67)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2067, 2066])).
% 35.56/23.41 tff(2069,plain,
% 35.56/23.41 (node3(c_bit0, s66, s67)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2068, 81, 2065])).
% 35.56/23.41 tff(2070,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2071,plain,
% 35.56/23.41 ((node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)) | m_counter_cell_v_value(c_bit0, s67)) <=> (m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2072,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)) | m_counter_cell_v_value(c_bit0, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67))))),
% 35.56/23.41 inference(monotonicity,[status(thm)],[2071])).
% 35.56/23.41 tff(2073,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)) | m_counter_cell_v_value(c_bit0, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)))),
% 35.56/23.41 inference(transitivity,[status(thm)],[2072, 2070])).
% 35.56/23.41 tff(2074,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s66) | (~node3(c_bit0, s66, s67)) | m_counter_cell_v_value(c_bit0, s67))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2075,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66) | (~node3(c_bit0, s66, s67))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 35.56/23.41 tff(2076,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s67) | node1(c_bit0, s66)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2075, 199, 2069])).
% 35.56/23.41 tff(2077,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s67)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2076, 2058])).
% 35.56/23.41 tff(2078,assumption,(~m_counter_cell_v_carry_in(c_bit0, s67)), introduced(assumption)).
% 35.56/23.41 tff(2079,plain,
% 35.56/23.41 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s67)),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2080,plain,
% 35.56/23.41 ($false),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2079, 158, 2078])).
% 35.56/23.41 tff(2081,plain,(m_counter_cell_v_carry_in(c_bit0, s67)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.41 tff(2082,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2083,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67)))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2084,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2083, 2082])).
% 35.56/23.41 tff(2085,plain,
% 35.56/23.41 ((~m_counter_cell_v_value(c_bit0, s67)) | (~node2(c_bit0, s67))),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2084, 219, 2081])).
% 35.56/23.41 tff(2086,plain,
% 35.56/23.41 (~node2(c_bit0, s67)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2085, 2077])).
% 35.56/23.41 tff(2087,plain,
% 35.56/23.41 (succ(s67, s68) <=> succ(s67, s68)),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2088,axiom,(succ(s67, s68)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound68')).
% 35.56/23.41 tff(2089,plain,
% 35.56/23.41 (succ(s67, s68)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2088, 2087])).
% 35.56/23.41 tff(2090,plain,
% 35.56/23.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s67, s68)) | trans(s67, s68))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s67, s68)) | trans(s67, s68))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2091,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s67, s68)) | trans(s67, s68))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2092,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s67, s68)) | trans(s67, s68)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 35.56/23.41 tff(2093,plain,
% 35.56/23.41 (trans(s67, s68)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2092, 2089, 8])).
% 35.56/23.41 tff(2094,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s67, s68)) | node3(c_bit0, s67, s68))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s67, s68)) | node3(c_bit0, s67, s68))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2095,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s67, s68)) | node3(c_bit0, s67, s68))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2096,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s67, s68)) | node3(c_bit0, s67, s68)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2095, 2094])).
% 35.56/23.41 tff(2097,plain,
% 35.56/23.41 (node3(c_bit0, s67, s68)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2096, 81, 2093])).
% 35.56/23.41 tff(2098,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2099,plain,
% 35.56/23.41 ((node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)) | (~m_counter_cell_v_value(c_bit0, s68))) <=> ((~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2100,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)) | (~m_counter_cell_v_value(c_bit0, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68))))),
% 35.56/23.41 inference(monotonicity,[status(thm)],[2099])).
% 35.56/23.41 tff(2101,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)) | (~m_counter_cell_v_value(c_bit0, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)))),
% 35.56/23.41 inference(transitivity,[status(thm)],[2100, 2098])).
% 35.56/23.41 tff(2102,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s67) | (~node3(c_bit0, s67, s68)) | (~m_counter_cell_v_value(c_bit0, s68)))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2103,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67) | (~node3(c_bit0, s67, s68))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 35.56/23.41 tff(2104,plain,
% 35.56/23.41 ((~m_counter_cell_v_value(c_bit0, s68)) | node2(c_bit0, s67)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2103, 234, 2097])).
% 35.56/23.41 tff(2105,plain,
% 35.56/23.41 (~m_counter_cell_v_value(c_bit0, s68)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2104, 2086])).
% 35.56/23.41 tff(2106,assumption,(~m_counter_cell_v_carry_in(c_bit0, s68)), introduced(assumption)).
% 35.56/23.41 tff(2107,plain,
% 35.56/23.41 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s68)),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2108,plain,
% 35.56/23.41 ($false),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2107, 158, 2106])).
% 35.56/23.41 tff(2109,plain,(m_counter_cell_v_carry_in(c_bit0, s68)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.41 tff(2110,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2111,plain,
% 35.56/23.41 (((~node1(c_bit0, s68)) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2112,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s68)) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68))))),
% 35.56/23.41 inference(monotonicity,[status(thm)],[2111])).
% 35.56/23.41 tff(2113,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s68)) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68)))),
% 35.56/23.41 inference(transitivity,[status(thm)],[2112, 2110])).
% 35.56/23.41 tff(2114,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s68)) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2115,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s68)) | m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2114, 2113])).
% 35.56/23.41 tff(2116,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s68) | (~node1(c_bit0, s68))),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2115, 170, 2109])).
% 35.56/23.41 tff(2117,plain,
% 35.56/23.41 (~node1(c_bit0, s68)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2116, 2105])).
% 35.56/23.41 tff(2118,plain,
% 35.56/23.41 (succ(s68, s69) <=> succ(s68, s69)),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2119,axiom,(succ(s68, s69)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound69')).
% 35.56/23.41 tff(2120,plain,
% 35.56/23.41 (succ(s68, s69)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 35.56/23.41 tff(2121,plain,
% 35.56/23.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s68, s69)) | trans(s68, s69))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s68, s69)) | trans(s68, s69))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2122,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s68, s69)) | trans(s68, s69))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2123,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s68, s69)) | trans(s68, s69)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 35.56/23.41 tff(2124,plain,
% 35.56/23.41 (trans(s68, s69)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2123, 2120, 8])).
% 35.56/23.41 tff(2125,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s68, s69)) | node3(c_bit0, s68, s69))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s68, s69)) | node3(c_bit0, s68, s69))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2126,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s68, s69)) | node3(c_bit0, s68, s69))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2127,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s68, s69)) | node3(c_bit0, s68, s69)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 35.56/23.41 tff(2128,plain,
% 35.56/23.41 (node3(c_bit0, s68, s69)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2127, 81, 2124])).
% 35.56/23.41 tff(2129,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2130,plain,
% 35.56/23.41 ((node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)) | m_counter_cell_v_value(c_bit0, s69)) <=> (m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2131,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)) | m_counter_cell_v_value(c_bit0, s69))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69))))),
% 35.56/23.41 inference(monotonicity,[status(thm)],[2130])).
% 35.56/23.41 tff(2132,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)) | m_counter_cell_v_value(c_bit0, s69))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)))),
% 35.56/23.41 inference(transitivity,[status(thm)],[2131, 2129])).
% 35.56/23.41 tff(2133,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s68) | (~node3(c_bit0, s68, s69)) | m_counter_cell_v_value(c_bit0, s69))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2134,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68) | (~node3(c_bit0, s68, s69))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2133, 2132])).
% 35.56/23.41 tff(2135,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s69) | node1(c_bit0, s68)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2134, 199, 2128])).
% 35.56/23.41 tff(2136,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s69)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2135, 2117])).
% 35.56/23.41 tff(2137,assumption,(~m_counter_cell_v_carry_in(c_bit0, s69)), introduced(assumption)).
% 35.56/23.41 tff(2138,plain,
% 35.56/23.41 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s69)),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2139,plain,
% 35.56/23.41 ($false),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2138, 158, 2137])).
% 35.56/23.41 tff(2140,plain,(m_counter_cell_v_carry_in(c_bit0, s69)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.41 tff(2141,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2142,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69)))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2143,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 35.56/23.41 tff(2144,plain,
% 35.56/23.41 ((~m_counter_cell_v_value(c_bit0, s69)) | (~node2(c_bit0, s69))),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2143, 219, 2140])).
% 35.56/23.41 tff(2145,plain,
% 35.56/23.41 (~node2(c_bit0, s69)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2144, 2136])).
% 35.56/23.41 tff(2146,plain,
% 35.56/23.41 (succ(s69, s70) <=> succ(s69, s70)),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2147,axiom,(succ(s69, s70)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound70')).
% 35.56/23.41 tff(2148,plain,
% 35.56/23.41 (succ(s69, s70)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 35.56/23.41 tff(2149,plain,
% 35.56/23.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s69, s70)) | trans(s69, s70))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s69, s70)) | trans(s69, s70))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2150,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s69, s70)) | trans(s69, s70))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2151,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s69, s70)) | trans(s69, s70)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 35.56/23.41 tff(2152,plain,
% 35.56/23.41 (trans(s69, s70)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2151, 2148, 8])).
% 35.56/23.41 tff(2153,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s69, s70)) | node3(c_bit0, s69, s70))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s69, s70)) | node3(c_bit0, s69, s70))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2154,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s69, s70)) | node3(c_bit0, s69, s70))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2155,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s69, s70)) | node3(c_bit0, s69, s70)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 35.56/23.41 tff(2156,plain,
% 35.56/23.41 (node3(c_bit0, s69, s70)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2155, 81, 2152])).
% 35.56/23.41 tff(2157,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2158,plain,
% 35.56/23.41 ((node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)) | (~m_counter_cell_v_value(c_bit0, s70))) <=> ((~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2159,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)) | (~m_counter_cell_v_value(c_bit0, s70)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70))))),
% 35.56/23.41 inference(monotonicity,[status(thm)],[2158])).
% 35.56/23.41 tff(2160,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)) | (~m_counter_cell_v_value(c_bit0, s70)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)))),
% 35.56/23.41 inference(transitivity,[status(thm)],[2159, 2157])).
% 35.56/23.41 tff(2161,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s69) | (~node3(c_bit0, s69, s70)) | (~m_counter_cell_v_value(c_bit0, s70)))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2162,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69) | (~node3(c_bit0, s69, s70))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2161, 2160])).
% 35.56/23.41 tff(2163,plain,
% 35.56/23.41 ((~m_counter_cell_v_value(c_bit0, s70)) | node2(c_bit0, s69)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2162, 234, 2156])).
% 35.56/23.41 tff(2164,plain,
% 35.56/23.41 (~m_counter_cell_v_value(c_bit0, s70)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2163, 2145])).
% 35.56/23.41 tff(2165,assumption,(~m_counter_cell_v_carry_in(c_bit0, s70)), introduced(assumption)).
% 35.56/23.41 tff(2166,plain,
% 35.56/23.41 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s70)),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2167,plain,
% 35.56/23.41 ($false),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2166, 158, 2165])).
% 35.56/23.41 tff(2168,plain,(m_counter_cell_v_carry_in(c_bit0, s70)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.41 tff(2169,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2170,plain,
% 35.56/23.41 (((~node1(c_bit0, s70)) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2171,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s70)) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70))))),
% 35.56/23.41 inference(monotonicity,[status(thm)],[2170])).
% 35.56/23.41 tff(2172,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s70)) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70)))),
% 35.56/23.41 inference(transitivity,[status(thm)],[2171, 2169])).
% 35.56/23.41 tff(2173,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s70)) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2174,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s70)) | m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 35.56/23.41 tff(2175,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s70) | (~node1(c_bit0, s70))),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2174, 170, 2168])).
% 35.56/23.41 tff(2176,plain,
% 35.56/23.41 (~node1(c_bit0, s70)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2175, 2164])).
% 35.56/23.41 tff(2177,plain,
% 35.56/23.41 (succ(s70, s71) <=> succ(s70, s71)),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2178,axiom,(succ(s70, s71)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound71')).
% 35.56/23.41 tff(2179,plain,
% 35.56/23.41 (succ(s70, s71)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2178, 2177])).
% 35.56/23.41 tff(2180,plain,
% 35.56/23.41 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s70, s71)) | trans(s70, s71))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s70, s71)) | trans(s70, s71))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2181,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s70, s71)) | trans(s70, s71))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2182,plain,
% 35.56/23.41 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s70, s71)) | trans(s70, s71)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2181, 2180])).
% 35.56/23.41 tff(2183,plain,
% 35.56/23.41 (trans(s70, s71)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2182, 2179, 8])).
% 35.56/23.41 tff(2184,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s70, s71)) | node3(c_bit0, s70, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s70, s71)) | node3(c_bit0, s70, s71))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2185,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s70, s71)) | node3(c_bit0, s70, s71))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2186,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s70, s71)) | node3(c_bit0, s70, s71)),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2185, 2184])).
% 35.56/23.41 tff(2187,plain,
% 35.56/23.41 (node3(c_bit0, s70, s71)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2186, 81, 2183])).
% 35.56/23.41 tff(2188,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2189,plain,
% 35.56/23.41 ((node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)) | m_counter_cell_v_value(c_bit0, s71)) <=> (m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2190,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)) | m_counter_cell_v_value(c_bit0, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71))))),
% 35.56/23.41 inference(monotonicity,[status(thm)],[2189])).
% 35.56/23.41 tff(2191,plain,
% 35.56/23.41 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)) | m_counter_cell_v_value(c_bit0, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)))),
% 35.56/23.41 inference(transitivity,[status(thm)],[2190, 2188])).
% 35.56/23.41 tff(2192,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s70) | (~node3(c_bit0, s70, s71)) | m_counter_cell_v_value(c_bit0, s71))),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2193,plain,
% 35.56/23.41 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70) | (~node3(c_bit0, s70, s71))),
% 35.56/23.41 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 35.56/23.41 tff(2194,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s71) | node1(c_bit0, s70)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2193, 199, 2187])).
% 35.56/23.41 tff(2195,plain,
% 35.56/23.41 (m_counter_cell_v_value(c_bit0, s71)),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2194, 2176])).
% 35.56/23.41 tff(2196,assumption,(~m_counter_cell_v_carry_in(c_bit0, s71)), introduced(assumption)).
% 35.56/23.41 tff(2197,plain,
% 35.56/23.41 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s71)),
% 35.56/23.41 inference(quant_inst,[status(thm)],[])).
% 35.56/23.41 tff(2198,plain,
% 35.56/23.41 ($false),
% 35.56/23.41 inference(unit_resolution,[status(thm)],[2197, 158, 2196])).
% 35.56/23.41 tff(2199,plain,(m_counter_cell_v_carry_in(c_bit0, s71)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.41 tff(2200,plain,
% 35.56/23.41 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71)))),
% 35.56/23.41 inference(rewrite,[status(thm)],[])).
% 35.56/23.41 tff(2201,plain,
% 35.56/23.41 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71)))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2202,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 35.56/23.42 tff(2203,plain,
% 35.56/23.42 ((~m_counter_cell_v_value(c_bit0, s71)) | (~node2(c_bit0, s71))),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2202, 219, 2199])).
% 35.56/23.42 tff(2204,plain,
% 35.56/23.42 (~node2(c_bit0, s71)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2203, 2195])).
% 35.56/23.42 tff(2205,plain,
% 35.56/23.42 (succ(s71, s72) <=> succ(s71, s72)),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2206,axiom,(succ(s71, s72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound72')).
% 35.56/23.42 tff(2207,plain,
% 35.56/23.42 (succ(s71, s72)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 35.56/23.42 tff(2208,plain,
% 35.56/23.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s71, s72)) | trans(s71, s72))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s71, s72)) | trans(s71, s72))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2209,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s71, s72)) | trans(s71, s72))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2210,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s71, s72)) | trans(s71, s72)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2209, 2208])).
% 35.56/23.42 tff(2211,plain,
% 35.56/23.42 (trans(s71, s72)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2210, 2207, 8])).
% 35.56/23.42 tff(2212,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s71, s72)) | node3(c_bit0, s71, s72))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s71, s72)) | node3(c_bit0, s71, s72))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2213,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s71, s72)) | node3(c_bit0, s71, s72))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2214,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s71, s72)) | node3(c_bit0, s71, s72)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 35.56/23.42 tff(2215,plain,
% 35.56/23.42 (node3(c_bit0, s71, s72)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2214, 81, 2211])).
% 35.56/23.42 tff(2216,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2217,plain,
% 35.56/23.42 ((node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)) | (~m_counter_cell_v_value(c_bit0, s72))) <=> ((~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2218,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)) | (~m_counter_cell_v_value(c_bit0, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72))))),
% 35.56/23.42 inference(monotonicity,[status(thm)],[2217])).
% 35.56/23.42 tff(2219,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)) | (~m_counter_cell_v_value(c_bit0, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)))),
% 35.56/23.42 inference(transitivity,[status(thm)],[2218, 2216])).
% 35.56/23.42 tff(2220,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s71) | (~node3(c_bit0, s71, s72)) | (~m_counter_cell_v_value(c_bit0, s72)))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2221,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71) | (~node3(c_bit0, s71, s72))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2220, 2219])).
% 35.56/23.42 tff(2222,plain,
% 35.56/23.42 ((~m_counter_cell_v_value(c_bit0, s72)) | node2(c_bit0, s71)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2221, 234, 2215])).
% 35.56/23.42 tff(2223,plain,
% 35.56/23.42 (~m_counter_cell_v_value(c_bit0, s72)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2222, 2204])).
% 35.56/23.42 tff(2224,assumption,(~m_counter_cell_v_carry_in(c_bit0, s72)), introduced(assumption)).
% 35.56/23.42 tff(2225,plain,
% 35.56/23.42 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s72)),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2226,plain,
% 35.56/23.42 ($false),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2225, 158, 2224])).
% 35.56/23.42 tff(2227,plain,(m_counter_cell_v_carry_in(c_bit0, s72)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.42 tff(2228,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2229,plain,
% 35.56/23.42 (((~node1(c_bit0, s72)) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2230,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s72)) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72))))),
% 35.56/23.42 inference(monotonicity,[status(thm)],[2229])).
% 35.56/23.42 tff(2231,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s72)) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72)))),
% 35.56/23.42 inference(transitivity,[status(thm)],[2230, 2228])).
% 35.56/23.42 tff(2232,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s72)) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2233,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s72)) | m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 35.56/23.42 tff(2234,plain,
% 35.56/23.42 (m_counter_cell_v_value(c_bit0, s72) | (~node1(c_bit0, s72))),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2233, 170, 2227])).
% 35.56/23.42 tff(2235,plain,
% 35.56/23.42 (~node1(c_bit0, s72)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2234, 2223])).
% 35.56/23.42 tff(2236,plain,
% 35.56/23.42 (succ(s72, s73) <=> succ(s72, s73)),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2237,axiom,(succ(s72, s73)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound73')).
% 35.56/23.42 tff(2238,plain,
% 35.56/23.42 (succ(s72, s73)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2237, 2236])).
% 35.56/23.42 tff(2239,plain,
% 35.56/23.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s72, s73)) | trans(s72, s73))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s72, s73)) | trans(s72, s73))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2240,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s72, s73)) | trans(s72, s73))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2241,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s72, s73)) | trans(s72, s73)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2240, 2239])).
% 35.56/23.42 tff(2242,plain,
% 35.56/23.42 (trans(s72, s73)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2241, 2238, 8])).
% 35.56/23.42 tff(2243,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s72, s73)) | node3(c_bit0, s72, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s72, s73)) | node3(c_bit0, s72, s73))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2244,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s72, s73)) | node3(c_bit0, s72, s73))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2245,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s72, s73)) | node3(c_bit0, s72, s73)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 35.56/23.42 tff(2246,plain,
% 35.56/23.42 (node3(c_bit0, s72, s73)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2245, 81, 2242])).
% 35.56/23.42 tff(2247,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2248,plain,
% 35.56/23.42 ((node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | m_counter_cell_v_value(c_bit0, s73)) <=> (m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2249,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | m_counter_cell_v_value(c_bit0, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73))))),
% 35.56/23.42 inference(monotonicity,[status(thm)],[2248])).
% 35.56/23.42 tff(2250,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | m_counter_cell_v_value(c_bit0, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 35.56/23.42 inference(transitivity,[status(thm)],[2249, 2247])).
% 35.56/23.42 tff(2251,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | m_counter_cell_v_value(c_bit0, s73))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2252,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72) | (~node3(c_bit0, s72, s73))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 35.56/23.42 tff(2253,plain,
% 35.56/23.42 (m_counter_cell_v_value(c_bit0, s73) | node1(c_bit0, s72)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2252, 199, 2246])).
% 35.56/23.42 tff(2254,plain,
% 35.56/23.42 (m_counter_cell_v_value(c_bit0, s73)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2253, 2235])).
% 35.56/23.42 tff(2255,assumption,(~m_counter_cell_v_carry_in(c_bit0, s73)), introduced(assumption)).
% 35.56/23.42 tff(2256,plain,
% 35.56/23.42 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s73)),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2257,plain,
% 35.56/23.42 ($false),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2256, 158, 2255])).
% 35.56/23.42 tff(2258,plain,(m_counter_cell_v_carry_in(c_bit0, s73)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.42 tff(2259,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2260,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73)))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2261,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 35.56/23.42 tff(2262,plain,
% 35.56/23.42 ((~m_counter_cell_v_value(c_bit0, s73)) | (~node2(c_bit0, s73))),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2261, 219, 2258])).
% 35.56/23.42 tff(2263,plain,
% 35.56/23.42 (~node2(c_bit0, s73)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2262, 2254])).
% 35.56/23.42 tff(2264,plain,
% 35.56/23.42 (succ(s73, s74) <=> succ(s73, s74)),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2265,axiom,(succ(s73, s74)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound74')).
% 35.56/23.42 tff(2266,plain,
% 35.56/23.42 (succ(s73, s74)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 35.56/23.42 tff(2267,plain,
% 35.56/23.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s73, s74)) | trans(s73, s74))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s73, s74)) | trans(s73, s74))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2268,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s73, s74)) | trans(s73, s74))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2269,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s73, s74)) | trans(s73, s74)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2268, 2267])).
% 35.56/23.42 tff(2270,plain,
% 35.56/23.42 (trans(s73, s74)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2269, 2266, 8])).
% 35.56/23.42 tff(2271,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s73, s74)) | node3(c_bit0, s73, s74))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s73, s74)) | node3(c_bit0, s73, s74))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2272,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s73, s74)) | node3(c_bit0, s73, s74))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2273,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s73, s74)) | node3(c_bit0, s73, s74)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2272, 2271])).
% 35.56/23.42 tff(2274,plain,
% 35.56/23.42 (node3(c_bit0, s73, s74)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2273, 81, 2270])).
% 35.56/23.42 tff(2275,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2276,plain,
% 35.56/23.42 ((node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)) | (~m_counter_cell_v_value(c_bit0, s74))) <=> ((~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2277,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)) | (~m_counter_cell_v_value(c_bit0, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74))))),
% 35.56/23.42 inference(monotonicity,[status(thm)],[2276])).
% 35.56/23.42 tff(2278,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)) | (~m_counter_cell_v_value(c_bit0, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)))),
% 35.56/23.42 inference(transitivity,[status(thm)],[2277, 2275])).
% 35.56/23.42 tff(2279,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s73) | (~node3(c_bit0, s73, s74)) | (~m_counter_cell_v_value(c_bit0, s74)))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2280,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73) | (~node3(c_bit0, s73, s74))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2279, 2278])).
% 35.56/23.42 tff(2281,plain,
% 35.56/23.42 ((~m_counter_cell_v_value(c_bit0, s74)) | node2(c_bit0, s73)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2280, 234, 2274])).
% 35.56/23.42 tff(2282,plain,
% 35.56/23.42 (~m_counter_cell_v_value(c_bit0, s74)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2281, 2263])).
% 35.56/23.42 tff(2283,assumption,(~m_counter_cell_v_carry_in(c_bit0, s74)), introduced(assumption)).
% 35.56/23.42 tff(2284,plain,
% 35.56/23.42 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s74)),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2285,plain,
% 35.56/23.42 ($false),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2284, 158, 2283])).
% 35.56/23.42 tff(2286,plain,(m_counter_cell_v_carry_in(c_bit0, s74)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.42 tff(2287,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2288,plain,
% 35.56/23.42 (((~node1(c_bit0, s74)) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2289,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s74)) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74))))),
% 35.56/23.42 inference(monotonicity,[status(thm)],[2288])).
% 35.56/23.42 tff(2290,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s74)) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74)))),
% 35.56/23.42 inference(transitivity,[status(thm)],[2289, 2287])).
% 35.56/23.42 tff(2291,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s74)) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2292,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s74)) | m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2291, 2290])).
% 35.56/23.42 tff(2293,plain,
% 35.56/23.42 (m_counter_cell_v_value(c_bit0, s74) | (~node1(c_bit0, s74))),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2292, 170, 2286])).
% 35.56/23.42 tff(2294,plain,
% 35.56/23.42 (~node1(c_bit0, s74)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2293, 2282])).
% 35.56/23.42 tff(2295,plain,
% 35.56/23.42 (succ(s74, s75) <=> succ(s74, s75)),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2296,axiom,(succ(s74, s75)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound75')).
% 35.56/23.42 tff(2297,plain,
% 35.56/23.42 (succ(s74, s75)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 35.56/23.42 tff(2298,plain,
% 35.56/23.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s74, s75)) | trans(s74, s75))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s74, s75)) | trans(s74, s75))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2299,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s74, s75)) | trans(s74, s75))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2300,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s74, s75)) | trans(s74, s75)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 35.56/23.42 tff(2301,plain,
% 35.56/23.42 (trans(s74, s75)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2300, 2297, 8])).
% 35.56/23.42 tff(2302,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s74, s75)) | node3(c_bit0, s74, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s74, s75)) | node3(c_bit0, s74, s75))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2303,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s74, s75)) | node3(c_bit0, s74, s75))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2304,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s74, s75)) | node3(c_bit0, s74, s75)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 35.56/23.42 tff(2305,plain,
% 35.56/23.42 (node3(c_bit0, s74, s75)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2304, 81, 2301])).
% 35.56/23.42 tff(2306,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2307,plain,
% 35.56/23.42 ((node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)) | m_counter_cell_v_value(c_bit0, s75)) <=> (m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2308,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)) | m_counter_cell_v_value(c_bit0, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75))))),
% 35.56/23.42 inference(monotonicity,[status(thm)],[2307])).
% 35.56/23.42 tff(2309,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)) | m_counter_cell_v_value(c_bit0, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)))),
% 35.56/23.42 inference(transitivity,[status(thm)],[2308, 2306])).
% 35.56/23.42 tff(2310,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s74) | (~node3(c_bit0, s74, s75)) | m_counter_cell_v_value(c_bit0, s75))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2311,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74) | (~node3(c_bit0, s74, s75))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 35.56/23.42 tff(2312,plain,
% 35.56/23.42 (m_counter_cell_v_value(c_bit0, s75) | node1(c_bit0, s74)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2311, 199, 2305])).
% 35.56/23.42 tff(2313,plain,
% 35.56/23.42 (m_counter_cell_v_value(c_bit0, s75)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2312, 2294])).
% 35.56/23.42 tff(2314,assumption,(~m_counter_cell_v_carry_in(c_bit0, s75)), introduced(assumption)).
% 35.56/23.42 tff(2315,plain,
% 35.56/23.42 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s75)),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2316,plain,
% 35.56/23.42 ($false),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2315, 158, 2314])).
% 35.56/23.42 tff(2317,plain,(m_counter_cell_v_carry_in(c_bit0, s75)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.42 tff(2318,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2319,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75)))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2320,plain,
% 35.56/23.42 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 35.56/23.42 tff(2321,plain,
% 35.56/23.42 ((~m_counter_cell_v_value(c_bit0, s75)) | (~node2(c_bit0, s75))),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2320, 219, 2317])).
% 35.56/23.42 tff(2322,plain,
% 35.56/23.42 (~node2(c_bit0, s75)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2321, 2313])).
% 35.56/23.42 tff(2323,plain,
% 35.56/23.42 (succ(s75, s76) <=> succ(s75, s76)),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2324,axiom,(succ(s75, s76)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound76')).
% 35.56/23.42 tff(2325,plain,
% 35.56/23.42 (succ(s75, s76)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 35.56/23.42 tff(2326,plain,
% 35.56/23.42 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s75, s76)) | trans(s75, s76))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s75, s76)) | trans(s75, s76))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2327,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s75, s76)) | trans(s75, s76))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2328,plain,
% 35.56/23.42 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s75, s76)) | trans(s75, s76)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 35.56/23.42 tff(2329,plain,
% 35.56/23.42 (trans(s75, s76)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2328, 2325, 8])).
% 35.56/23.42 tff(2330,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s75, s76)) | node3(c_bit0, s75, s76))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s75, s76)) | node3(c_bit0, s75, s76))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2331,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s75, s76)) | node3(c_bit0, s75, s76))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2332,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s75, s76)) | node3(c_bit0, s75, s76)),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 35.56/23.42 tff(2333,plain,
% 35.56/23.42 (node3(c_bit0, s75, s76)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2332, 81, 2329])).
% 35.56/23.42 tff(2334,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2335,plain,
% 35.56/23.42 ((node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)) | (~m_counter_cell_v_value(c_bit0, s76))) <=> ((~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2336,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)) | (~m_counter_cell_v_value(c_bit0, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76))))),
% 35.56/23.42 inference(monotonicity,[status(thm)],[2335])).
% 35.56/23.42 tff(2337,plain,
% 35.56/23.42 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)) | (~m_counter_cell_v_value(c_bit0, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)))),
% 35.56/23.42 inference(transitivity,[status(thm)],[2336, 2334])).
% 35.56/23.42 tff(2338,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s75) | (~node3(c_bit0, s75, s76)) | (~m_counter_cell_v_value(c_bit0, s76)))),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2339,plain,
% 35.56/23.42 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75) | (~node3(c_bit0, s75, s76))),
% 35.56/23.42 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 35.56/23.42 tff(2340,plain,
% 35.56/23.42 ((~m_counter_cell_v_value(c_bit0, s76)) | node2(c_bit0, s75)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2339, 234, 2333])).
% 35.56/23.42 tff(2341,plain,
% 35.56/23.42 (~m_counter_cell_v_value(c_bit0, s76)),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2340, 2322])).
% 35.56/23.42 tff(2342,assumption,(~m_counter_cell_v_carry_in(c_bit0, s76)), introduced(assumption)).
% 35.56/23.42 tff(2343,plain,
% 35.56/23.42 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s76)),
% 35.56/23.42 inference(quant_inst,[status(thm)],[])).
% 35.56/23.42 tff(2344,plain,
% 35.56/23.42 ($false),
% 35.56/23.42 inference(unit_resolution,[status(thm)],[2343, 158, 2342])).
% 35.56/23.42 tff(2345,plain,(m_counter_cell_v_carry_in(c_bit0, s76)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.42 tff(2346,plain,
% 35.56/23.42 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.42 tff(2347,plain,
% 35.56/23.42 (((~node1(c_bit0, s76)) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76)))),
% 35.56/23.42 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2348,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s76)) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76))))),
% 35.56/23.43 inference(monotonicity,[status(thm)],[2347])).
% 35.56/23.43 tff(2349,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s76)) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76)))),
% 35.56/23.43 inference(transitivity,[status(thm)],[2348, 2346])).
% 35.56/23.43 tff(2350,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s76)) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2351,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s76)) | m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2350, 2349])).
% 35.56/23.43 tff(2352,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s76) | (~node1(c_bit0, s76))),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2351, 170, 2345])).
% 35.56/23.43 tff(2353,plain,
% 35.56/23.43 (~node1(c_bit0, s76)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2352, 2341])).
% 35.56/23.43 tff(2354,plain,
% 35.56/23.43 (succ(s76, s77) <=> succ(s76, s77)),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2355,axiom,(succ(s76, s77)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound77')).
% 35.56/23.43 tff(2356,plain,
% 35.56/23.43 (succ(s76, s77)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2355, 2354])).
% 35.56/23.43 tff(2357,plain,
% 35.56/23.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s76, s77)) | trans(s76, s77))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s76, s77)) | trans(s76, s77))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2358,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s76, s77)) | trans(s76, s77))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2359,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s76, s77)) | trans(s76, s77)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2358, 2357])).
% 35.56/23.43 tff(2360,plain,
% 35.56/23.43 (trans(s76, s77)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2359, 2356, 8])).
% 35.56/23.43 tff(2361,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s76, s77)) | node3(c_bit0, s76, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s76, s77)) | node3(c_bit0, s76, s77))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2362,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s76, s77)) | node3(c_bit0, s76, s77))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2363,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s76, s77)) | node3(c_bit0, s76, s77)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2362, 2361])).
% 35.56/23.43 tff(2364,plain,
% 35.56/23.43 (node3(c_bit0, s76, s77)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2363, 81, 2360])).
% 35.56/23.43 tff(2365,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | ((~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2366,plain,
% 35.56/23.43 ((node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77)) <=> ((~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2367,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | ((~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76)))),
% 35.56/23.43 inference(monotonicity,[status(thm)],[2366])).
% 35.56/23.43 tff(2368,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76))),
% 35.56/23.43 inference(transitivity,[status(thm)],[2367, 2365])).
% 35.56/23.43 tff(2369,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s76) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2370,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (~node3(c_bit0, s76, s77)) | m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2369, 2368])).
% 35.56/23.43 tff(2371,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s77) | node1(c_bit0, s76)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2370, 199, 2364])).
% 35.56/23.43 tff(2372,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s77)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2371, 2353])).
% 35.56/23.43 tff(2373,assumption,(~m_counter_cell_v_carry_in(c_bit0, s77)), introduced(assumption)).
% 35.56/23.43 tff(2374,plain,
% 35.56/23.43 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s77)),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2375,plain,
% 35.56/23.43 ($false),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2374, 158, 2373])).
% 35.56/23.43 tff(2376,plain,(m_counter_cell_v_carry_in(c_bit0, s77)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.43 tff(2377,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2378,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77)))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2379,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2378, 2377])).
% 35.56/23.43 tff(2380,plain,
% 35.56/23.43 ((~m_counter_cell_v_value(c_bit0, s77)) | (~node2(c_bit0, s77))),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2379, 219, 2376])).
% 35.56/23.43 tff(2381,plain,
% 35.56/23.43 (~node2(c_bit0, s77)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2380, 2372])).
% 35.56/23.43 tff(2382,plain,
% 35.56/23.43 (succ(s77, s78) <=> succ(s77, s78)),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2383,axiom,(succ(s77, s78)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound78')).
% 35.56/23.43 tff(2384,plain,
% 35.56/23.43 (succ(s77, s78)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 35.56/23.43 tff(2385,plain,
% 35.56/23.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s77, s78)) | trans(s77, s78))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s77, s78)) | trans(s77, s78))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2386,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s77, s78)) | trans(s77, s78))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2387,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s77, s78)) | trans(s77, s78)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 35.56/23.43 tff(2388,plain,
% 35.56/23.43 (trans(s77, s78)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2387, 2384, 8])).
% 35.56/23.43 tff(2389,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s77, s78)) | node3(c_bit0, s77, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s77, s78)) | node3(c_bit0, s77, s78))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2390,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s77, s78)) | node3(c_bit0, s77, s78))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2391,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s77, s78)) | node3(c_bit0, s77, s78)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2390, 2389])).
% 35.56/23.43 tff(2392,plain,
% 35.56/23.43 (node3(c_bit0, s77, s78)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2391, 81, 2388])).
% 35.56/23.43 tff(2393,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2394,plain,
% 35.56/23.43 ((node2(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | (~m_counter_cell_v_value(c_bit0, s78))) <=> (node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2395,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | (~m_counter_cell_v_value(c_bit0, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78))))),
% 35.56/23.43 inference(monotonicity,[status(thm)],[2394])).
% 35.56/23.43 tff(2396,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | (~m_counter_cell_v_value(c_bit0, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78)))),
% 35.56/23.43 inference(transitivity,[status(thm)],[2395, 2393])).
% 35.56/23.43 tff(2397,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | (~m_counter_cell_v_value(c_bit0, s78)))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2398,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node3(c_bit0, s77, s78))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2397, 2396])).
% 35.56/23.43 tff(2399,plain,
% 35.56/23.43 (node2(c_bit0, s77) | (~m_counter_cell_v_value(c_bit0, s78))),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2398, 234, 2392])).
% 35.56/23.43 tff(2400,plain,
% 35.56/23.43 (~m_counter_cell_v_value(c_bit0, s78)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2399, 2381])).
% 35.56/23.43 tff(2401,assumption,(~m_counter_cell_v_carry_in(c_bit0, s78)), introduced(assumption)).
% 35.56/23.43 tff(2402,plain,
% 35.56/23.43 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s78)),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2403,plain,
% 35.56/23.43 ($false),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2402, 158, 2401])).
% 35.56/23.43 tff(2404,plain,(m_counter_cell_v_carry_in(c_bit0, s78)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.43 tff(2405,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2406,plain,
% 35.56/23.43 (((~node1(c_bit0, s78)) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2407,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s78)) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78))))),
% 35.56/23.43 inference(monotonicity,[status(thm)],[2406])).
% 35.56/23.43 tff(2408,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s78)) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78)))),
% 35.56/23.43 inference(transitivity,[status(thm)],[2407, 2405])).
% 35.56/23.43 tff(2409,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s78)) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2410,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s78)) | m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 35.56/23.43 tff(2411,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s78) | (~node1(c_bit0, s78))),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2410, 170, 2404])).
% 35.56/23.43 tff(2412,plain,
% 35.56/23.43 (~node1(c_bit0, s78)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2411, 2400])).
% 35.56/23.43 tff(2413,plain,
% 35.56/23.43 (succ(s78, s79) <=> succ(s78, s79)),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2414,axiom,(succ(s78, s79)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound79')).
% 35.56/23.43 tff(2415,plain,
% 35.56/23.43 (succ(s78, s79)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2414, 2413])).
% 35.56/23.43 tff(2416,plain,
% 35.56/23.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s78, s79)) | trans(s78, s79))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s78, s79)) | trans(s78, s79))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2417,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s78, s79)) | trans(s78, s79))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2418,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s78, s79)) | trans(s78, s79)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 35.56/23.43 tff(2419,plain,
% 35.56/23.43 (trans(s78, s79)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2418, 2415, 8])).
% 35.56/23.43 tff(2420,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s78, s79)) | node3(c_bit0, s78, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s78, s79)) | node3(c_bit0, s78, s79))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2421,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s78, s79)) | node3(c_bit0, s78, s79))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2422,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s78, s79)) | node3(c_bit0, s78, s79)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2421, 2420])).
% 35.56/23.43 tff(2423,plain,
% 35.56/23.43 (node3(c_bit0, s78, s79)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2422, 81, 2419])).
% 35.56/23.43 tff(2424,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2425,plain,
% 35.56/23.43 ((node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | m_counter_cell_v_value(c_bit0, s79)) <=> (m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2426,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | m_counter_cell_v_value(c_bit0, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79))))),
% 35.56/23.43 inference(monotonicity,[status(thm)],[2425])).
% 35.56/23.43 tff(2427,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | m_counter_cell_v_value(c_bit0, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 35.56/23.43 inference(transitivity,[status(thm)],[2426, 2424])).
% 35.56/23.43 tff(2428,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | m_counter_cell_v_value(c_bit0, s79))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2429,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78) | (~node3(c_bit0, s78, s79))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2428, 2427])).
% 35.56/23.43 tff(2430,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s79) | node1(c_bit0, s78)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2429, 199, 2423])).
% 35.56/23.43 tff(2431,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s79)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2430, 2412])).
% 35.56/23.43 tff(2432,assumption,(~m_counter_cell_v_carry_in(c_bit0, s79)), introduced(assumption)).
% 35.56/23.43 tff(2433,plain,
% 35.56/23.43 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s79)),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2434,plain,
% 35.56/23.43 ($false),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2433, 158, 2432])).
% 35.56/23.43 tff(2435,plain,(m_counter_cell_v_carry_in(c_bit0, s79)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.43 tff(2436,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2437,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79)))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2438,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2437, 2436])).
% 35.56/23.43 tff(2439,plain,
% 35.56/23.43 ((~m_counter_cell_v_value(c_bit0, s79)) | (~node2(c_bit0, s79))),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2438, 219, 2435])).
% 35.56/23.43 tff(2440,plain,
% 35.56/23.43 (~node2(c_bit0, s79)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2439, 2431])).
% 35.56/23.43 tff(2441,plain,
% 35.56/23.43 (succ(s79, s80) <=> succ(s79, s80)),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2442,axiom,(succ(s79, s80)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound80')).
% 35.56/23.43 tff(2443,plain,
% 35.56/23.43 (succ(s79, s80)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2442, 2441])).
% 35.56/23.43 tff(2444,plain,
% 35.56/23.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s79, s80)) | trans(s79, s80))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s79, s80)) | trans(s79, s80))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2445,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s79, s80)) | trans(s79, s80))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2446,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s79, s80)) | trans(s79, s80)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2445, 2444])).
% 35.56/23.43 tff(2447,plain,
% 35.56/23.43 (trans(s79, s80)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2446, 2443, 8])).
% 35.56/23.43 tff(2448,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s79, s80)) | node3(c_bit0, s79, s80))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s79, s80)) | node3(c_bit0, s79, s80))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2449,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s79, s80)) | node3(c_bit0, s79, s80))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2450,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s79, s80)) | node3(c_bit0, s79, s80)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2449, 2448])).
% 35.56/23.43 tff(2451,plain,
% 35.56/23.43 (node3(c_bit0, s79, s80)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2450, 81, 2447])).
% 35.56/23.43 tff(2452,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2453,plain,
% 35.56/23.43 ((node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | (~m_counter_cell_v_value(c_bit0, s80))) <=> ((~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2454,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | (~m_counter_cell_v_value(c_bit0, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80))))),
% 35.56/23.43 inference(monotonicity,[status(thm)],[2453])).
% 35.56/23.43 tff(2455,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | (~m_counter_cell_v_value(c_bit0, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 35.56/23.43 inference(transitivity,[status(thm)],[2454, 2452])).
% 35.56/23.43 tff(2456,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | (~m_counter_cell_v_value(c_bit0, s80)))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2457,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79) | (~node3(c_bit0, s79, s80))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2456, 2455])).
% 35.56/23.43 tff(2458,plain,
% 35.56/23.43 ((~m_counter_cell_v_value(c_bit0, s80)) | node2(c_bit0, s79)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2457, 234, 2451])).
% 35.56/23.43 tff(2459,plain,
% 35.56/23.43 (~m_counter_cell_v_value(c_bit0, s80)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2458, 2440])).
% 35.56/23.43 tff(2460,assumption,(~m_counter_cell_v_carry_in(c_bit0, s80)), introduced(assumption)).
% 35.56/23.43 tff(2461,plain,
% 35.56/23.43 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s80)),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2462,plain,
% 35.56/23.43 ($false),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2461, 158, 2460])).
% 35.56/23.43 tff(2463,plain,(m_counter_cell_v_carry_in(c_bit0, s80)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.43 tff(2464,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2465,plain,
% 35.56/23.43 (((~node1(c_bit0, s80)) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2466,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s80)) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80))))),
% 35.56/23.43 inference(monotonicity,[status(thm)],[2465])).
% 35.56/23.43 tff(2467,plain,
% 35.56/23.43 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s80)) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80)))),
% 35.56/23.43 inference(transitivity,[status(thm)],[2466, 2464])).
% 35.56/23.43 tff(2468,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s80)) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2469,plain,
% 35.56/23.43 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s80)) | m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 35.56/23.43 tff(2470,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s80) | (~node1(c_bit0, s80))),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2469, 170, 2463])).
% 35.56/23.43 tff(2471,plain,
% 35.56/23.43 (~node1(c_bit0, s80)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2470, 2459])).
% 35.56/23.43 tff(2472,plain,
% 35.56/23.43 (succ(s80, s81) <=> succ(s80, s81)),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2473,axiom,(succ(s80, s81)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound81')).
% 35.56/23.43 tff(2474,plain,
% 35.56/23.43 (succ(s80, s81)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 35.56/23.43 tff(2475,plain,
% 35.56/23.43 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s80, s81)) | trans(s80, s81))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s80, s81)) | trans(s80, s81))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2476,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s80, s81)) | trans(s80, s81))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2477,plain,
% 35.56/23.43 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s80, s81)) | trans(s80, s81)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2476, 2475])).
% 35.56/23.43 tff(2478,plain,
% 35.56/23.43 (trans(s80, s81)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2477, 2474, 8])).
% 35.56/23.43 tff(2479,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s80, s81)) | node3(c_bit0, s80, s81))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s80, s81)) | node3(c_bit0, s80, s81))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2480,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s80, s81)) | node3(c_bit0, s80, s81))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2481,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s80, s81)) | node3(c_bit0, s80, s81)),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 35.56/23.43 tff(2482,plain,
% 35.56/23.43 (node3(c_bit0, s80, s81)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2481, 81, 2478])).
% 35.56/23.43 tff(2483,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2484,plain,
% 35.56/23.43 ((node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | m_counter_cell_v_value(c_bit0, s81)) <=> (m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 35.56/23.43 inference(rewrite,[status(thm)],[])).
% 35.56/23.43 tff(2485,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | m_counter_cell_v_value(c_bit0, s81))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81))))),
% 35.56/23.43 inference(monotonicity,[status(thm)],[2484])).
% 35.56/23.43 tff(2486,plain,
% 35.56/23.43 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | m_counter_cell_v_value(c_bit0, s81))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 35.56/23.43 inference(transitivity,[status(thm)],[2485, 2483])).
% 35.56/23.43 tff(2487,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | m_counter_cell_v_value(c_bit0, s81))),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.43 tff(2488,plain,
% 35.56/23.43 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80) | (~node3(c_bit0, s80, s81))),
% 35.56/23.43 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 35.56/23.43 tff(2489,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s81) | node1(c_bit0, s80)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2488, 199, 2482])).
% 35.56/23.43 tff(2490,plain,
% 35.56/23.43 (m_counter_cell_v_value(c_bit0, s81)),
% 35.56/23.43 inference(unit_resolution,[status(thm)],[2489, 2471])).
% 35.56/23.43 tff(2491,assumption,(~m_counter_cell_v_carry_in(c_bit0, s81)), introduced(assumption)).
% 35.56/23.43 tff(2492,plain,
% 35.56/23.43 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s81)),
% 35.56/23.43 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2493,plain,
% 35.56/23.44 ($false),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2492, 158, 2491])).
% 35.56/23.44 tff(2494,plain,(m_counter_cell_v_carry_in(c_bit0, s81)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.44 tff(2495,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2496,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81)))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2497,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2496, 2495])).
% 35.56/23.44 tff(2498,plain,
% 35.56/23.44 ((~m_counter_cell_v_value(c_bit0, s81)) | (~node2(c_bit0, s81))),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2497, 219, 2494])).
% 35.56/23.44 tff(2499,plain,
% 35.56/23.44 (~node2(c_bit0, s81)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2498, 2490])).
% 35.56/23.44 tff(2500,plain,
% 35.56/23.44 (succ(s81, s82) <=> succ(s81, s82)),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2501,axiom,(succ(s81, s82)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound82')).
% 35.56/23.44 tff(2502,plain,
% 35.56/23.44 (succ(s81, s82)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2501, 2500])).
% 35.56/23.44 tff(2503,plain,
% 35.56/23.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s81, s82)) | trans(s81, s82))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s81, s82)) | trans(s81, s82))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2504,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s81, s82)) | trans(s81, s82))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2505,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s81, s82)) | trans(s81, s82)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2504, 2503])).
% 35.56/23.44 tff(2506,plain,
% 35.56/23.44 (trans(s81, s82)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2505, 2502, 8])).
% 35.56/23.44 tff(2507,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s81, s82)) | node3(c_bit0, s81, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s81, s82)) | node3(c_bit0, s81, s82))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2508,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s81, s82)) | node3(c_bit0, s81, s82))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2509,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s81, s82)) | node3(c_bit0, s81, s82)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2508, 2507])).
% 35.56/23.44 tff(2510,plain,
% 35.56/23.44 (node3(c_bit0, s81, s82)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2509, 81, 2506])).
% 35.56/23.44 tff(2511,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2512,plain,
% 35.56/23.44 ((node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | (~m_counter_cell_v_value(c_bit0, s82))) <=> ((~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2513,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | (~m_counter_cell_v_value(c_bit0, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82))))),
% 35.56/23.44 inference(monotonicity,[status(thm)],[2512])).
% 35.56/23.44 tff(2514,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | (~m_counter_cell_v_value(c_bit0, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 35.56/23.44 inference(transitivity,[status(thm)],[2513, 2511])).
% 35.56/23.44 tff(2515,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | (~m_counter_cell_v_value(c_bit0, s82)))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2516,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81) | (~node3(c_bit0, s81, s82))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2515, 2514])).
% 35.56/23.44 tff(2517,plain,
% 35.56/23.44 ((~m_counter_cell_v_value(c_bit0, s82)) | node2(c_bit0, s81)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2516, 234, 2510])).
% 35.56/23.44 tff(2518,plain,
% 35.56/23.44 (~m_counter_cell_v_value(c_bit0, s82)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2517, 2499])).
% 35.56/23.44 tff(2519,assumption,(~m_counter_cell_v_carry_in(c_bit0, s82)), introduced(assumption)).
% 35.56/23.44 tff(2520,plain,
% 35.56/23.44 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s82)),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2521,plain,
% 35.56/23.44 ($false),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2520, 158, 2519])).
% 35.56/23.44 tff(2522,plain,(m_counter_cell_v_carry_in(c_bit0, s82)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.44 tff(2523,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2524,plain,
% 35.56/23.44 (((~node1(c_bit0, s82)) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2525,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s82)) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82))))),
% 35.56/23.44 inference(monotonicity,[status(thm)],[2524])).
% 35.56/23.44 tff(2526,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s82)) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82)))),
% 35.56/23.44 inference(transitivity,[status(thm)],[2525, 2523])).
% 35.56/23.44 tff(2527,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s82)) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2528,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s82)) | m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2527, 2526])).
% 35.56/23.44 tff(2529,plain,
% 35.56/23.44 (m_counter_cell_v_value(c_bit0, s82) | (~node1(c_bit0, s82))),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2528, 170, 2522])).
% 35.56/23.44 tff(2530,plain,
% 35.56/23.44 (~node1(c_bit0, s82)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2529, 2518])).
% 35.56/23.44 tff(2531,plain,
% 35.56/23.44 (succ(s82, s83) <=> succ(s82, s83)),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2532,axiom,(succ(s82, s83)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound83')).
% 35.56/23.44 tff(2533,plain,
% 35.56/23.44 (succ(s82, s83)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2532, 2531])).
% 35.56/23.44 tff(2534,plain,
% 35.56/23.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s82, s83)) | trans(s82, s83))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s82, s83)) | trans(s82, s83))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2535,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s82, s83)) | trans(s82, s83))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2536,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s82, s83)) | trans(s82, s83)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2535, 2534])).
% 35.56/23.44 tff(2537,plain,
% 35.56/23.44 (trans(s82, s83)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2536, 2533, 8])).
% 35.56/23.44 tff(2538,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s82, s83)) | node3(c_bit0, s82, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s82, s83)) | node3(c_bit0, s82, s83))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2539,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s82, s83)) | node3(c_bit0, s82, s83))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2540,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s82, s83)) | node3(c_bit0, s82, s83)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 35.56/23.44 tff(2541,plain,
% 35.56/23.44 (node3(c_bit0, s82, s83)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2540, 81, 2537])).
% 35.56/23.44 tff(2542,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2543,plain,
% 35.56/23.44 ((node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | m_counter_cell_v_value(c_bit0, s83)) <=> (m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2544,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | m_counter_cell_v_value(c_bit0, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83))))),
% 35.56/23.44 inference(monotonicity,[status(thm)],[2543])).
% 35.56/23.44 tff(2545,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | m_counter_cell_v_value(c_bit0, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 35.56/23.44 inference(transitivity,[status(thm)],[2544, 2542])).
% 35.56/23.44 tff(2546,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | m_counter_cell_v_value(c_bit0, s83))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2547,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82) | (~node3(c_bit0, s82, s83))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 35.56/23.44 tff(2548,plain,
% 35.56/23.44 (m_counter_cell_v_value(c_bit0, s83) | node1(c_bit0, s82)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2547, 199, 2541])).
% 35.56/23.44 tff(2549,plain,
% 35.56/23.44 (m_counter_cell_v_value(c_bit0, s83)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2548, 2530])).
% 35.56/23.44 tff(2550,assumption,(~m_counter_cell_v_carry_in(c_bit0, s83)), introduced(assumption)).
% 35.56/23.44 tff(2551,plain,
% 35.56/23.44 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s83)),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2552,plain,
% 35.56/23.44 ($false),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2551, 158, 2550])).
% 35.56/23.44 tff(2553,plain,(m_counter_cell_v_carry_in(c_bit0, s83)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.44 tff(2554,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2555,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83)))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2556,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2555, 2554])).
% 35.56/23.44 tff(2557,plain,
% 35.56/23.44 ((~m_counter_cell_v_value(c_bit0, s83)) | (~node2(c_bit0, s83))),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2556, 219, 2553])).
% 35.56/23.44 tff(2558,plain,
% 35.56/23.44 (~node2(c_bit0, s83)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2557, 2549])).
% 35.56/23.44 tff(2559,plain,
% 35.56/23.44 (succ(s83, s84) <=> succ(s83, s84)),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2560,axiom,(succ(s83, s84)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound84')).
% 35.56/23.44 tff(2561,plain,
% 35.56/23.44 (succ(s83, s84)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 35.56/23.44 tff(2562,plain,
% 35.56/23.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s83, s84)) | trans(s83, s84))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s83, s84)) | trans(s83, s84))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2563,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s83, s84)) | trans(s83, s84))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2564,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s83, s84)) | trans(s83, s84)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 35.56/23.44 tff(2565,plain,
% 35.56/23.44 (trans(s83, s84)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2564, 2561, 8])).
% 35.56/23.44 tff(2566,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s83, s84)) | node3(c_bit0, s83, s84))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s83, s84)) | node3(c_bit0, s83, s84))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2567,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s83, s84)) | node3(c_bit0, s83, s84))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2568,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s83, s84)) | node3(c_bit0, s83, s84)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2567, 2566])).
% 35.56/23.44 tff(2569,plain,
% 35.56/23.44 (node3(c_bit0, s83, s84)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2568, 81, 2565])).
% 35.56/23.44 tff(2570,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2571,plain,
% 35.56/23.44 ((node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | (~m_counter_cell_v_value(c_bit0, s84))) <=> ((~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2572,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | (~m_counter_cell_v_value(c_bit0, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84))))),
% 35.56/23.44 inference(monotonicity,[status(thm)],[2571])).
% 35.56/23.44 tff(2573,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | (~m_counter_cell_v_value(c_bit0, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 35.56/23.44 inference(transitivity,[status(thm)],[2572, 2570])).
% 35.56/23.44 tff(2574,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | (~m_counter_cell_v_value(c_bit0, s84)))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2575,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83) | (~node3(c_bit0, s83, s84))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2574, 2573])).
% 35.56/23.44 tff(2576,plain,
% 35.56/23.44 ((~m_counter_cell_v_value(c_bit0, s84)) | node2(c_bit0, s83)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2575, 234, 2569])).
% 35.56/23.44 tff(2577,plain,
% 35.56/23.44 (~m_counter_cell_v_value(c_bit0, s84)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2576, 2558])).
% 35.56/23.44 tff(2578,assumption,(~m_counter_cell_v_carry_in(c_bit0, s84)), introduced(assumption)).
% 35.56/23.44 tff(2579,plain,
% 35.56/23.44 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s84)),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2580,plain,
% 35.56/23.44 ($false),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2579, 158, 2578])).
% 35.56/23.44 tff(2581,plain,(m_counter_cell_v_carry_in(c_bit0, s84)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.44 tff(2582,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2583,plain,
% 35.56/23.44 (((~node1(c_bit0, s84)) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2584,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s84)) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84))))),
% 35.56/23.44 inference(monotonicity,[status(thm)],[2583])).
% 35.56/23.44 tff(2585,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s84)) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84)))),
% 35.56/23.44 inference(transitivity,[status(thm)],[2584, 2582])).
% 35.56/23.44 tff(2586,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s84)) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2587,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s84)) | m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2586, 2585])).
% 35.56/23.44 tff(2588,plain,
% 35.56/23.44 (m_counter_cell_v_value(c_bit0, s84) | (~node1(c_bit0, s84))),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2587, 170, 2581])).
% 35.56/23.44 tff(2589,plain,
% 35.56/23.44 (~node1(c_bit0, s84)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2588, 2577])).
% 35.56/23.44 tff(2590,plain,
% 35.56/23.44 (succ(s84, s85) <=> succ(s84, s85)),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2591,axiom,(succ(s84, s85)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound85')).
% 35.56/23.44 tff(2592,plain,
% 35.56/23.44 (succ(s84, s85)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 35.56/23.44 tff(2593,plain,
% 35.56/23.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s84, s85)) | trans(s84, s85))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s84, s85)) | trans(s84, s85))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2594,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s84, s85)) | trans(s84, s85))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2595,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s84, s85)) | trans(s84, s85)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2594, 2593])).
% 35.56/23.44 tff(2596,plain,
% 35.56/23.44 (trans(s84, s85)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2595, 2592, 8])).
% 35.56/23.44 tff(2597,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s84, s85)) | node3(c_bit0, s84, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s84, s85)) | node3(c_bit0, s84, s85))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2598,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s84, s85)) | node3(c_bit0, s84, s85))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2599,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s84, s85)) | node3(c_bit0, s84, s85)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2598, 2597])).
% 35.56/23.44 tff(2600,plain,
% 35.56/23.44 (node3(c_bit0, s84, s85)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2599, 81, 2596])).
% 35.56/23.44 tff(2601,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2602,plain,
% 35.56/23.44 ((node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | m_counter_cell_v_value(c_bit0, s85)) <=> (m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2603,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | m_counter_cell_v_value(c_bit0, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85))))),
% 35.56/23.44 inference(monotonicity,[status(thm)],[2602])).
% 35.56/23.44 tff(2604,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | m_counter_cell_v_value(c_bit0, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 35.56/23.44 inference(transitivity,[status(thm)],[2603, 2601])).
% 35.56/23.44 tff(2605,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | m_counter_cell_v_value(c_bit0, s85))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2606,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84) | (~node3(c_bit0, s84, s85))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2605, 2604])).
% 35.56/23.44 tff(2607,plain,
% 35.56/23.44 (m_counter_cell_v_value(c_bit0, s85) | node1(c_bit0, s84)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2606, 199, 2600])).
% 35.56/23.44 tff(2608,plain,
% 35.56/23.44 (m_counter_cell_v_value(c_bit0, s85)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2607, 2589])).
% 35.56/23.44 tff(2609,assumption,(~m_counter_cell_v_carry_in(c_bit0, s85)), introduced(assumption)).
% 35.56/23.44 tff(2610,plain,
% 35.56/23.44 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s85)),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2611,plain,
% 35.56/23.44 ($false),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2610, 158, 2609])).
% 35.56/23.44 tff(2612,plain,(m_counter_cell_v_carry_in(c_bit0, s85)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.44 tff(2613,plain,
% 35.56/23.44 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2614,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85)))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2615,plain,
% 35.56/23.44 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2614, 2613])).
% 35.56/23.44 tff(2616,plain,
% 35.56/23.44 ((~m_counter_cell_v_value(c_bit0, s85)) | (~node2(c_bit0, s85))),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2615, 219, 2612])).
% 35.56/23.44 tff(2617,plain,
% 35.56/23.44 (~node2(c_bit0, s85)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2616, 2608])).
% 35.56/23.44 tff(2618,plain,
% 35.56/23.44 (succ(s85, s86) <=> succ(s85, s86)),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2619,axiom,(succ(s85, s86)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound86')).
% 35.56/23.44 tff(2620,plain,
% 35.56/23.44 (succ(s85, s86)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2619, 2618])).
% 35.56/23.44 tff(2621,plain,
% 35.56/23.44 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s85, s86)) | trans(s85, s86))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s85, s86)) | trans(s85, s86))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2622,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s85, s86)) | trans(s85, s86))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2623,plain,
% 35.56/23.44 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s85, s86)) | trans(s85, s86)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2622, 2621])).
% 35.56/23.44 tff(2624,plain,
% 35.56/23.44 (trans(s85, s86)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2623, 2620, 8])).
% 35.56/23.44 tff(2625,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s85, s86)) | node3(c_bit0, s85, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s85, s86)) | node3(c_bit0, s85, s86))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2626,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s85, s86)) | node3(c_bit0, s85, s86))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2627,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s85, s86)) | node3(c_bit0, s85, s86)),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 35.56/23.44 tff(2628,plain,
% 35.56/23.44 (node3(c_bit0, s85, s86)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2627, 81, 2624])).
% 35.56/23.44 tff(2629,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2630,plain,
% 35.56/23.44 ((node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | (~m_counter_cell_v_value(c_bit0, s86))) <=> ((~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 35.56/23.44 inference(rewrite,[status(thm)],[])).
% 35.56/23.44 tff(2631,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | (~m_counter_cell_v_value(c_bit0, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86))))),
% 35.56/23.44 inference(monotonicity,[status(thm)],[2630])).
% 35.56/23.44 tff(2632,plain,
% 35.56/23.44 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | (~m_counter_cell_v_value(c_bit0, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 35.56/23.44 inference(transitivity,[status(thm)],[2631, 2629])).
% 35.56/23.44 tff(2633,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | (~m_counter_cell_v_value(c_bit0, s86)))),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2634,plain,
% 35.56/23.44 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85) | (~node3(c_bit0, s85, s86))),
% 35.56/23.44 inference(modus_ponens,[status(thm)],[2633, 2632])).
% 35.56/23.44 tff(2635,plain,
% 35.56/23.44 ((~m_counter_cell_v_value(c_bit0, s86)) | node2(c_bit0, s85)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2634, 234, 2628])).
% 35.56/23.44 tff(2636,plain,
% 35.56/23.44 (~m_counter_cell_v_value(c_bit0, s86)),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2635, 2617])).
% 35.56/23.44 tff(2637,assumption,(~m_counter_cell_v_carry_in(c_bit0, s86)), introduced(assumption)).
% 35.56/23.44 tff(2638,plain,
% 35.56/23.44 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s86)),
% 35.56/23.44 inference(quant_inst,[status(thm)],[])).
% 35.56/23.44 tff(2639,plain,
% 35.56/23.44 ($false),
% 35.56/23.44 inference(unit_resolution,[status(thm)],[2638, 158, 2637])).
% 35.56/23.44 tff(2640,plain,(m_counter_cell_v_carry_in(c_bit0, s86)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.45 tff(2641,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2642,plain,
% 35.56/23.45 (((~node1(c_bit0, s86)) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2643,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s86)) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86))))),
% 35.56/23.45 inference(monotonicity,[status(thm)],[2642])).
% 35.56/23.45 tff(2644,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s86)) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86)))),
% 35.56/23.45 inference(transitivity,[status(thm)],[2643, 2641])).
% 35.56/23.45 tff(2645,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s86)) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2646,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s86)) | m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 35.56/23.45 tff(2647,plain,
% 35.56/23.45 (m_counter_cell_v_value(c_bit0, s86) | (~node1(c_bit0, s86))),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2646, 170, 2640])).
% 35.56/23.45 tff(2648,plain,
% 35.56/23.45 (~node1(c_bit0, s86)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2647, 2636])).
% 35.56/23.45 tff(2649,plain,
% 35.56/23.45 (succ(s86, s87) <=> succ(s86, s87)),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2650,axiom,(succ(s86, s87)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound87')).
% 35.56/23.45 tff(2651,plain,
% 35.56/23.45 (succ(s86, s87)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2650, 2649])).
% 35.56/23.45 tff(2652,plain,
% 35.56/23.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s86, s87)) | trans(s86, s87))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s86, s87)) | trans(s86, s87))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2653,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s86, s87)) | trans(s86, s87))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2654,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s86, s87)) | trans(s86, s87)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2653, 2652])).
% 35.56/23.45 tff(2655,plain,
% 35.56/23.45 (trans(s86, s87)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2654, 2651, 8])).
% 35.56/23.45 tff(2656,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s86, s87)) | node3(c_bit0, s86, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s86, s87)) | node3(c_bit0, s86, s87))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2657,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s86, s87)) | node3(c_bit0, s86, s87))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2658,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s86, s87)) | node3(c_bit0, s86, s87)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 35.56/23.45 tff(2659,plain,
% 35.56/23.45 (node3(c_bit0, s86, s87)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2658, 81, 2655])).
% 35.56/23.45 tff(2660,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2661,plain,
% 35.56/23.45 ((node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | m_counter_cell_v_value(c_bit0, s87)) <=> (m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2662,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | m_counter_cell_v_value(c_bit0, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87))))),
% 35.56/23.45 inference(monotonicity,[status(thm)],[2661])).
% 35.56/23.45 tff(2663,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | m_counter_cell_v_value(c_bit0, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 35.56/23.45 inference(transitivity,[status(thm)],[2662, 2660])).
% 35.56/23.45 tff(2664,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | m_counter_cell_v_value(c_bit0, s87))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2665,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86) | (~node3(c_bit0, s86, s87))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2664, 2663])).
% 35.56/23.45 tff(2666,plain,
% 35.56/23.45 (m_counter_cell_v_value(c_bit0, s87) | node1(c_bit0, s86)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2665, 199, 2659])).
% 35.56/23.45 tff(2667,plain,
% 35.56/23.45 (m_counter_cell_v_value(c_bit0, s87)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2666, 2648])).
% 35.56/23.45 tff(2668,assumption,(~m_counter_cell_v_carry_in(c_bit0, s87)), introduced(assumption)).
% 35.56/23.45 tff(2669,plain,
% 35.56/23.45 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s87)),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2670,plain,
% 35.56/23.45 ($false),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2669, 158, 2668])).
% 35.56/23.45 tff(2671,plain,(m_counter_cell_v_carry_in(c_bit0, s87)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.45 tff(2672,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2673,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87)))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2674,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 35.56/23.45 tff(2675,plain,
% 35.56/23.45 ((~m_counter_cell_v_value(c_bit0, s87)) | (~node2(c_bit0, s87))),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2674, 219, 2671])).
% 35.56/23.45 tff(2676,plain,
% 35.56/23.45 (~node2(c_bit0, s87)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2675, 2667])).
% 35.56/23.45 tff(2677,plain,
% 35.56/23.45 (succ(s87, s88) <=> succ(s87, s88)),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2678,axiom,(succ(s87, s88)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound88')).
% 35.56/23.45 tff(2679,plain,
% 35.56/23.45 (succ(s87, s88)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2678, 2677])).
% 35.56/23.45 tff(2680,plain,
% 35.56/23.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s87, s88)) | trans(s87, s88))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s87, s88)) | trans(s87, s88))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2681,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s87, s88)) | trans(s87, s88))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2682,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s87, s88)) | trans(s87, s88)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 35.56/23.45 tff(2683,plain,
% 35.56/23.45 (trans(s87, s88)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2682, 2679, 8])).
% 35.56/23.45 tff(2684,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s87, s88)) | node3(c_bit0, s87, s88))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s87, s88)) | node3(c_bit0, s87, s88))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2685,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s87, s88)) | node3(c_bit0, s87, s88))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2686,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s87, s88)) | node3(c_bit0, s87, s88)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2685, 2684])).
% 35.56/23.45 tff(2687,plain,
% 35.56/23.45 (node3(c_bit0, s87, s88)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2686, 81, 2683])).
% 35.56/23.45 tff(2688,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2689,plain,
% 35.56/23.45 ((node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | (~m_counter_cell_v_value(c_bit0, s88))) <=> ((~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2690,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | (~m_counter_cell_v_value(c_bit0, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88))))),
% 35.56/23.45 inference(monotonicity,[status(thm)],[2689])).
% 35.56/23.45 tff(2691,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | (~m_counter_cell_v_value(c_bit0, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 35.56/23.45 inference(transitivity,[status(thm)],[2690, 2688])).
% 35.56/23.45 tff(2692,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | (~m_counter_cell_v_value(c_bit0, s88)))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2693,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87) | (~node3(c_bit0, s87, s88))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 35.56/23.45 tff(2694,plain,
% 35.56/23.45 ((~m_counter_cell_v_value(c_bit0, s88)) | node2(c_bit0, s87)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2693, 234, 2687])).
% 35.56/23.45 tff(2695,plain,
% 35.56/23.45 (~m_counter_cell_v_value(c_bit0, s88)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2694, 2676])).
% 35.56/23.45 tff(2696,assumption,(~m_counter_cell_v_carry_in(c_bit0, s88)), introduced(assumption)).
% 35.56/23.45 tff(2697,plain,
% 35.56/23.45 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s88)),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2698,plain,
% 35.56/23.45 ($false),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2697, 158, 2696])).
% 35.56/23.45 tff(2699,plain,(m_counter_cell_v_carry_in(c_bit0, s88)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.45 tff(2700,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2701,plain,
% 35.56/23.45 (((~node1(c_bit0, s88)) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2702,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s88)) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88))))),
% 35.56/23.45 inference(monotonicity,[status(thm)],[2701])).
% 35.56/23.45 tff(2703,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s88)) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88)))),
% 35.56/23.45 inference(transitivity,[status(thm)],[2702, 2700])).
% 35.56/23.45 tff(2704,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s88)) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2705,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s88)) | m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2704, 2703])).
% 35.56/23.45 tff(2706,plain,
% 35.56/23.45 (m_counter_cell_v_value(c_bit0, s88) | (~node1(c_bit0, s88))),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2705, 170, 2699])).
% 35.56/23.45 tff(2707,plain,
% 35.56/23.45 (~node1(c_bit0, s88)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2706, 2695])).
% 35.56/23.45 tff(2708,plain,
% 35.56/23.45 (succ(s88, s89) <=> succ(s88, s89)),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2709,axiom,(succ(s88, s89)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound89')).
% 35.56/23.45 tff(2710,plain,
% 35.56/23.45 (succ(s88, s89)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2709, 2708])).
% 35.56/23.45 tff(2711,plain,
% 35.56/23.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s88, s89)) | trans(s88, s89))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s88, s89)) | trans(s88, s89))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2712,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s88, s89)) | trans(s88, s89))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2713,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s88, s89)) | trans(s88, s89)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2712, 2711])).
% 35.56/23.45 tff(2714,plain,
% 35.56/23.45 (trans(s88, s89)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2713, 2710, 8])).
% 35.56/23.45 tff(2715,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s88, s89)) | node3(c_bit0, s88, s89))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s88, s89)) | node3(c_bit0, s88, s89))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2716,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s88, s89)) | node3(c_bit0, s88, s89))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2717,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s88, s89)) | node3(c_bit0, s88, s89)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 35.56/23.45 tff(2718,plain,
% 35.56/23.45 (node3(c_bit0, s88, s89)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2717, 81, 2714])).
% 35.56/23.45 tff(2719,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2720,plain,
% 35.56/23.45 ((node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | m_counter_cell_v_value(c_bit0, s89)) <=> (m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2721,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | m_counter_cell_v_value(c_bit0, s89))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89))))),
% 35.56/23.45 inference(monotonicity,[status(thm)],[2720])).
% 35.56/23.45 tff(2722,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | m_counter_cell_v_value(c_bit0, s89))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 35.56/23.45 inference(transitivity,[status(thm)],[2721, 2719])).
% 35.56/23.45 tff(2723,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | m_counter_cell_v_value(c_bit0, s89))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2724,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88) | (~node3(c_bit0, s88, s89))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2723, 2722])).
% 35.56/23.45 tff(2725,plain,
% 35.56/23.45 (m_counter_cell_v_value(c_bit0, s89) | node1(c_bit0, s88)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2724, 199, 2718])).
% 35.56/23.45 tff(2726,plain,
% 35.56/23.45 (m_counter_cell_v_value(c_bit0, s89)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2725, 2707])).
% 35.56/23.45 tff(2727,assumption,(~m_counter_cell_v_carry_in(c_bit0, s89)), introduced(assumption)).
% 35.56/23.45 tff(2728,plain,
% 35.56/23.45 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s89)),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2729,plain,
% 35.56/23.45 ($false),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2728, 158, 2727])).
% 35.56/23.45 tff(2730,plain,(m_counter_cell_v_carry_in(c_bit0, s89)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.45 tff(2731,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2732,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89)))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2733,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2732, 2731])).
% 35.56/23.45 tff(2734,plain,
% 35.56/23.45 ((~m_counter_cell_v_value(c_bit0, s89)) | (~node2(c_bit0, s89))),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2733, 219, 2730])).
% 35.56/23.45 tff(2735,plain,
% 35.56/23.45 (~node2(c_bit0, s89)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2734, 2726])).
% 35.56/23.45 tff(2736,plain,
% 35.56/23.45 (succ(s89, s90) <=> succ(s89, s90)),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2737,axiom,(succ(s89, s90)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound90')).
% 35.56/23.45 tff(2738,plain,
% 35.56/23.45 (succ(s89, s90)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2737, 2736])).
% 35.56/23.45 tff(2739,plain,
% 35.56/23.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s89, s90)) | trans(s89, s90))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s89, s90)) | trans(s89, s90))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2740,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s89, s90)) | trans(s89, s90))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2741,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s89, s90)) | trans(s89, s90)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2740, 2739])).
% 35.56/23.45 tff(2742,plain,
% 35.56/23.45 (trans(s89, s90)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2741, 2738, 8])).
% 35.56/23.45 tff(2743,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s89, s90)) | node3(c_bit0, s89, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s89, s90)) | node3(c_bit0, s89, s90))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2744,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s89, s90)) | node3(c_bit0, s89, s90))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2745,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s89, s90)) | node3(c_bit0, s89, s90)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2744, 2743])).
% 35.56/23.45 tff(2746,plain,
% 35.56/23.45 (node3(c_bit0, s89, s90)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2745, 81, 2742])).
% 35.56/23.45 tff(2747,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2748,plain,
% 35.56/23.45 ((node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | (~m_counter_cell_v_value(c_bit0, s90))) <=> ((~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2749,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | (~m_counter_cell_v_value(c_bit0, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90))))),
% 35.56/23.45 inference(monotonicity,[status(thm)],[2748])).
% 35.56/23.45 tff(2750,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | (~m_counter_cell_v_value(c_bit0, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 35.56/23.45 inference(transitivity,[status(thm)],[2749, 2747])).
% 35.56/23.45 tff(2751,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | (~m_counter_cell_v_value(c_bit0, s90)))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2752,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89) | (~node3(c_bit0, s89, s90))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2751, 2750])).
% 35.56/23.45 tff(2753,plain,
% 35.56/23.45 ((~m_counter_cell_v_value(c_bit0, s90)) | node2(c_bit0, s89)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2752, 234, 2746])).
% 35.56/23.45 tff(2754,plain,
% 35.56/23.45 (~m_counter_cell_v_value(c_bit0, s90)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2753, 2735])).
% 35.56/23.45 tff(2755,plain,
% 35.56/23.45 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s90)),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2756,plain,
% 35.56/23.45 (m_counter_cell_v_carry_in(c_bit0, s90)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2755, 158])).
% 35.56/23.45 tff(2757,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2758,plain,
% 35.56/23.45 (((~node1(c_bit0, s90)) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2759,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s90)) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90))))),
% 35.56/23.45 inference(monotonicity,[status(thm)],[2758])).
% 35.56/23.45 tff(2760,plain,
% 35.56/23.45 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s90)) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90)))),
% 35.56/23.45 inference(transitivity,[status(thm)],[2759, 2757])).
% 35.56/23.45 tff(2761,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s90)) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2762,plain,
% 35.56/23.45 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s90)) | m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90))),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2761, 2760])).
% 35.56/23.45 tff(2763,plain,
% 35.56/23.45 (m_counter_cell_v_value(c_bit0, s90) | (~node1(c_bit0, s90))),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2762, 170, 2756])).
% 35.56/23.45 tff(2764,plain,
% 35.56/23.45 (~node1(c_bit0, s90)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2763, 2754])).
% 35.56/23.45 tff(2765,plain,
% 35.56/23.45 (succ(s90, s91) <=> succ(s90, s91)),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2766,axiom,(succ(s90, s91)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound91')).
% 35.56/23.45 tff(2767,plain,
% 35.56/23.45 (succ(s90, s91)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2766, 2765])).
% 35.56/23.45 tff(2768,plain,
% 35.56/23.45 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s90, s91)) | trans(s90, s91))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s90, s91)) | trans(s90, s91))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2769,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s90, s91)) | trans(s90, s91))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2770,plain,
% 35.56/23.45 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s90, s91)) | trans(s90, s91)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 35.56/23.45 tff(2771,plain,
% 35.56/23.45 (trans(s90, s91)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2770, 2767, 8])).
% 35.56/23.45 tff(2772,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s90, s91)) | node3(c_bit0, s90, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s90, s91)) | node3(c_bit0, s90, s91))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2773,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s90, s91)) | node3(c_bit0, s90, s91))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2774,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s90, s91)) | node3(c_bit0, s90, s91)),
% 35.56/23.45 inference(modus_ponens,[status(thm)],[2773, 2772])).
% 35.56/23.45 tff(2775,plain,
% 35.56/23.45 (node3(c_bit0, s90, s91)),
% 35.56/23.45 inference(unit_resolution,[status(thm)],[2774, 81, 2771])).
% 35.56/23.45 tff(2776,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2777,plain,
% 35.56/23.45 ((node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | m_counter_cell_v_value(c_bit0, s91)) <=> (m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 35.56/23.45 inference(rewrite,[status(thm)],[])).
% 35.56/23.45 tff(2778,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | m_counter_cell_v_value(c_bit0, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91))))),
% 35.56/23.45 inference(monotonicity,[status(thm)],[2777])).
% 35.56/23.45 tff(2779,plain,
% 35.56/23.45 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | m_counter_cell_v_value(c_bit0, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 35.56/23.45 inference(transitivity,[status(thm)],[2778, 2776])).
% 35.56/23.45 tff(2780,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | m_counter_cell_v_value(c_bit0, s91))),
% 35.56/23.45 inference(quant_inst,[status(thm)],[])).
% 35.56/23.45 tff(2781,plain,
% 35.56/23.45 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90) | (~node3(c_bit0, s90, s91))),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2780, 2779])).
% 35.56/23.46 tff(2782,plain,
% 35.56/23.46 (m_counter_cell_v_value(c_bit0, s91) | node1(c_bit0, s90)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2781, 199, 2775])).
% 35.56/23.46 tff(2783,plain,
% 35.56/23.46 (m_counter_cell_v_value(c_bit0, s91)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2782, 2764])).
% 35.56/23.46 tff(2784,plain,
% 35.56/23.46 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s91)),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2785,plain,
% 35.56/23.46 (m_counter_cell_v_carry_in(c_bit0, s91)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2784, 158])).
% 35.56/23.46 tff(2786,plain,
% 35.56/23.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91)))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2787,plain,
% 35.56/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91)))),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2788,plain,
% 35.56/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91))),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2787, 2786])).
% 35.56/23.46 tff(2789,plain,
% 35.56/23.46 ((~m_counter_cell_v_value(c_bit0, s91)) | (~node2(c_bit0, s91))),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2788, 219, 2785])).
% 35.56/23.46 tff(2790,plain,
% 35.56/23.46 (~node2(c_bit0, s91)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2789, 2783])).
% 35.56/23.46 tff(2791,plain,
% 35.56/23.46 (succ(s91, s92) <=> succ(s91, s92)),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2792,axiom,(succ(s91, s92)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound92')).
% 35.56/23.46 tff(2793,plain,
% 35.56/23.46 (succ(s91, s92)),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 35.56/23.46 tff(2794,plain,
% 35.56/23.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s91, s92)) | trans(s91, s92))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s91, s92)) | trans(s91, s92))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2795,plain,
% 35.56/23.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s91, s92)) | trans(s91, s92))),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2796,plain,
% 35.56/23.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s91, s92)) | trans(s91, s92)),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2795, 2794])).
% 35.56/23.46 tff(2797,plain,
% 35.56/23.46 (trans(s91, s92)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2796, 2793, 8])).
% 35.56/23.46 tff(2798,plain,
% 35.56/23.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s91, s92)) | node3(c_bit0, s91, s92))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s91, s92)) | node3(c_bit0, s91, s92))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2799,plain,
% 35.56/23.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s91, s92)) | node3(c_bit0, s91, s92))),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2800,plain,
% 35.56/23.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s91, s92)) | node3(c_bit0, s91, s92)),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 35.56/23.46 tff(2801,plain,
% 35.56/23.46 (node3(c_bit0, s91, s92)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2800, 81, 2797])).
% 35.56/23.46 tff(2802,plain,
% 35.56/23.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2803,plain,
% 35.56/23.46 ((node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | (~m_counter_cell_v_value(c_bit0, s92))) <=> ((~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2804,plain,
% 35.56/23.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | (~m_counter_cell_v_value(c_bit0, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92))))),
% 35.56/23.46 inference(monotonicity,[status(thm)],[2803])).
% 35.56/23.46 tff(2805,plain,
% 35.56/23.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | (~m_counter_cell_v_value(c_bit0, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 35.56/23.46 inference(transitivity,[status(thm)],[2804, 2802])).
% 35.56/23.46 tff(2806,plain,
% 35.56/23.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | (~m_counter_cell_v_value(c_bit0, s92)))),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2807,plain,
% 35.56/23.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91) | (~node3(c_bit0, s91, s92))),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2806, 2805])).
% 35.56/23.46 tff(2808,plain,
% 35.56/23.46 ((~m_counter_cell_v_value(c_bit0, s92)) | node2(c_bit0, s91)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2807, 234, 2801])).
% 35.56/23.46 tff(2809,plain,
% 35.56/23.46 (~m_counter_cell_v_value(c_bit0, s92)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2808, 2790])).
% 35.56/23.46 tff(2810,assumption,(~m_counter_cell_v_carry_in(c_bit0, s92)), introduced(assumption)).
% 35.56/23.46 tff(2811,plain,
% 35.56/23.46 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s92)),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2812,plain,
% 35.56/23.46 ($false),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2811, 158, 2810])).
% 35.56/23.46 tff(2813,plain,(m_counter_cell_v_carry_in(c_bit0, s92)), inference(lemma,lemma(discharge,[]))).
% 35.56/23.46 tff(2814,plain,
% 35.56/23.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92)))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2815,plain,
% 35.56/23.46 (((~node1(c_bit0, s92)) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92)))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2816,plain,
% 35.56/23.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s92)) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92))))),
% 35.56/23.46 inference(monotonicity,[status(thm)],[2815])).
% 35.56/23.46 tff(2817,plain,
% 35.56/23.46 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s92)) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92)))),
% 35.56/23.46 inference(transitivity,[status(thm)],[2816, 2814])).
% 35.56/23.46 tff(2818,plain,
% 35.56/23.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s92)) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92))),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2819,plain,
% 35.56/23.46 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92))),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2818, 2817])).
% 35.56/23.46 tff(2820,plain,
% 35.56/23.46 (m_counter_cell_v_value(c_bit0, s92) | (~node1(c_bit0, s92))),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2819, 170, 2813])).
% 35.56/23.46 tff(2821,plain,
% 35.56/23.46 (~node1(c_bit0, s92)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2820, 2809])).
% 35.56/23.46 tff(2822,plain,
% 35.56/23.46 (succ(s92, s93) <=> succ(s92, s93)),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2823,axiom,(succ(s92, s93)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound93')).
% 35.56/23.46 tff(2824,plain,
% 35.56/23.46 (succ(s92, s93)),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2823, 2822])).
% 35.56/23.46 tff(2825,plain,
% 35.56/23.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s92, s93)) | trans(s92, s93))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s92, s93)) | trans(s92, s93))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2826,plain,
% 35.56/23.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s92, s93)) | trans(s92, s93))),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2827,plain,
% 35.56/23.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s92, s93)) | trans(s92, s93)),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2826, 2825])).
% 35.56/23.46 tff(2828,plain,
% 35.56/23.46 (trans(s92, s93)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2827, 2824, 8])).
% 35.56/23.46 tff(2829,plain,
% 35.56/23.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s92, s93)) | node3(c_bit0, s92, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s92, s93)) | node3(c_bit0, s92, s93))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2830,plain,
% 35.56/23.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s92, s93)) | node3(c_bit0, s92, s93))),
% 35.56/23.46 inference(quant_inst,[status(thm)],[])).
% 35.56/23.46 tff(2831,plain,
% 35.56/23.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s92, s93)) | node3(c_bit0, s92, s93)),
% 35.56/23.46 inference(modus_ponens,[status(thm)],[2830, 2829])).
% 35.56/23.46 tff(2832,plain,
% 35.56/23.46 (node3(c_bit0, s92, s93)),
% 35.56/23.46 inference(unit_resolution,[status(thm)],[2831, 81, 2828])).
% 35.56/23.46 tff(2833,plain,
% 35.56/23.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2834,plain,
% 35.56/23.46 ((node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | m_counter_cell_v_value(c_bit0, s93)) <=> (m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 35.56/23.46 inference(rewrite,[status(thm)],[])).
% 35.56/23.46 tff(2835,plain,
% 35.56/23.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | m_counter_cell_v_value(c_bit0, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93))))),
% 35.56/23.46 inference(monotonicity,[status(thm)],[2834])).
% 35.65/23.46 tff(2836,plain,
% 35.65/23.46 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | m_counter_cell_v_value(c_bit0, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 35.65/23.46 inference(transitivity,[status(thm)],[2835, 2833])).
% 35.65/23.46 tff(2837,plain,
% 35.65/23.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | m_counter_cell_v_value(c_bit0, s93))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2838,plain,
% 35.65/23.46 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92) | (~node3(c_bit0, s92, s93))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2837, 2836])).
% 35.65/23.46 tff(2839,plain,
% 35.65/23.46 (m_counter_cell_v_value(c_bit0, s93) | node1(c_bit0, s92)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2838, 199, 2832])).
% 35.65/23.46 tff(2840,plain,
% 35.65/23.46 (m_counter_cell_v_value(c_bit0, s93)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2839, 2821])).
% 35.65/23.46 tff(2841,assumption,(~m_counter_cell_v_carry_in(c_bit0, s93)), introduced(assumption)).
% 35.65/23.46 tff(2842,plain,
% 35.65/23.46 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s93)),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2843,plain,
% 35.65/23.46 ($false),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2842, 158, 2841])).
% 35.65/23.46 tff(2844,plain,(m_counter_cell_v_carry_in(c_bit0, s93)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.46 tff(2845,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93)))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2846,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93)))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2847,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2846, 2845])).
% 35.65/23.46 tff(2848,plain,
% 35.65/23.46 ((~m_counter_cell_v_value(c_bit0, s93)) | (~node2(c_bit0, s93))),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2847, 219, 2844])).
% 35.65/23.46 tff(2849,plain,
% 35.65/23.46 (~node2(c_bit0, s93)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2848, 2840])).
% 35.65/23.46 tff(2850,plain,
% 35.65/23.46 (succ(s93, s94) <=> succ(s93, s94)),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2851,axiom,(succ(s93, s94)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound94')).
% 35.65/23.46 tff(2852,plain,
% 35.65/23.46 (succ(s93, s94)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2851, 2850])).
% 35.65/23.46 tff(2853,plain,
% 35.65/23.46 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s93, s94)) | trans(s93, s94))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s93, s94)) | trans(s93, s94))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2854,plain,
% 35.65/23.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s93, s94)) | trans(s93, s94))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2855,plain,
% 35.65/23.46 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s93, s94)) | trans(s93, s94)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2854, 2853])).
% 35.65/23.46 tff(2856,plain,
% 35.65/23.46 (trans(s93, s94)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2855, 2852, 8])).
% 35.65/23.46 tff(2857,plain,
% 35.65/23.46 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s93, s94)) | node3(c_bit0, s93, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s93, s94)) | node3(c_bit0, s93, s94))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2858,plain,
% 35.65/23.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s93, s94)) | node3(c_bit0, s93, s94))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2859,plain,
% 35.65/23.46 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s93, s94)) | node3(c_bit0, s93, s94)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2858, 2857])).
% 35.65/23.46 tff(2860,plain,
% 35.65/23.46 (node3(c_bit0, s93, s94)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2859, 81, 2856])).
% 35.65/23.46 tff(2861,plain,
% 35.65/23.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2862,plain,
% 35.65/23.46 ((node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | (~m_counter_cell_v_value(c_bit0, s94))) <=> ((~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2863,plain,
% 35.65/23.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | (~m_counter_cell_v_value(c_bit0, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94))))),
% 35.65/23.46 inference(monotonicity,[status(thm)],[2862])).
% 35.65/23.46 tff(2864,plain,
% 35.65/23.46 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | (~m_counter_cell_v_value(c_bit0, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 35.65/23.46 inference(transitivity,[status(thm)],[2863, 2861])).
% 35.65/23.46 tff(2865,plain,
% 35.65/23.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | (~m_counter_cell_v_value(c_bit0, s94)))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2866,plain,
% 35.65/23.46 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93) | (~node3(c_bit0, s93, s94))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 35.65/23.46 tff(2867,plain,
% 35.65/23.46 ((~m_counter_cell_v_value(c_bit0, s94)) | node2(c_bit0, s93)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2866, 234, 2860])).
% 35.65/23.46 tff(2868,plain,
% 35.65/23.46 (~m_counter_cell_v_value(c_bit0, s94)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2867, 2849])).
% 35.65/23.46 tff(2869,plain,
% 35.65/23.46 (^[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))))),
% 35.65/23.46 inference(bind,[status(th)],[])).
% 35.65/23.46 tff(2870,plain,
% 35.65/23.46 (![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)))),
% 35.65/23.46 inference(quant_intro,[status(thm)],[2869])).
% 35.65/23.46 tff(2871,plain,
% 35.65/23.46 (![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)))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2872,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')).
% 35.65/23.46 tff(2873,plain,
% 35.65/23.46 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 35.65/23.46 tff(2874,plain,(
% 35.65/23.46 ![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 35.65/23.46 inference(skolemize,[status(sab)],[2873])).
% 35.65/23.46 tff(2875,plain,
% 35.65/23.46 (![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2874, 2870])).
% 35.65/23.46 tff(2876,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s94) | (~node4(c_bit0, s94)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s94) | (~node4(c_bit0, s94)))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2877,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s94) | (~node4(c_bit0, s94)))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2878,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s94) | (~node4(c_bit0, s94))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2877, 2876])).
% 35.65/23.46 tff(2879,plain,
% 35.65/23.46 (~node4(c_bit0, s94)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2878, 2875, 2868])).
% 35.65/23.46 tff(2880,assumption,(m_counter_cell_v_carry_out(c_bit0, s94)), introduced(assumption)).
% 35.65/23.46 tff(2881,plain,
% 35.65/23.46 (^[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)))),
% 35.65/23.46 inference(bind,[status(th)],[])).
% 35.65/23.46 tff(2882,plain,
% 35.65/23.46 (![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))),
% 35.65/23.46 inference(quant_intro,[status(thm)],[2881])).
% 35.65/23.46 tff(2883,plain,
% 35.65/23.46 (![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))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2884,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')).
% 35.65/23.46 tff(2885,plain,
% 35.65/23.46 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2884, 2883])).
% 35.65/23.46 tff(2886,plain,(
% 35.65/23.46 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 35.65/23.46 inference(skolemize,[status(sab)],[2885])).
% 35.65/23.46 tff(2887,plain,
% 35.65/23.46 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2886, 2882])).
% 35.65/23.46 tff(2888,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2889,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2890,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s94)) | node4(c_bit0, s94)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2889, 2888])).
% 35.65/23.46 tff(2891,plain,
% 35.65/23.46 ($false),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2890, 2887, 2880, 2879])).
% 35.65/23.46 tff(2892,plain,(~m_counter_cell_v_carry_out(c_bit0, s94)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.46 tff(2893,assumption,(m_counter_cell_v_carry_in(c_bit1, s94)), introduced(assumption)).
% 35.65/23.46 tff(2894,assumption,(~m_counter_cell_v_carry_out(c_bit0, s94)), introduced(assumption)).
% 35.65/23.46 tff(2895,plain,
% 35.65/23.46 (^[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)))),
% 35.65/23.46 inference(bind,[status(th)],[])).
% 35.65/23.46 tff(2896,plain,
% 35.65/23.46 (![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))),
% 35.65/23.46 inference(quant_intro,[status(thm)],[2895])).
% 35.65/23.46 tff(2897,plain,
% 35.65/23.46 (![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))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2898,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')).
% 35.65/23.46 tff(2899,plain,
% 35.65/23.46 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2898, 2897])).
% 35.65/23.46 tff(2900,plain,(
% 35.65/23.46 ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 35.65/23.46 inference(skolemize,[status(sab)],[2899])).
% 35.65/23.46 tff(2901,plain,
% 35.65/23.46 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2900, 2896])).
% 35.65/23.46 tff(2902,plain,
% 35.65/23.46 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s94)) | m_counter_cell_v_carry_out(c_bit0, s94))) <=> ((~![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, s94)) | m_counter_cell_v_carry_out(c_bit0, s94))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2903,plain,
% 35.65/23.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s94)) | m_counter_cell_v_carry_out(c_bit0, s94))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2904,plain,
% 35.65/23.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s94)) | m_counter_cell_v_carry_out(c_bit0, s94)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2903, 2902])).
% 35.65/23.46 tff(2905,plain,
% 35.65/23.46 ($false),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2904, 2901, 2894, 2893])).
% 35.65/23.46 tff(2906,plain,(m_counter_cell_v_carry_out(c_bit0, s94) | (~m_counter_cell_v_carry_in(c_bit1, s94))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.46 tff(2907,plain,
% 35.65/23.46 (~m_counter_cell_v_carry_in(c_bit1, s94)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2906, 2892])).
% 35.65/23.46 tff(2908,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s84) | (~node4(c_bit0, s84)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s84) | (~node4(c_bit0, s84)))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2909,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s84) | (~node4(c_bit0, s84)))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2910,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s84) | (~node4(c_bit0, s84))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2909, 2908])).
% 35.65/23.46 tff(2911,plain,
% 35.65/23.46 (~node4(c_bit0, s84)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2910, 2875, 2577])).
% 35.65/23.46 tff(2912,assumption,(~node4(c_bit0, s84)), introduced(assumption)).
% 35.65/23.46 tff(2913,assumption,(m_counter_cell_v_carry_out(c_bit0, s84)), introduced(assumption)).
% 35.65/23.46 tff(2914,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2915,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2916,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 35.65/23.46 tff(2917,plain,
% 35.65/23.46 ($false),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2916, 2887, 2913, 2912])).
% 35.65/23.46 tff(2918,plain,((~m_counter_cell_v_carry_out(c_bit0, s84)) | node4(c_bit0, s84)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.46 tff(2919,plain,
% 35.65/23.46 (~m_counter_cell_v_carry_out(c_bit0, s84)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2918, 2911])).
% 35.65/23.46 tff(2920,assumption,(m_counter_cell_v_carry_in(c_bit1, s84)), introduced(assumption)).
% 35.65/23.46 tff(2921,assumption,(~m_counter_cell_v_carry_out(c_bit0, s84)), introduced(assumption)).
% 35.65/23.46 tff(2922,plain,
% 35.65/23.46 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s84)) | m_counter_cell_v_carry_out(c_bit0, s84))) <=> ((~![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, s84)) | m_counter_cell_v_carry_out(c_bit0, s84))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2923,plain,
% 35.65/23.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s84)) | m_counter_cell_v_carry_out(c_bit0, s84))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2924,plain,
% 35.65/23.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s84)) | m_counter_cell_v_carry_out(c_bit0, s84)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 35.65/23.46 tff(2925,plain,
% 35.65/23.46 ($false),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2924, 2901, 2921, 2920])).
% 35.65/23.46 tff(2926,plain,((~m_counter_cell_v_carry_in(c_bit1, s84)) | m_counter_cell_v_carry_out(c_bit0, s84)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.46 tff(2927,plain,
% 35.65/23.46 (~m_counter_cell_v_carry_in(c_bit1, s84)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2926, 2919])).
% 35.65/23.46 tff(2928,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s78) | (~node4(c_bit0, s78)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s78) | (~node4(c_bit0, s78)))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2929,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s78) | (~node4(c_bit0, s78)))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2930,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s78) | (~node4(c_bit0, s78))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 35.65/23.46 tff(2931,plain,
% 35.65/23.46 (~node4(c_bit0, s78)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2930, 2875, 2400])).
% 35.65/23.46 tff(2932,assumption,(~node4(c_bit0, s78)), introduced(assumption)).
% 35.65/23.46 tff(2933,assumption,(m_counter_cell_v_carry_out(c_bit0, s78)), introduced(assumption)).
% 35.65/23.46 tff(2934,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2935,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2936,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2935, 2934])).
% 35.65/23.46 tff(2937,plain,
% 35.65/23.46 ($false),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2936, 2887, 2933, 2932])).
% 35.65/23.46 tff(2938,plain,((~m_counter_cell_v_carry_out(c_bit0, s78)) | node4(c_bit0, s78)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.46 tff(2939,plain,
% 35.65/23.46 (~m_counter_cell_v_carry_out(c_bit0, s78)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2938, 2931])).
% 35.65/23.46 tff(2940,assumption,(m_counter_cell_v_carry_in(c_bit1, s78)), introduced(assumption)).
% 35.65/23.46 tff(2941,assumption,(~m_counter_cell_v_carry_out(c_bit0, s78)), introduced(assumption)).
% 35.65/23.46 tff(2942,plain,
% 35.65/23.46 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78))) <=> ((~![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, s78)) | m_counter_cell_v_carry_out(c_bit0, s78))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2943,plain,
% 35.65/23.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2944,plain,
% 35.65/23.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2943, 2942])).
% 35.65/23.46 tff(2945,plain,
% 35.65/23.46 ($false),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2944, 2901, 2941, 2940])).
% 35.65/23.46 tff(2946,plain,((~m_counter_cell_v_carry_in(c_bit1, s78)) | m_counter_cell_v_carry_out(c_bit0, s78)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.46 tff(2947,plain,
% 35.65/23.46 (~m_counter_cell_v_carry_in(c_bit1, s78)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2946, 2939])).
% 35.65/23.46 tff(2948,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s70) | (~node4(c_bit0, s70)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s70) | (~node4(c_bit0, s70)))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2949,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s70) | (~node4(c_bit0, s70)))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2950,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s70) | (~node4(c_bit0, s70))),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2949, 2948])).
% 35.65/23.46 tff(2951,plain,
% 35.65/23.46 (~node4(c_bit0, s70)),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2950, 2875, 2164])).
% 35.65/23.46 tff(2952,assumption,(m_counter_cell_v_carry_out(c_bit0, s70)), introduced(assumption)).
% 35.65/23.46 tff(2953,plain,
% 35.65/23.46 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s70)) | node4(c_bit0, s70))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s70)) | node4(c_bit0, s70))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2954,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s70)) | node4(c_bit0, s70))),
% 35.65/23.46 inference(quant_inst,[status(thm)],[])).
% 35.65/23.46 tff(2955,plain,
% 35.65/23.46 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s70)) | node4(c_bit0, s70)),
% 35.65/23.46 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 35.65/23.46 tff(2956,plain,
% 35.65/23.46 ($false),
% 35.65/23.46 inference(unit_resolution,[status(thm)],[2955, 2887, 2952, 2951])).
% 35.65/23.46 tff(2957,plain,(~m_counter_cell_v_carry_out(c_bit0, s70)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.46 tff(2958,assumption,(m_counter_cell_v_carry_in(c_bit1, s70)), introduced(assumption)).
% 35.65/23.46 tff(2959,assumption,(~m_counter_cell_v_carry_out(c_bit0, s70)), introduced(assumption)).
% 35.65/23.46 tff(2960,plain,
% 35.65/23.46 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s70)) | m_counter_cell_v_carry_out(c_bit0, s70))) <=> ((~![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, s70)) | m_counter_cell_v_carry_out(c_bit0, s70))),
% 35.65/23.46 inference(rewrite,[status(thm)],[])).
% 35.65/23.46 tff(2961,plain,
% 35.65/23.46 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s70)) | m_counter_cell_v_carry_out(c_bit0, s70))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(2962,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s70)) | m_counter_cell_v_carry_out(c_bit0, s70)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[2961, 2960])).
% 35.65/23.47 tff(2963,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2962, 2901, 2959, 2958])).
% 35.65/23.47 tff(2964,plain,((~m_counter_cell_v_carry_in(c_bit1, s70)) | m_counter_cell_v_carry_out(c_bit0, s70)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(2965,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit1, s70)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2964, 2957])).
% 35.65/23.47 tff(2966,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s68) | (~node4(c_bit0, s68)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s68) | (~node4(c_bit0, s68)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(2967,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s68) | (~node4(c_bit0, s68)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(2968,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s68) | (~node4(c_bit0, s68))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[2967, 2966])).
% 35.65/23.47 tff(2969,plain,
% 35.65/23.47 (~node4(c_bit0, s68)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2968, 2875, 2105])).
% 35.65/23.47 tff(2970,assumption,(m_counter_cell_v_carry_out(c_bit0, s68)), introduced(assumption)).
% 35.65/23.47 tff(2971,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s68)) | node4(c_bit0, s68))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s68)) | node4(c_bit0, s68))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(2972,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s68)) | node4(c_bit0, s68))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(2973,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s68)) | node4(c_bit0, s68)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[2972, 2971])).
% 35.65/23.47 tff(2974,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2973, 2887, 2970, 2969])).
% 35.65/23.47 tff(2975,plain,(~m_counter_cell_v_carry_out(c_bit0, s68)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(2976,assumption,(m_counter_cell_v_carry_in(c_bit1, s68)), introduced(assumption)).
% 35.65/23.47 tff(2977,assumption,(~m_counter_cell_v_carry_out(c_bit0, s68)), introduced(assumption)).
% 35.65/23.47 tff(2978,plain,
% 35.65/23.47 (((~![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, s68)) | m_counter_cell_v_carry_out(c_bit0, s68))) <=> ((~![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, s68)) | m_counter_cell_v_carry_out(c_bit0, s68))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(2979,plain,
% 35.65/23.47 ((~![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, s68)) | m_counter_cell_v_carry_out(c_bit0, s68))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(2980,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s68)) | m_counter_cell_v_carry_out(c_bit0, s68)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[2979, 2978])).
% 35.65/23.47 tff(2981,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2980, 2901, 2977, 2976])).
% 35.65/23.47 tff(2982,plain,(m_counter_cell_v_carry_out(c_bit0, s68) | (~m_counter_cell_v_carry_in(c_bit1, s68))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(2983,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit1, s68)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2982, 2975])).
% 35.65/23.47 tff(2984,assumption,(node2(c_bit1, s68)), introduced(assumption)).
% 35.65/23.47 tff(2985,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s66) | (~node4(c_bit0, s66)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s66) | (~node4(c_bit0, s66)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(2986,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s66) | (~node4(c_bit0, s66)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(2987,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s66) | (~node4(c_bit0, s66))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[2986, 2985])).
% 35.65/23.47 tff(2988,plain,
% 35.65/23.47 (~node4(c_bit0, s66)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2987, 2875, 2046])).
% 35.65/23.47 tff(2989,assumption,(m_counter_cell_v_carry_out(c_bit0, s66)), introduced(assumption)).
% 35.65/23.47 tff(2990,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s66)) | node4(c_bit0, s66))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s66)) | node4(c_bit0, s66))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(2991,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s66)) | node4(c_bit0, s66))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(2992,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s66)) | node4(c_bit0, s66)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[2991, 2990])).
% 35.65/23.47 tff(2993,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2992, 2887, 2989, 2988])).
% 35.65/23.47 tff(2994,plain,(~m_counter_cell_v_carry_out(c_bit0, s66)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(2995,assumption,(m_counter_cell_v_carry_in(c_bit1, s66)), introduced(assumption)).
% 35.65/23.47 tff(2996,assumption,(~m_counter_cell_v_carry_out(c_bit0, s66)), introduced(assumption)).
% 35.65/23.47 tff(2997,plain,
% 35.65/23.47 (((~![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, s66)) | m_counter_cell_v_carry_out(c_bit0, s66))) <=> ((~![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, s66)) | m_counter_cell_v_carry_out(c_bit0, s66))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(2998,plain,
% 35.65/23.47 ((~![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, s66)) | m_counter_cell_v_carry_out(c_bit0, s66))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(2999,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s66)) | m_counter_cell_v_carry_out(c_bit0, s66)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[2998, 2997])).
% 35.65/23.47 tff(3000,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[2999, 2901, 2996, 2995])).
% 35.65/23.47 tff(3001,plain,(m_counter_cell_v_carry_out(c_bit0, s66) | (~m_counter_cell_v_carry_in(c_bit1, s66))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3002,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit1, s66)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3001, 2994])).
% 35.65/23.47 tff(3003,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3004,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3005,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s64) | (~node4(c_bit0, s64))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3004, 3003])).
% 35.65/23.47 tff(3006,plain,
% 35.65/23.47 (~node4(c_bit0, s64)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3005, 2875, 1987])).
% 35.65/23.47 tff(3007,assumption,(m_counter_cell_v_carry_out(c_bit0, s64)), introduced(assumption)).
% 35.65/23.47 tff(3008,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3009,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3010,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s64)) | node4(c_bit0, s64)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3009, 3008])).
% 35.65/23.47 tff(3011,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3010, 2887, 3007, 3006])).
% 35.65/23.47 tff(3012,plain,(~m_counter_cell_v_carry_out(c_bit0, s64)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3013,assumption,(m_counter_cell_v_carry_in(c_bit1, s64)), introduced(assumption)).
% 35.65/23.47 tff(3014,assumption,(~m_counter_cell_v_carry_out(c_bit0, s64)), introduced(assumption)).
% 35.65/23.47 tff(3015,plain,
% 35.65/23.47 (((~![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, s64)) | m_counter_cell_v_carry_out(c_bit0, s64))) <=> ((~![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, s64)) | m_counter_cell_v_carry_out(c_bit0, s64))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3016,plain,
% 35.65/23.47 ((~![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, s64)) | m_counter_cell_v_carry_out(c_bit0, s64))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3017,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s64)) | m_counter_cell_v_carry_out(c_bit0, s64)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3016, 3015])).
% 35.65/23.47 tff(3018,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3017, 2901, 3014, 3013])).
% 35.65/23.47 tff(3019,plain,(m_counter_cell_v_carry_out(c_bit0, s64) | (~m_counter_cell_v_carry_in(c_bit1, s64))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3020,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit1, s64)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3019, 3012])).
% 35.65/23.47 tff(3021,assumption,(node2(c_bit1, s63)), introduced(assumption)).
% 35.65/23.47 tff(3022,plain,
% 35.65/23.47 (^[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)))),
% 35.65/23.47 inference(bind,[status(th)],[])).
% 35.65/23.47 tff(3023,plain,
% 35.65/23.47 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 35.65/23.47 inference(quant_intro,[status(thm)],[3022])).
% 35.65/23.47 tff(3024,plain,
% 35.65/23.47 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X)) <=> ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3025,plain,
% 35.65/23.47 (^[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))))),
% 35.65/23.47 inference(bind,[status(th)],[])).
% 35.65/23.47 tff(3026,plain,
% 35.65/23.47 (![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))),
% 35.65/23.47 inference(quant_intro,[status(thm)],[3025])).
% 35.65/23.47 tff(3027,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')).
% 35.65/23.47 tff(3028,plain,
% 35.65/23.47 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3027, 3026])).
% 35.65/23.47 tff(3029,plain,
% 35.65/23.47 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3028, 3024])).
% 35.65/23.47 tff(3030,plain,(
% 35.65/23.47 ![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 35.65/23.47 inference(skolemize,[status(sab)],[3029])).
% 35.65/23.47 tff(3031,plain,
% 35.65/23.47 (![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3030, 3023])).
% 35.65/23.47 tff(3032,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3033,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3034,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s63)) | (~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3033, 3032])).
% 35.65/23.47 tff(3035,plain,
% 35.65/23.47 ((~m_counter_cell_v_value(c_bit0, s63)) | m_counter_cell_v_carry_out(c_bit0, s63)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3034, 3031, 1963])).
% 35.65/23.47 tff(3036,plain,
% 35.65/23.47 (m_counter_cell_v_carry_out(c_bit0, s63)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3035, 1959])).
% 35.65/23.47 tff(3037,plain,
% 35.65/23.47 (^[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)))),
% 35.65/23.47 inference(bind,[status(th)],[])).
% 35.65/23.47 tff(3038,plain,
% 35.65/23.47 (![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))),
% 35.65/23.47 inference(quant_intro,[status(thm)],[3037])).
% 35.65/23.47 tff(3039,plain,
% 35.65/23.47 (![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))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3040,plain,
% 35.65/23.47 (^[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)))),
% 35.65/23.47 inference(bind,[status(th)],[])).
% 35.65/23.47 tff(3041,plain,
% 35.65/23.47 (![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))),
% 35.65/23.47 inference(quant_intro,[status(thm)],[3040])).
% 35.65/23.47 tff(3042,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')).
% 35.65/23.47 tff(3043,plain,
% 35.65/23.47 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 35.65/23.47 tff(3044,plain,
% 35.65/23.47 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3043, 3039])).
% 35.65/23.47 tff(3045,plain,(
% 35.65/23.47 ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 35.65/23.47 inference(skolemize,[status(sab)],[3044])).
% 35.65/23.47 tff(3046,plain,
% 35.65/23.47 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3045, 3038])).
% 35.65/23.47 tff(3047,plain,
% 35.65/23.47 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s63)) | m_counter_cell_v_carry_in(c_bit1, s63))) <=> ((~![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, s63)) | m_counter_cell_v_carry_in(c_bit1, s63))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3048,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s63)) | m_counter_cell_v_carry_in(c_bit1, s63))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3049,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s63)) | m_counter_cell_v_carry_in(c_bit1, s63)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 35.65/23.47 tff(3050,plain,
% 35.65/23.47 (m_counter_cell_v_carry_in(c_bit1, s63)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3049, 3046, 3036])).
% 35.65/23.47 tff(3051,assumption,(node4(c_bit0, s62)), introduced(assumption)).
% 35.65/23.47 tff(3052,assumption,(~m_counter_cell_v_value(c_bit0, s62)), introduced(assumption)).
% 35.65/23.47 tff(3053,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3054,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3055,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3054, 3053])).
% 35.65/23.47 tff(3056,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3055, 2875, 3052, 3051])).
% 35.65/23.47 tff(3057,plain,(m_counter_cell_v_value(c_bit0, s62) | (~node4(c_bit0, s62))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3058,plain,
% 35.65/23.47 (~node4(c_bit0, s62)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3057, 1928])).
% 35.65/23.47 tff(3059,assumption,(m_counter_cell_v_carry_out(c_bit0, s62)), introduced(assumption)).
% 35.65/23.47 tff(3060,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s62)) | node4(c_bit0, s62))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s62)) | node4(c_bit0, s62))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3061,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s62)) | node4(c_bit0, s62))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3062,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s62)) | node4(c_bit0, s62)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 35.65/23.47 tff(3063,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3062, 2887, 3059, 3058])).
% 35.65/23.47 tff(3064,plain,(~m_counter_cell_v_carry_out(c_bit0, s62)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3065,plain,
% 35.65/23.47 (((~![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, s62)) | m_counter_cell_v_carry_out(c_bit0, s62))) <=> ((~![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, s62)) | m_counter_cell_v_carry_out(c_bit0, s62))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3066,plain,
% 35.65/23.47 ((~![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, s62)) | m_counter_cell_v_carry_out(c_bit0, s62))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3067,plain,
% 35.65/23.47 ((~![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, s62)) | m_counter_cell_v_carry_out(c_bit0, s62)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3066, 3065])).
% 35.65/23.47 tff(3068,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit1, s62)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3067, 2901, 3064])).
% 35.65/23.47 tff(3069,assumption,(node4(c_bit1, s62)), introduced(assumption)).
% 35.65/23.47 tff(3070,plain,
% 35.65/23.47 (^[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))))),
% 35.65/23.47 inference(bind,[status(th)],[])).
% 35.65/23.47 tff(3071,plain,
% 35.65/23.47 (![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)))),
% 35.65/23.47 inference(quant_intro,[status(thm)],[3070])).
% 35.65/23.47 tff(3072,plain,
% 35.65/23.47 (![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)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3073,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')).
% 35.65/23.47 tff(3074,plain,
% 35.65/23.47 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3073, 3072])).
% 35.65/23.47 tff(3075,plain,(
% 35.65/23.47 ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 35.65/23.47 inference(skolemize,[status(sab)],[3074])).
% 35.65/23.47 tff(3076,plain,
% 35.65/23.47 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3075, 3071])).
% 35.65/23.47 tff(3077,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s62) | (~node4(c_bit1, s62)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s62) | (~node4(c_bit1, s62)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3078,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s62) | (~node4(c_bit1, s62)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3079,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s62) | (~node4(c_bit1, s62))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3078, 3077])).
% 35.65/23.47 tff(3080,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3079, 3076, 3069, 3068])).
% 35.65/23.47 tff(3081,plain,(~node4(c_bit1, s62)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3082,assumption,(m_counter_cell_v_carry_out(c_bit1, s62)), introduced(assumption)).
% 35.65/23.47 tff(3083,assumption,(~node4(c_bit1, s62)), introduced(assumption)).
% 35.65/23.47 tff(3084,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s62)) | node4(c_bit1, s62))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s62)) | node4(c_bit1, s62))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3085,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s62)) | node4(c_bit1, s62))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3086,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s62)) | node4(c_bit1, s62)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3085, 3084])).
% 35.65/23.47 tff(3087,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3086, 2887, 3083, 3082])).
% 35.65/23.47 tff(3088,plain,((~m_counter_cell_v_carry_out(c_bit1, s62)) | node4(c_bit1, s62)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3089,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_out(c_bit1, s62)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3088, 3081])).
% 35.65/23.47 tff(3090,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s60) | (~node4(c_bit0, s60)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s60) | (~node4(c_bit0, s60)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3091,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s60) | (~node4(c_bit0, s60)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3092,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s60) | (~node4(c_bit0, s60))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3091, 3090])).
% 35.65/23.47 tff(3093,plain,
% 35.65/23.47 (~node4(c_bit0, s60)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3092, 2875, 1869])).
% 35.65/23.47 tff(3094,assumption,(m_counter_cell_v_carry_out(c_bit0, s60)), introduced(assumption)).
% 35.65/23.47 tff(3095,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s60)) | node4(c_bit0, s60))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s60)) | node4(c_bit0, s60))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3096,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s60)) | node4(c_bit0, s60))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3097,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s60)) | node4(c_bit0, s60)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3096, 3095])).
% 35.65/23.47 tff(3098,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3097, 2887, 3094, 3093])).
% 35.65/23.47 tff(3099,plain,(~m_counter_cell_v_carry_out(c_bit0, s60)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3100,assumption,(m_counter_cell_v_carry_in(c_bit1, s60)), introduced(assumption)).
% 35.65/23.47 tff(3101,assumption,(~m_counter_cell_v_carry_out(c_bit0, s60)), introduced(assumption)).
% 35.65/23.47 tff(3102,plain,
% 35.65/23.47 (((~![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, s60)) | m_counter_cell_v_carry_out(c_bit0, s60))) <=> ((~![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, s60)) | m_counter_cell_v_carry_out(c_bit0, s60))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3103,plain,
% 35.65/23.47 ((~![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, s60)) | m_counter_cell_v_carry_out(c_bit0, s60))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3104,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s60)) | m_counter_cell_v_carry_out(c_bit0, s60)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3103, 3102])).
% 35.65/23.47 tff(3105,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3104, 2901, 3101, 3100])).
% 35.65/23.47 tff(3106,plain,(m_counter_cell_v_carry_out(c_bit0, s60) | (~m_counter_cell_v_carry_in(c_bit1, s60))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3107,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit1, s60)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3106, 3099])).
% 35.65/23.47 tff(3108,assumption,(~m_counter_cell_v_carry_in(c_bit1, s60)), introduced(assumption)).
% 35.65/23.47 tff(3109,plain,
% 35.65/23.47 (((~![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)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3110,plain,
% 35.65/23.47 ((~![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)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3111,plain,
% 35.65/23.47 ((~![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))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3110, 3109])).
% 35.65/23.47 tff(3112,plain,
% 35.65/23.47 (~node4(c_bit0, s50)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3111, 2875, 1586])).
% 35.65/23.47 tff(3113,assumption,(~node4(c_bit0, s50)), introduced(assumption)).
% 35.65/23.47 tff(3114,assumption,(m_counter_cell_v_carry_out(c_bit0, s50)), introduced(assumption)).
% 35.65/23.47 tff(3115,plain,
% 35.65/23.47 (((~![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))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3116,plain,
% 35.65/23.47 ((~![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))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3117,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 35.65/23.47 tff(3118,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3117, 2887, 3114, 3113])).
% 35.65/23.47 tff(3119,plain,((~m_counter_cell_v_carry_out(c_bit0, s50)) | node4(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3120,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_out(c_bit0, s50)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3119, 3112])).
% 35.65/23.47 tff(3121,assumption,(m_counter_cell_v_carry_in(c_bit1, s50)), introduced(assumption)).
% 35.65/23.47 tff(3122,assumption,(~m_counter_cell_v_carry_out(c_bit0, s50)), introduced(assumption)).
% 35.65/23.47 tff(3123,plain,
% 35.65/23.47 (((~![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))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3124,plain,
% 35.65/23.47 ((~![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))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3125,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3124, 3123])).
% 35.65/23.47 tff(3126,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3125, 2901, 3122, 3121])).
% 35.65/23.47 tff(3127,plain,((~m_counter_cell_v_carry_in(c_bit1, s50)) | m_counter_cell_v_carry_out(c_bit0, s50)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3128,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit1, s50)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3127, 3120])).
% 35.65/23.47 tff(3129,plain,
% 35.65/23.47 (((~![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)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3130,plain,
% 35.65/23.47 ((~![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)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3131,plain,
% 35.65/23.47 ((~![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))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3130, 3129])).
% 35.65/23.47 tff(3132,plain,
% 35.65/23.47 (~node4(c_bit0, s42)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3131, 2875, 1352])).
% 35.65/23.47 tff(3133,assumption,(m_counter_cell_v_carry_out(c_bit0, s42)), introduced(assumption)).
% 35.65/23.47 tff(3134,plain,
% 35.65/23.47 (((~![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))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3135,plain,
% 35.65/23.47 ((~![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))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3136,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s42)) | node4(c_bit0, s42)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3135, 3134])).
% 35.65/23.47 tff(3137,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3136, 2887, 3133, 3132])).
% 35.65/23.47 tff(3138,plain,(~m_counter_cell_v_carry_out(c_bit0, s42)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3139,assumption,(m_counter_cell_v_carry_in(c_bit1, s42)), introduced(assumption)).
% 35.65/23.47 tff(3140,assumption,(~m_counter_cell_v_carry_out(c_bit0, s42)), introduced(assumption)).
% 35.65/23.47 tff(3141,plain,
% 35.65/23.47 (((~![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))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3142,plain,
% 35.65/23.47 ((~![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))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3143,plain,
% 35.65/23.47 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s42)) | m_counter_cell_v_carry_out(c_bit0, s42)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3142, 3141])).
% 35.65/23.47 tff(3144,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3143, 2901, 3140, 3139])).
% 35.65/23.47 tff(3145,plain,(m_counter_cell_v_carry_out(c_bit0, s42) | (~m_counter_cell_v_carry_in(c_bit1, s42))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3146,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit1, s42)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3145, 3138])).
% 35.65/23.47 tff(3147,assumption,(node4(c_bit1, s42)), introduced(assumption)).
% 35.65/23.47 tff(3148,assumption,(~m_counter_cell_v_carry_in(c_bit1, s42)), introduced(assumption)).
% 35.65/23.47 tff(3149,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s42) | (~node4(c_bit1, s42)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~node4(c_bit1, s42)))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3150,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s42) | (~node4(c_bit1, s42)))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3151,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s42) | (~node4(c_bit1, s42))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3150, 3149])).
% 35.65/23.47 tff(3152,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3151, 3076, 3148, 3147])).
% 35.65/23.47 tff(3153,plain,((~node4(c_bit1, s42)) | m_counter_cell_v_carry_in(c_bit1, s42)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3154,plain,
% 35.65/23.47 (~node4(c_bit1, s42)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3153, 3146])).
% 35.65/23.47 tff(3155,assumption,(m_counter_cell_v_carry_out(c_bit1, s42)), introduced(assumption)).
% 35.65/23.47 tff(3156,plain,
% 35.65/23.47 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s42)) | node4(c_bit1, s42))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s42)) | node4(c_bit1, s42))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3157,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s42)) | node4(c_bit1, s42))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3158,plain,
% 35.65/23.47 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s42)) | node4(c_bit1, s42)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 35.65/23.47 tff(3159,plain,
% 35.65/23.47 ($false),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3158, 2887, 3155, 3154])).
% 35.65/23.47 tff(3160,plain,(~m_counter_cell_v_carry_out(c_bit1, s42)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.47 tff(3161,plain,
% 35.65/23.47 (^[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)))),
% 35.65/23.47 inference(bind,[status(th)],[])).
% 35.65/23.47 tff(3162,plain,
% 35.65/23.47 (![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))),
% 35.65/23.47 inference(quant_intro,[status(thm)],[3161])).
% 35.65/23.47 tff(3163,plain,
% 35.65/23.47 (![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))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3164,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')).
% 35.65/23.47 tff(3165,plain,
% 35.65/23.47 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 35.65/23.47 tff(3166,plain,(
% 35.65/23.47 ![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 35.65/23.47 inference(skolemize,[status(sab)],[3165])).
% 35.65/23.47 tff(3167,plain,
% 35.65/23.47 (![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3166, 3162])).
% 35.65/23.47 tff(3168,plain,
% 35.65/23.47 (((~![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, s42)) | m_counter_cell_v_carry_out(c_bit1, s42))) <=> ((~![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, s42)) | m_counter_cell_v_carry_out(c_bit1, s42))),
% 35.65/23.47 inference(rewrite,[status(thm)],[])).
% 35.65/23.47 tff(3169,plain,
% 35.65/23.47 ((~![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, s42)) | m_counter_cell_v_carry_out(c_bit1, s42))),
% 35.65/23.47 inference(quant_inst,[status(thm)],[])).
% 35.65/23.47 tff(3170,plain,
% 35.65/23.47 ((~![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, s42)) | m_counter_cell_v_carry_out(c_bit1, s42)),
% 35.65/23.47 inference(modus_ponens,[status(thm)],[3169, 3168])).
% 35.65/23.47 tff(3171,plain,
% 35.65/23.47 (~m_counter_cell_v_carry_in(c_bit2, s42)),
% 35.65/23.47 inference(unit_resolution,[status(thm)],[3170, 3167, 3160])).
% 35.65/23.47 tff(3172,plain,
% 35.65/23.47 (((~![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)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3173,plain,
% 35.65/23.48 ((~![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)))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3174,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 35.65/23.48 tff(3175,plain,
% 35.65/23.48 (~node4(c_bit0, s18)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3174, 2875, 650])).
% 35.65/23.48 tff(3176,assumption,(m_counter_cell_v_carry_out(c_bit0, s18)), introduced(assumption)).
% 35.65/23.48 tff(3177,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3178,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3179,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s18)) | node4(c_bit0, s18)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3178, 3177])).
% 35.65/23.48 tff(3180,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3179, 2887, 3176, 3175])).
% 35.65/23.48 tff(3181,plain,(~m_counter_cell_v_carry_out(c_bit0, s18)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3182,assumption,(m_counter_cell_v_carry_in(c_bit1, s18)), introduced(assumption)).
% 35.65/23.48 tff(3183,assumption,(~m_counter_cell_v_carry_out(c_bit0, s18)), introduced(assumption)).
% 35.65/23.48 tff(3184,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3185,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3186,plain,
% 35.65/23.48 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit0, s18)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3185, 3184])).
% 35.65/23.48 tff(3187,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3186, 2901, 3183, 3182])).
% 35.65/23.48 tff(3188,plain,(m_counter_cell_v_carry_out(c_bit0, s18) | (~m_counter_cell_v_carry_in(c_bit1, s18))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3189,plain,
% 35.65/23.48 (~m_counter_cell_v_carry_in(c_bit1, s18)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3188, 3181])).
% 35.65/23.48 tff(3190,plain,
% 35.65/23.48 (((~![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)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3191,plain,
% 35.65/23.48 ((~![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)))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3192,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3191, 3190])).
% 35.65/23.48 tff(3193,plain,
% 35.65/23.48 (~node4(c_bit0, s14)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3192, 2875, 534])).
% 35.65/23.48 tff(3194,assumption,(m_counter_cell_v_carry_out(c_bit0, s14)), introduced(assumption)).
% 35.65/23.48 tff(3195,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3196,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3197,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s14)) | node4(c_bit0, s14)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3196, 3195])).
% 35.65/23.48 tff(3198,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3197, 2887, 3194, 3193])).
% 35.65/23.48 tff(3199,plain,(~m_counter_cell_v_carry_out(c_bit0, s14)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3200,assumption,(m_counter_cell_v_carry_in(c_bit1, s14)), introduced(assumption)).
% 35.65/23.48 tff(3201,assumption,(~m_counter_cell_v_carry_out(c_bit0, s14)), introduced(assumption)).
% 35.65/23.48 tff(3202,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3203,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3204,plain,
% 35.65/23.48 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s14)) | m_counter_cell_v_carry_out(c_bit0, s14)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3203, 3202])).
% 35.65/23.48 tff(3205,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3204, 2901, 3201, 3200])).
% 35.65/23.48 tff(3206,plain,(m_counter_cell_v_carry_out(c_bit0, s14) | (~m_counter_cell_v_carry_in(c_bit1, s14))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3207,plain,
% 35.65/23.48 (~m_counter_cell_v_carry_in(c_bit1, s14)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3206, 3199])).
% 35.65/23.48 tff(3208,assumption,(~m_counter_cell_v_carry_in(c_bit1, s14)), introduced(assumption)).
% 35.65/23.48 tff(3209,plain,
% 35.65/23.48 (((~![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)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3210,plain,
% 35.65/23.48 ((~![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)))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3211,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 35.65/23.48 tff(3212,plain,
% 35.65/23.48 (~node4(c_bit0, s10)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3211, 2875, 416])).
% 35.65/23.48 tff(3213,assumption,(m_counter_cell_v_carry_out(c_bit0, s10)), introduced(assumption)).
% 35.65/23.48 tff(3214,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3215,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3216,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s10)) | node4(c_bit0, s10)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3215, 3214])).
% 35.65/23.48 tff(3217,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3216, 2887, 3213, 3212])).
% 35.65/23.48 tff(3218,plain,(~m_counter_cell_v_carry_out(c_bit0, s10)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3219,assumption,(m_counter_cell_v_carry_in(c_bit1, s10)), introduced(assumption)).
% 35.65/23.48 tff(3220,assumption,(~m_counter_cell_v_carry_out(c_bit0, s10)), introduced(assumption)).
% 35.65/23.48 tff(3221,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3222,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3223,plain,
% 35.65/23.48 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s10)) | m_counter_cell_v_carry_out(c_bit0, s10)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3222, 3221])).
% 35.65/23.48 tff(3224,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3223, 2901, 3220, 3219])).
% 35.65/23.48 tff(3225,plain,(m_counter_cell_v_carry_out(c_bit0, s10) | (~m_counter_cell_v_carry_in(c_bit1, s10))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3226,plain,
% 35.65/23.48 (~m_counter_cell_v_carry_in(c_bit1, s10)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3225, 3218])).
% 35.65/23.48 tff(3227,plain,
% 35.65/23.48 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3228,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3229,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3228, 3227])).
% 35.65/23.48 tff(3230,plain,
% 35.65/23.48 ((~m_counter_cell_v_value(c_bit0, s7)) | m_counter_cell_v_carry_out(c_bit0, s7)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3229, 3031, 337])).
% 35.65/23.48 tff(3231,plain,
% 35.65/23.48 (m_counter_cell_v_carry_out(c_bit0, s7)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3230, 333])).
% 35.65/23.48 tff(3232,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3233,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3234,plain,
% 35.65/23.48 ((~![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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3233, 3232])).
% 35.65/23.48 tff(3235,plain,
% 35.65/23.48 (m_counter_cell_v_carry_in(c_bit1, s7)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3234, 3046, 3231])).
% 35.65/23.48 tff(3236,assumption,(node2(c_bit1, s7)), introduced(assumption)).
% 35.65/23.48 tff(3237,assumption,(node4(c_bit0, s6)), introduced(assumption)).
% 35.65/23.48 tff(3238,assumption,(~m_counter_cell_v_value(c_bit0, s6)), introduced(assumption)).
% 35.65/23.48 tff(3239,plain,
% 35.65/23.48 (((~![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)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3240,plain,
% 35.65/23.48 ((~![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)))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3241,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3240, 3239])).
% 35.65/23.48 tff(3242,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3241, 2875, 3238, 3237])).
% 35.65/23.48 tff(3243,plain,(m_counter_cell_v_value(c_bit0, s6) | (~node4(c_bit0, s6))), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3244,plain,
% 35.65/23.48 (~node4(c_bit0, s6)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3243, 302])).
% 35.65/23.48 tff(3245,assumption,(m_counter_cell_v_carry_out(c_bit0, s6)), introduced(assumption)).
% 35.65/23.48 tff(3246,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3247,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3248,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s6)) | node4(c_bit0, s6)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3247, 3246])).
% 35.65/23.48 tff(3249,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3248, 2887, 3245, 3244])).
% 35.65/23.48 tff(3250,plain,(~m_counter_cell_v_carry_out(c_bit0, s6)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3251,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3252,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3253,plain,
% 35.65/23.48 ((~![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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3252, 3251])).
% 35.65/23.48 tff(3254,plain,
% 35.65/23.48 (~m_counter_cell_v_carry_in(c_bit1, s6)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3253, 2901, 3250])).
% 35.65/23.48 tff(3255,assumption,(node1(c_bit1, s6)), introduced(assumption)).
% 35.65/23.48 tff(3256,assumption,(node1(c_bit1, s5)), introduced(assumption)).
% 35.65/23.48 tff(3257,plain,
% 35.65/23.48 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3258,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3259,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 35.65/23.48 tff(3260,plain,
% 35.65/23.48 ((~m_counter_cell_v_value(c_bit0, s5)) | m_counter_cell_v_carry_out(c_bit0, s5)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3259, 3031, 290])).
% 35.65/23.48 tff(3261,plain,
% 35.65/23.48 (m_counter_cell_v_carry_out(c_bit0, s5)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3260, 286])).
% 35.65/23.48 tff(3262,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3263,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3264,plain,
% 35.65/23.48 ((~![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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3263, 3262])).
% 35.65/23.48 tff(3265,plain,
% 35.65/23.48 (m_counter_cell_v_carry_in(c_bit1, s5)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3264, 3046, 3261])).
% 35.65/23.48 tff(3266,assumption,(m_counter_cell_v_value(c_bit1, s0)), introduced(assumption)).
% 35.65/23.48 tff(3267,plain,
% 35.65/23.48 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit1, s0))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3268,plain,
% 35.65/23.48 ($false),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3267, 148, 3266])).
% 35.65/23.48 tff(3269,plain,(~m_counter_cell_v_value(c_bit1, s0)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.48 tff(3270,plain,
% 35.65/23.48 (((~![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)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3271,plain,
% 35.65/23.48 ((~![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)))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3272,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3271, 3270])).
% 35.65/23.48 tff(3273,plain,
% 35.65/23.48 (~node4(c_bit0, s0)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3272, 2875, 151])).
% 35.65/23.48 tff(3274,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3275,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3276,plain,
% 35.65/23.48 ((~![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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3275, 3274])).
% 35.65/23.48 tff(3277,plain,
% 35.65/23.48 (~m_counter_cell_v_carry_out(c_bit0, s0)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3276, 2887, 3273])).
% 35.65/23.48 tff(3278,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3279,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3280,plain,
% 35.65/23.48 ((~![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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3279, 3278])).
% 35.65/23.48 tff(3281,plain,
% 35.65/23.48 (~m_counter_cell_v_carry_in(c_bit1, s0)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3280, 2901, 3277])).
% 35.65/23.48 tff(3282,plain,
% 35.65/23.48 (^[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))))),
% 35.65/23.48 inference(bind,[status(th)],[])).
% 35.65/23.48 tff(3283,plain,
% 35.65/23.48 (![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)))),
% 35.65/23.48 inference(quant_intro,[status(thm)],[3282])).
% 35.65/23.48 tff(3284,plain,
% 35.65/23.48 (![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)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3285,plain,
% 35.65/23.48 (^[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)))))),
% 35.65/23.48 inference(bind,[status(th)],[])).
% 35.65/23.48 tff(3286,plain,
% 35.65/23.48 (![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)))),
% 35.65/23.48 inference(quant_intro,[status(thm)],[3285])).
% 35.65/23.48 tff(3287,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')).
% 35.65/23.48 tff(3288,plain,
% 35.65/23.48 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3287, 3286])).
% 35.65/23.48 tff(3289,plain,
% 35.65/23.48 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3288, 3284])).
% 35.65/23.48 tff(3290,plain,(
% 35.65/23.48 ![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 35.65/23.48 inference(skolemize,[status(sab)],[3289])).
% 35.65/23.48 tff(3291,plain,
% 35.65/23.48 (![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3290, 3283])).
% 35.65/23.48 tff(3292,plain,
% 35.65/23.48 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3293,plain,
% 35.65/23.48 ((m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0))) <=> (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3294,plain,
% 35.65/23.48 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0)))),
% 35.65/23.48 inference(monotonicity,[status(thm)],[3293])).
% 35.65/23.48 tff(3295,plain,
% 35.65/23.48 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s0) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0))),
% 35.65/23.48 inference(transitivity,[status(thm)],[3294, 3292])).
% 35.65/23.48 tff(3296,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : (m_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)))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3297,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0)) | m_counter_cell_v_carry_in(c_bit1, s0)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 35.65/23.48 tff(3298,plain,
% 35.65/23.48 (m_counter_cell_v_value(c_bit1, s0) | (~node2(c_bit1, s0))),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3297, 3291, 3281])).
% 35.65/23.48 tff(3299,plain,
% 35.65/23.48 (~node2(c_bit1, s0)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3298, 3269])).
% 35.65/23.48 tff(3300,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3301,plain,
% 35.65/23.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit1, s0, s1))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3302,plain,
% 35.65/23.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit1, s0, s1)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3301, 3300])).
% 35.65/23.48 tff(3303,plain,
% 35.65/23.48 (node3(c_bit1, s0, s1)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3302, 81, 185])).
% 35.65/23.48 tff(3304,plain,
% 35.65/23.48 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s0) | (~node3(c_bit1, s0, s1)) | (~m_counter_cell_v_value(c_bit1, s1)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3305,plain,
% 35.65/23.48 ((~![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)))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3306,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3305, 3304])).
% 35.65/23.48 tff(3307,plain,
% 35.65/23.48 (node2(c_bit1, s0) | (~m_counter_cell_v_value(c_bit1, s1))),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3306, 234, 3303])).
% 35.65/23.48 tff(3308,plain,
% 35.65/23.48 (~m_counter_cell_v_value(c_bit1, s1)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3307, 3299])).
% 35.65/23.48 tff(3309,plain,
% 35.65/23.48 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3310,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3311,plain,
% 35.65/23.48 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3310, 3309])).
% 35.65/23.48 tff(3312,plain,
% 35.65/23.48 ((~m_counter_cell_v_value(c_bit0, s1)) | m_counter_cell_v_carry_out(c_bit0, s1)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3311, 3031, 209])).
% 35.65/23.48 tff(3313,plain,
% 35.65/23.48 (m_counter_cell_v_carry_out(c_bit0, s1)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3312, 207])).
% 35.65/23.48 tff(3314,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3315,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3316,plain,
% 35.65/23.48 ((~![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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3315, 3314])).
% 35.65/23.48 tff(3317,plain,
% 35.65/23.48 (m_counter_cell_v_carry_in(c_bit1, s1)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3316, 3046, 3313])).
% 35.65/23.48 tff(3318,plain,
% 35.65/23.48 (((~![I0: $i, 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) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~node1(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) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~node1(c_bit1, s1)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3319,plain,
% 35.65/23.48 (((~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) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~node1(c_bit1, s1)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3320,plain,
% 35.65/23.48 (((~![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) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~node1(c_bit1, s1))))),
% 35.65/23.48 inference(monotonicity,[status(thm)],[3319])).
% 35.65/23.48 tff(3321,plain,
% 35.65/23.48 (((~![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) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~node1(c_bit1, s1)))),
% 35.65/23.48 inference(transitivity,[status(thm)],[3320, 3318])).
% 35.65/23.48 tff(3322,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3323,plain,
% 35.65/23.48 ((~![I0: $i, 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) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~node1(c_bit1, s1))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3322, 3321])).
% 35.65/23.48 tff(3324,plain,
% 35.65/23.48 (m_counter_cell_v_value(c_bit1, s1) | (~node1(c_bit1, s1))),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3323, 170, 3317])).
% 35.65/23.48 tff(3325,plain,
% 35.65/23.48 (~node1(c_bit1, s1)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3324, 3308])).
% 35.65/23.48 tff(3326,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3327,plain,
% 35.65/23.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit1, s1, s2))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3328,plain,
% 35.65/23.48 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit1, s1, s2)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3327, 3326])).
% 35.65/23.48 tff(3329,plain,
% 35.65/23.48 (node3(c_bit1, s1, s2)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3328, 81, 136])).
% 35.65/23.48 tff(3330,plain,
% 35.65/23.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s2) | (~node3(c_bit1, s1, 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))) | m_counter_cell_v_value(c_bit1, s2) | (~node3(c_bit1, s1, s2)) | node1(c_bit1, s1))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3331,plain,
% 35.65/23.48 ((node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2)) <=> (m_counter_cell_v_value(c_bit1, s2) | (~node3(c_bit1, s1, s2)) | node1(c_bit1, s1))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3332,plain,
% 35.65/23.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s2) | (~node3(c_bit1, s1, s2)) | node1(c_bit1, s1)))),
% 35.65/23.48 inference(monotonicity,[status(thm)],[3331])).
% 35.65/23.48 tff(3333,plain,
% 35.65/23.48 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | m_counter_cell_v_value(c_bit1, s2))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s2) | (~node3(c_bit1, s1, s2)) | node1(c_bit1, s1))),
% 35.65/23.48 inference(transitivity,[status(thm)],[3332, 3330])).
% 35.65/23.48 tff(3334,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3335,plain,
% 35.65/23.48 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s2) | (~node3(c_bit1, s1, s2)) | node1(c_bit1, s1)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 35.65/23.48 tff(3336,plain,
% 35.65/23.48 (m_counter_cell_v_value(c_bit1, s2) | node1(c_bit1, s1)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3335, 199, 3329])).
% 35.65/23.48 tff(3337,plain,
% 35.65/23.48 (m_counter_cell_v_value(c_bit1, s2)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3336, 3325])).
% 35.65/23.48 tff(3338,plain,
% 35.65/23.48 (((~![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)))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3339,plain,
% 35.65/23.48 ((~![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)))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3340,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 35.65/23.48 tff(3341,plain,
% 35.65/23.48 (~node4(c_bit0, s2)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3340, 2875, 241])).
% 35.65/23.48 tff(3342,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.48 inference(rewrite,[status(thm)],[])).
% 35.65/23.48 tff(3343,plain,
% 35.65/23.48 ((~![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))),
% 35.65/23.48 inference(quant_inst,[status(thm)],[])).
% 35.65/23.48 tff(3344,plain,
% 35.65/23.48 ((~![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)),
% 35.65/23.48 inference(modus_ponens,[status(thm)],[3343, 3342])).
% 35.65/23.48 tff(3345,plain,
% 35.65/23.48 (~m_counter_cell_v_carry_out(c_bit0, s2)),
% 35.65/23.48 inference(unit_resolution,[status(thm)],[3344, 2887, 3341])).
% 35.65/23.48 tff(3346,plain,
% 35.65/23.48 (((~![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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3347,plain,
% 35.65/23.49 ((~![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))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3348,plain,
% 35.65/23.49 ((~![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)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3347, 3346])).
% 35.65/23.49 tff(3349,plain,
% 35.65/23.49 (~m_counter_cell_v_carry_in(c_bit1, s2)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3348, 2901, 3345])).
% 35.65/23.49 tff(3350,plain,
% 35.65/23.49 (^[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))))),
% 35.65/23.49 inference(bind,[status(th)],[])).
% 35.65/23.49 tff(3351,plain,
% 35.65/23.49 (![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)))),
% 35.65/23.49 inference(quant_intro,[status(thm)],[3350])).
% 35.65/23.49 tff(3352,plain,
% 35.65/23.49 (![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)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3353,plain,
% 35.65/23.49 (^[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))))),
% 35.65/23.49 inference(bind,[status(th)],[])).
% 35.65/23.49 tff(3354,plain,
% 35.65/23.49 (![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)))),
% 35.65/23.49 inference(quant_intro,[status(thm)],[3353])).
% 35.65/23.49 tff(3355,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')).
% 35.65/23.49 tff(3356,plain,
% 35.65/23.49 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 35.65/23.49 tff(3357,plain,
% 35.65/23.49 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3356, 3352])).
% 35.65/23.49 tff(3358,plain,(
% 35.65/23.49 ![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 35.65/23.49 inference(skolemize,[status(sab)],[3357])).
% 35.65/23.49 tff(3359,plain,
% 35.65/23.49 (![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3358, 3351])).
% 35.65/23.49 tff(3360,plain,
% 35.65/23.49 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3361,plain,
% 35.65/23.49 (((~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)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3362,plain,
% 35.65/23.49 (((~![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))))),
% 35.65/23.49 inference(monotonicity,[status(thm)],[3361])).
% 35.65/23.49 tff(3363,plain,
% 35.65/23.49 (((~![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)))),
% 35.65/23.49 inference(transitivity,[status(thm)],[3362, 3360])).
% 35.65/23.49 tff(3364,plain,
% 35.65/23.49 ((~![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)))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3365,plain,
% 35.65/23.49 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3364, 3363])).
% 35.65/23.49 tff(3366,plain,
% 35.65/23.49 ((~m_counter_cell_v_value(c_bit1, s2)) | (~node1(c_bit1, s2))),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3365, 3359, 3349])).
% 35.65/23.49 tff(3367,plain,
% 35.65/23.49 (~node1(c_bit1, s2)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3366, 3337])).
% 35.65/23.49 tff(3368,plain,
% 35.65/23.49 (((~![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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3369,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit1, s2, s3))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3370,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit1, s2, s3)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3369, 3368])).
% 35.65/23.49 tff(3371,plain,
% 35.65/23.49 (node3(c_bit1, s2, s3)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3370, 81, 125])).
% 35.65/23.49 tff(3372,plain,
% 35.65/23.49 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3373,plain,
% 35.65/23.49 ((node1(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | m_counter_cell_v_value(c_bit1, s3)) <=> (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3374,plain,
% 35.65/23.49 (((~![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))) | (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3))))),
% 35.65/23.49 inference(monotonicity,[status(thm)],[3373])).
% 35.65/23.49 tff(3375,plain,
% 35.65/23.49 (((~![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))) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3)))),
% 35.65/23.49 inference(transitivity,[status(thm)],[3374, 3372])).
% 35.65/23.49 tff(3376,plain,
% 35.65/23.49 ((~![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))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3377,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3) | (~node3(c_bit1, s2, s3))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3376, 3375])).
% 35.65/23.49 tff(3378,plain,
% 35.65/23.49 (node1(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s3)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3377, 199, 3371])).
% 35.65/23.49 tff(3379,plain,
% 35.65/23.49 (m_counter_cell_v_value(c_bit1, s3)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3378, 3367])).
% 35.65/23.49 tff(3380,plain,
% 35.65/23.49 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3381,plain,
% 35.65/23.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3382,plain,
% 35.65/23.49 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3381, 3380])).
% 35.65/23.49 tff(3383,plain,
% 35.65/23.49 ((~m_counter_cell_v_value(c_bit0, s3)) | m_counter_cell_v_carry_out(c_bit0, s3)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3382, 3031, 260])).
% 35.65/23.49 tff(3384,plain,
% 35.65/23.49 (m_counter_cell_v_carry_out(c_bit0, s3)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3383, 258])).
% 35.65/23.49 tff(3385,plain,
% 35.65/23.49 (((~![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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3386,plain,
% 35.65/23.49 ((~![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))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3387,plain,
% 35.65/23.49 ((~![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)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3386, 3385])).
% 35.65/23.49 tff(3388,plain,
% 35.65/23.49 (m_counter_cell_v_carry_in(c_bit1, s3)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3387, 3046, 3384])).
% 35.65/23.49 tff(3389,plain,
% 35.65/23.49 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3390,plain,
% 35.65/23.49 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3391,plain,
% 35.65/23.49 ((~![I0: $i, X: $i] : ((~m_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))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3390, 3389])).
% 35.65/23.49 tff(3392,plain,
% 35.65/23.49 ((~m_counter_cell_v_value(c_bit1, s3)) | (~node2(c_bit1, s3))),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3391, 219, 3388])).
% 35.65/23.49 tff(3393,plain,
% 35.65/23.49 (~node2(c_bit1, s3)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3392, 3379])).
% 35.65/23.49 tff(3394,plain,
% 35.65/23.49 (((~![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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3395,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit1, s3, s4))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3396,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit1, s3, s4)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3395, 3394])).
% 35.65/23.49 tff(3397,plain,
% 35.65/23.49 (node3(c_bit1, s3, s4)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3396, 81, 114])).
% 35.65/23.49 tff(3398,plain,
% 35.65/23.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, 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_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3399,plain,
% 35.65/23.49 ((node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | (~m_counter_cell_v_value(c_bit1, s4))) <=> ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3400,plain,
% 35.65/23.49 (((~![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)))) | ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4))))),
% 35.65/23.49 inference(monotonicity,[status(thm)],[3399])).
% 35.65/23.49 tff(3401,plain,
% 35.65/23.49 (((~![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)))) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 35.65/23.49 inference(transitivity,[status(thm)],[3400, 3398])).
% 35.65/23.49 tff(3402,plain,
% 35.65/23.49 ((~![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)))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3403,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3) | (~node3(c_bit1, s3, s4))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3402, 3401])).
% 35.65/23.49 tff(3404,plain,
% 35.65/23.49 ((~m_counter_cell_v_value(c_bit1, s4)) | node2(c_bit1, s3)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3403, 234, 3397])).
% 35.65/23.49 tff(3405,plain,
% 35.65/23.49 (~m_counter_cell_v_value(c_bit1, s4)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3404, 3393])).
% 35.65/23.49 tff(3406,plain,
% 35.65/23.49 (((~![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)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3407,plain,
% 35.65/23.49 ((~![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)))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3408,plain,
% 35.65/23.49 ((~![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))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3407, 3406])).
% 35.65/23.49 tff(3409,plain,
% 35.65/23.49 (~node4(c_bit0, s4)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3408, 2875, 272])).
% 35.65/23.49 tff(3410,plain,
% 35.65/23.49 (((~![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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3411,plain,
% 35.65/23.49 ((~![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))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3412,plain,
% 35.65/23.49 ((~![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)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3411, 3410])).
% 35.65/23.49 tff(3413,plain,
% 35.65/23.49 (~m_counter_cell_v_carry_out(c_bit0, s4)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3412, 2887, 3409])).
% 35.65/23.49 tff(3414,plain,
% 35.65/23.49 (((~![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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3415,plain,
% 35.65/23.49 ((~![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))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3416,plain,
% 35.65/23.49 ((~![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)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3415, 3414])).
% 35.65/23.49 tff(3417,plain,
% 35.65/23.49 (~m_counter_cell_v_carry_in(c_bit1, s4)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3416, 2901, 3413])).
% 35.65/23.49 tff(3418,plain,
% 35.65/23.49 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s4) | m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3419,plain,
% 35.65/23.49 ((~![I0: $i, X: $i] : (m_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)))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3420,plain,
% 35.65/23.49 ((~![I0: $i, X: $i] : (m_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))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3419, 3418])).
% 35.65/23.49 tff(3421,plain,
% 35.65/23.49 (m_counter_cell_v_value(c_bit1, s4) | (~node2(c_bit1, s4))),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3420, 3291, 3417])).
% 35.65/23.49 tff(3422,plain,
% 35.65/23.49 (~node2(c_bit1, s4)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3421, 3405])).
% 35.65/23.49 tff(3423,plain,
% 35.65/23.49 (((~![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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3424,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit1, s4, s5))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3425,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit1, s4, s5)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3424, 3423])).
% 35.65/23.49 tff(3426,plain,
% 35.65/23.49 (node3(c_bit1, s4, s5)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3425, 81, 103])).
% 35.65/23.49 tff(3427,plain,
% 35.65/23.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3428,plain,
% 35.65/23.49 ((node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5))) <=> ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3429,plain,
% 35.65/23.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5))))),
% 35.65/23.49 inference(monotonicity,[status(thm)],[3428])).
% 35.65/23.49 tff(3430,plain,
% 35.65/23.49 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | (~m_counter_cell_v_value(c_bit1, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 35.65/23.49 inference(transitivity,[status(thm)],[3429, 3427])).
% 35.65/23.49 tff(3431,plain,
% 35.65/23.49 ((~![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)))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3432,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4) | (~node3(c_bit1, s4, s5))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3431, 3430])).
% 35.65/23.49 tff(3433,plain,
% 35.65/23.49 ((~m_counter_cell_v_value(c_bit1, s5)) | node2(c_bit1, s4)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3432, 234, 3426])).
% 35.65/23.49 tff(3434,plain,
% 35.65/23.49 (~m_counter_cell_v_value(c_bit1, s5)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3433, 3422])).
% 35.65/23.49 tff(3435,plain,
% 35.65/23.49 (((~![I0: $i, X: $i] : ((~node1(I0, 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)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(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)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3436,plain,
% 35.65/23.49 (((~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)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3437,plain,
% 35.65/23.49 (((~![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)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5))))),
% 35.65/23.49 inference(monotonicity,[status(thm)],[3436])).
% 35.65/23.49 tff(3438,plain,
% 35.65/23.49 (((~![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)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5)))),
% 35.65/23.49 inference(transitivity,[status(thm)],[3437, 3435])).
% 35.65/23.49 tff(3439,plain,
% 35.65/23.49 ((~![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))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3440,plain,
% 35.65/23.49 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s5)) | m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit1, s5))),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3439, 3438])).
% 35.65/23.49 tff(3441,plain,
% 35.65/23.49 ($false),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3440, 170, 3434, 3265, 3256])).
% 35.65/23.49 tff(3442,plain,(~node1(c_bit1, s5)), inference(lemma,lemma(discharge,[]))).
% 35.65/23.49 tff(3443,plain,
% 35.65/23.49 (((~![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))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3444,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit1, s5, s6))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.65/23.49 tff(3445,plain,
% 35.65/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit1, s5, s6)),
% 35.65/23.49 inference(modus_ponens,[status(thm)],[3444, 3443])).
% 35.65/23.49 tff(3446,plain,
% 35.65/23.49 (node3(c_bit1, s5, s6)),
% 35.65/23.49 inference(unit_resolution,[status(thm)],[3445, 81, 92])).
% 35.65/23.49 tff(3447,plain,
% 35.65/23.49 (((~![Y: $i, I0: $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)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3448,plain,
% 35.65/23.49 ((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)))),
% 35.65/23.49 inference(rewrite,[status(thm)],[])).
% 35.65/23.49 tff(3449,plain,
% 35.65/23.49 (((~![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))))),
% 35.65/23.49 inference(monotonicity,[status(thm)],[3448])).
% 35.65/23.49 tff(3450,plain,
% 35.65/23.49 (((~![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)))),
% 35.65/23.49 inference(transitivity,[status(thm)],[3449, 3447])).
% 35.65/23.49 tff(3451,plain,
% 35.65/23.49 ((~![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))),
% 35.65/23.49 inference(quant_inst,[status(thm)],[])).
% 35.69/23.49 tff(3452,plain,
% 35.69/23.49 ((~![Y: $i, I0: $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))),
% 35.69/23.49 inference(modus_ponens,[status(thm)],[3451, 3450])).
% 35.69/23.49 tff(3453,plain,
% 35.69/23.49 (m_counter_cell_v_value(c_bit1, s6) | node1(c_bit1, s5)),
% 35.69/23.49 inference(unit_resolution,[status(thm)],[3452, 199, 3446])).
% 35.69/23.49 tff(3454,plain,
% 35.69/23.49 (m_counter_cell_v_value(c_bit1, s6)),
% 35.69/23.49 inference(unit_resolution,[status(thm)],[3453, 3442])).
% 35.69/23.49 tff(3455,plain,
% 35.69/23.49 (((~![I0: $i, X: $i] : ((~node1(I0, 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) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(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) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6)))),
% 35.69/23.49 inference(rewrite,[status(thm)],[])).
% 35.69/23.49 tff(3456,plain,
% 35.69/23.49 (((~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) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6)))),
% 35.69/23.49 inference(rewrite,[status(thm)],[])).
% 35.69/23.49 tff(3457,plain,
% 35.69/23.49 (((~![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) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6))))),
% 35.69/23.49 inference(monotonicity,[status(thm)],[3456])).
% 35.69/23.49 tff(3458,plain,
% 35.69/23.49 (((~![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) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6)))),
% 35.69/23.49 inference(transitivity,[status(thm)],[3457, 3455])).
% 35.69/23.49 tff(3459,plain,
% 35.69/23.49 ((~![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)))),
% 35.69/23.49 inference(quant_inst,[status(thm)],[])).
% 35.69/23.49 tff(3460,plain,
% 35.69/23.49 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~m_counter_cell_v_value(c_bit1, s6)) | (~node1(c_bit1, s6))),
% 35.69/23.49 inference(modus_ponens,[status(thm)],[3459, 3458])).
% 35.69/23.49 tff(3461,plain,
% 35.69/23.49 ($false),
% 35.69/23.49 inference(unit_resolution,[status(thm)],[3460, 3359, 3454, 3255, 3254])).
% 35.69/23.49 tff(3462,plain,(~node1(c_bit1, s6)), inference(lemma,lemma(discharge,[]))).
% 35.69/23.49 tff(3463,plain,
% 35.69/23.49 (((~![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))),
% 35.69/23.49 inference(rewrite,[status(thm)],[])).
% 35.69/23.49 tff(3464,plain,
% 35.69/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit1, s6, s7))),
% 35.69/23.49 inference(quant_inst,[status(thm)],[])).
% 35.69/23.49 tff(3465,plain,
% 35.69/23.49 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit1, s6, s7)),
% 35.69/23.49 inference(modus_ponens,[status(thm)],[3464, 3463])).
% 35.69/23.49 tff(3466,plain,
% 35.69/23.49 (node3(c_bit1, s6, s7)),
% 35.69/23.49 inference(unit_resolution,[status(thm)],[3465, 81, 321])).
% 35.69/23.49 tff(3467,plain,
% 35.69/23.49 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3468,plain,
% 35.69/23.50 ((node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)) | m_counter_cell_v_value(c_bit1, s7)) <=> (m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3469,plain,
% 35.69/23.50 (((~![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))) | (m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7))))),
% 35.69/23.50 inference(monotonicity,[status(thm)],[3468])).
% 35.69/23.50 tff(3470,plain,
% 35.69/23.50 (((~![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))) | m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7)))),
% 35.69/23.50 inference(transitivity,[status(thm)],[3469, 3467])).
% 35.69/23.50 tff(3471,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3472,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6) | (~node3(c_bit1, s6, s7))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3471, 3470])).
% 35.69/23.50 tff(3473,plain,
% 35.69/23.50 (m_counter_cell_v_value(c_bit1, s7) | node1(c_bit1, s6)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3472, 199, 3466])).
% 35.69/23.50 tff(3474,plain,
% 35.69/23.50 (m_counter_cell_v_value(c_bit1, s7)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3473, 3462])).
% 35.69/23.50 tff(3475,plain,
% 35.69/23.50 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3476,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3477,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | (~node2(c_bit1, s7))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 35.69/23.50 tff(3478,plain,
% 35.69/23.50 ($false),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3477, 219, 3474, 3236, 3235])).
% 35.69/23.50 tff(3479,plain,(~node2(c_bit1, s7)), inference(lemma,lemma(discharge,[]))).
% 35.69/23.50 tff(3480,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3481,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit1, s7, s8))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3482,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit1, s7, s8)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 35.69/23.50 tff(3483,plain,
% 35.69/23.50 (node3(c_bit1, s7, s8)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3482, 81, 349])).
% 35.69/23.50 tff(3484,plain,
% 35.69/23.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~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)))) | (~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3485,plain,
% 35.69/23.50 ((node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8))) <=> ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3486,plain,
% 35.69/23.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8))))),
% 35.69/23.50 inference(monotonicity,[status(thm)],[3485])).
% 35.69/23.50 tff(3487,plain,
% 35.69/23.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)) | (~m_counter_cell_v_value(c_bit1, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8)))),
% 35.69/23.50 inference(transitivity,[status(thm)],[3486, 3484])).
% 35.69/23.50 tff(3488,plain,
% 35.69/23.50 ((~![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)))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3489,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7) | (~node3(c_bit1, s7, s8))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3488, 3487])).
% 35.69/23.50 tff(3490,plain,
% 35.69/23.50 ((~m_counter_cell_v_value(c_bit1, s8)) | node2(c_bit1, s7)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3489, 234, 3483])).
% 35.69/23.50 tff(3491,plain,
% 35.69/23.50 (~m_counter_cell_v_value(c_bit1, s8)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3490, 3479])).
% 35.69/23.50 tff(3492,plain,
% 35.69/23.50 (((~![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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3493,plain,
% 35.69/23.50 ((~![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)))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3494,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3493, 3492])).
% 35.69/23.50 tff(3495,plain,
% 35.69/23.50 (~node4(c_bit0, s8)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3494, 2875, 361])).
% 35.69/23.50 tff(3496,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3497,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3498,plain,
% 35.69/23.50 ((~![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)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3497, 3496])).
% 35.69/23.50 tff(3499,plain,
% 35.69/23.50 (~m_counter_cell_v_carry_out(c_bit0, s8)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3498, 2887, 3495])).
% 35.69/23.50 tff(3500,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3501,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3502,plain,
% 35.69/23.50 ((~![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)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3501, 3500])).
% 35.69/23.50 tff(3503,plain,
% 35.69/23.50 (~m_counter_cell_v_carry_in(c_bit1, s8)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3502, 2901, 3499])).
% 35.69/23.50 tff(3504,plain,
% 35.69/23.50 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s8) | m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3505,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : (m_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)))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3506,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : (m_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))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3505, 3504])).
% 35.69/23.50 tff(3507,plain,
% 35.69/23.50 (m_counter_cell_v_value(c_bit1, s8) | (~node2(c_bit1, s8))),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3506, 3291, 3503])).
% 35.69/23.50 tff(3508,plain,
% 35.69/23.50 (~node2(c_bit1, s8)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3507, 3491])).
% 35.69/23.50 tff(3509,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3510,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit1, s8, s9))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3511,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit1, s8, s9)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3510, 3509])).
% 35.69/23.50 tff(3512,plain,
% 35.69/23.50 (node3(c_bit1, s8, s9)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3511, 81, 378])).
% 35.69/23.50 tff(3513,plain,
% 35.69/23.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3514,plain,
% 35.69/23.50 ((node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9))) <=> ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3515,plain,
% 35.69/23.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9))))),
% 35.69/23.50 inference(monotonicity,[status(thm)],[3514])).
% 35.69/23.50 tff(3516,plain,
% 35.69/23.50 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)) | (~m_counter_cell_v_value(c_bit1, s9)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9)))),
% 35.69/23.50 inference(transitivity,[status(thm)],[3515, 3513])).
% 35.69/23.50 tff(3517,plain,
% 35.69/23.50 ((~![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)))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3518,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8) | (~node3(c_bit1, s8, s9))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3517, 3516])).
% 35.69/23.50 tff(3519,plain,
% 35.69/23.50 ((~m_counter_cell_v_value(c_bit1, s9)) | node2(c_bit1, s8)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3518, 234, 3512])).
% 35.69/23.50 tff(3520,plain,
% 35.69/23.50 (~m_counter_cell_v_value(c_bit1, s9)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3519, 3508])).
% 35.69/23.50 tff(3521,plain,
% 35.69/23.50 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3522,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3523,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3522, 3521])).
% 35.69/23.50 tff(3524,plain,
% 35.69/23.50 ((~m_counter_cell_v_value(c_bit0, s9)) | m_counter_cell_v_carry_out(c_bit0, s9)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3523, 3031, 392])).
% 35.69/23.50 tff(3525,plain,
% 35.69/23.50 (m_counter_cell_v_carry_out(c_bit0, s9)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3524, 390])).
% 35.69/23.50 tff(3526,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3527,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3528,plain,
% 35.69/23.50 ((~![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)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3527, 3526])).
% 35.69/23.50 tff(3529,plain,
% 35.69/23.50 (m_counter_cell_v_carry_in(c_bit1, s9)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3528, 3046, 3525])).
% 35.69/23.50 tff(3530,plain,
% 35.69/23.50 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3531,plain,
% 35.69/23.50 (((~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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3532,plain,
% 35.69/23.50 (((~![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))))),
% 35.69/23.50 inference(monotonicity,[status(thm)],[3531])).
% 35.69/23.50 tff(3533,plain,
% 35.69/23.50 (((~![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)))),
% 35.69/23.50 inference(transitivity,[status(thm)],[3532, 3530])).
% 35.69/23.50 tff(3534,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3535,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 35.69/23.50 tff(3536,plain,
% 35.69/23.50 (m_counter_cell_v_value(c_bit1, s9) | (~node1(c_bit1, s9))),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3535, 170, 3529])).
% 35.69/23.50 tff(3537,plain,
% 35.69/23.50 (~node1(c_bit1, s9)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3536, 3520])).
% 35.69/23.50 tff(3538,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3539,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit1, s9, s10))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3540,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit1, s9, s10)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3539, 3538])).
% 35.69/23.50 tff(3541,plain,
% 35.69/23.50 (node3(c_bit1, s9, s10)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3540, 81, 404])).
% 35.69/23.50 tff(3542,plain,
% 35.69/23.50 (((~![Y: $i, I0: $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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3543,plain,
% 35.69/23.50 ((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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3544,plain,
% 35.69/23.50 (((~![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))))),
% 35.69/23.50 inference(monotonicity,[status(thm)],[3543])).
% 35.69/23.50 tff(3545,plain,
% 35.69/23.50 (((~![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)))),
% 35.69/23.50 inference(transitivity,[status(thm)],[3544, 3542])).
% 35.69/23.50 tff(3546,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3547,plain,
% 35.69/23.50 ((~![Y: $i, I0: $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))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 35.69/23.50 tff(3548,plain,
% 35.69/23.50 (m_counter_cell_v_value(c_bit1, s10) | node1(c_bit1, s9)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3547, 199, 3541])).
% 35.69/23.50 tff(3549,plain,
% 35.69/23.50 (m_counter_cell_v_value(c_bit1, s10)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3548, 3537])).
% 35.69/23.50 tff(3550,assumption,(~m_counter_cell_v_carry_in(c_bit1, s10)), introduced(assumption)).
% 35.69/23.50 tff(3551,assumption,(m_counter_cell_v_value(c_bit1, s10)), introduced(assumption)).
% 35.69/23.50 tff(3552,assumption,(node1(c_bit1, s10)), introduced(assumption)).
% 35.69/23.50 tff(3553,plain,
% 35.69/23.50 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3554,plain,
% 35.69/23.50 (((~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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3555,plain,
% 35.69/23.50 (((~![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))))),
% 35.69/23.50 inference(monotonicity,[status(thm)],[3554])).
% 35.69/23.50 tff(3556,plain,
% 35.69/23.50 (((~![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)))),
% 35.69/23.50 inference(transitivity,[status(thm)],[3555, 3553])).
% 35.69/23.50 tff(3557,plain,
% 35.69/23.50 ((~![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)))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3558,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~m_counter_cell_v_value(c_bit1, s10)) | (~node1(c_bit1, s10))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3557, 3556])).
% 35.69/23.50 tff(3559,plain,
% 35.69/23.50 ($false),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3558, 3359, 3552, 3551, 3550])).
% 35.69/23.50 tff(3560,plain,(m_counter_cell_v_carry_in(c_bit1, s10) | (~node1(c_bit1, s10)) | (~m_counter_cell_v_value(c_bit1, s10))), inference(lemma,lemma(discharge,[]))).
% 35.69/23.50 tff(3561,plain,
% 35.69/23.50 (m_counter_cell_v_carry_in(c_bit1, s10) | (~node1(c_bit1, s10))),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3560, 3549])).
% 35.69/23.50 tff(3562,plain,
% 35.69/23.50 (~node1(c_bit1, s10)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3561, 3226])).
% 35.69/23.50 tff(3563,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3564,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit1, s10, s11))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3565,plain,
% 35.69/23.50 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit1, s10, s11)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3564, 3563])).
% 35.69/23.50 tff(3566,plain,
% 35.69/23.50 (node3(c_bit1, s10, s11)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3565, 81, 435])).
% 35.69/23.50 tff(3567,plain,
% 35.69/23.50 (((~![Y: $i, I0: $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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3568,plain,
% 35.69/23.50 ((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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3569,plain,
% 35.69/23.50 (((~![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))))),
% 35.69/23.50 inference(monotonicity,[status(thm)],[3568])).
% 35.69/23.50 tff(3570,plain,
% 35.69/23.50 (((~![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)))),
% 35.69/23.50 inference(transitivity,[status(thm)],[3569, 3567])).
% 35.69/23.50 tff(3571,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3572,plain,
% 35.69/23.50 ((~![Y: $i, I0: $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))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3571, 3570])).
% 35.69/23.50 tff(3573,plain,
% 35.69/23.50 (m_counter_cell_v_value(c_bit1, s11) | node1(c_bit1, s10)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3572, 199, 3566])).
% 35.69/23.50 tff(3574,plain,
% 35.69/23.50 (m_counter_cell_v_value(c_bit1, s11)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3573, 3562])).
% 35.69/23.50 tff(3575,plain,
% 35.69/23.50 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3576,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3577,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3576, 3575])).
% 35.69/23.50 tff(3578,plain,
% 35.69/23.50 ((~m_counter_cell_v_value(c_bit0, s11)) | m_counter_cell_v_carry_out(c_bit0, s11)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3577, 3031, 451])).
% 35.69/23.50 tff(3579,plain,
% 35.69/23.50 (m_counter_cell_v_carry_out(c_bit0, s11)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3578, 447])).
% 35.69/23.50 tff(3580,assumption,(~m_counter_cell_v_carry_in(c_bit1, s11)), introduced(assumption)).
% 35.69/23.50 tff(3581,assumption,(m_counter_cell_v_carry_out(c_bit0, s11)), introduced(assumption)).
% 35.69/23.50 tff(3582,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3583,plain,
% 35.69/23.50 ((~![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))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3584,plain,
% 35.69/23.50 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11)),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3583, 3582])).
% 35.69/23.50 tff(3585,plain,
% 35.69/23.50 ($false),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3584, 3046, 3581, 3580])).
% 35.69/23.50 tff(3586,plain,((~m_counter_cell_v_carry_out(c_bit0, s11)) | m_counter_cell_v_carry_in(c_bit1, s11)), inference(lemma,lemma(discharge,[]))).
% 35.69/23.50 tff(3587,plain,
% 35.69/23.50 (m_counter_cell_v_carry_in(c_bit1, s11)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3586, 3579])).
% 35.69/23.50 tff(3588,assumption,(m_counter_cell_v_carry_in(c_bit1, s11)), introduced(assumption)).
% 35.69/23.50 tff(3589,assumption,(node2(c_bit1, s11)), introduced(assumption)).
% 35.69/23.50 tff(3590,assumption,(m_counter_cell_v_value(c_bit1, s11)), introduced(assumption)).
% 35.69/23.50 tff(3591,plain,
% 35.69/23.50 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.50 tff(3592,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.69/23.50 inference(quant_inst,[status(thm)],[])).
% 35.69/23.50 tff(3593,plain,
% 35.69/23.50 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~node2(c_bit1, s11))),
% 35.69/23.50 inference(modus_ponens,[status(thm)],[3592, 3591])).
% 35.69/23.50 tff(3594,plain,
% 35.69/23.50 ($false),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3593, 219, 3590, 3589, 3588])).
% 35.69/23.50 tff(3595,plain,((~node2(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | (~m_counter_cell_v_carry_in(c_bit1, s11))), inference(lemma,lemma(discharge,[]))).
% 35.69/23.50 tff(3596,plain,
% 35.69/23.50 ((~node2(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11))),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3595, 3587])).
% 35.69/23.50 tff(3597,plain,
% 35.69/23.50 (~node2(c_bit1, s11)),
% 35.69/23.50 inference(unit_resolution,[status(thm)],[3596, 3574])).
% 35.69/23.50 tff(3598,plain,
% 35.69/23.50 (((~![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))),
% 35.69/23.50 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3599,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit1, s11, s12))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3600,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit1, s11, s12)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3599, 3598])).
% 35.69/23.51 tff(3601,plain,
% 35.69/23.51 (node3(c_bit1, s11, s12)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3600, 81, 463])).
% 35.69/23.51 tff(3602,plain,
% 35.69/23.51 (((~![Y: $i, I0: $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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3603,plain,
% 35.69/23.51 ((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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3604,plain,
% 35.69/23.51 (((~![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))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3603])).
% 35.69/23.51 tff(3605,plain,
% 35.69/23.51 (((~![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)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3604, 3602])).
% 35.69/23.51 tff(3606,plain,
% 35.69/23.51 ((~![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)))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3607,plain,
% 35.69/23.51 ((~![Y: $i, I0: $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))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3606, 3605])).
% 35.69/23.51 tff(3608,plain,
% 35.69/23.51 ((~m_counter_cell_v_value(c_bit1, s12)) | node2(c_bit1, s11)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3607, 234, 3601])).
% 35.69/23.51 tff(3609,plain,
% 35.69/23.51 (~m_counter_cell_v_value(c_bit1, s12)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3608, 3597])).
% 35.69/23.51 tff(3610,plain,
% 35.69/23.51 (((~![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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3611,plain,
% 35.69/23.51 ((~![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)))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3612,plain,
% 35.69/23.51 ((~![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))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3611, 3610])).
% 35.69/23.51 tff(3613,plain,
% 35.69/23.51 (~node4(c_bit0, s12)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3612, 2875, 475])).
% 35.69/23.51 tff(3614,assumption,(m_counter_cell_v_carry_out(c_bit0, s12)), introduced(assumption)).
% 35.69/23.51 tff(3615,plain,
% 35.69/23.51 (((~![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))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3616,plain,
% 35.69/23.51 ((~![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))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3617,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s12)) | node4(c_bit0, s12)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3616, 3615])).
% 35.69/23.51 tff(3618,plain,
% 35.69/23.51 ($false),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3617, 2887, 3614, 3613])).
% 35.69/23.51 tff(3619,plain,(~m_counter_cell_v_carry_out(c_bit0, s12)), inference(lemma,lemma(discharge,[]))).
% 35.69/23.51 tff(3620,assumption,(m_counter_cell_v_carry_in(c_bit1, s12)), introduced(assumption)).
% 35.69/23.51 tff(3621,assumption,(~m_counter_cell_v_carry_out(c_bit0, s12)), introduced(assumption)).
% 35.69/23.51 tff(3622,plain,
% 35.69/23.51 (((~![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))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3623,plain,
% 35.69/23.51 ((~![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))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3624,plain,
% 35.69/23.51 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3623, 3622])).
% 35.69/23.51 tff(3625,plain,
% 35.69/23.51 ($false),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3624, 2901, 3621, 3620])).
% 35.69/23.51 tff(3626,plain,((~m_counter_cell_v_carry_in(c_bit1, s12)) | m_counter_cell_v_carry_out(c_bit0, s12)), inference(lemma,lemma(discharge,[]))).
% 35.69/23.51 tff(3627,plain,
% 35.69/23.51 (~m_counter_cell_v_carry_in(c_bit1, s12)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3626, 3619])).
% 35.69/23.51 tff(3628,plain,
% 35.69/23.51 (((~![I0: $i, X: $i] : (m_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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3629,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : (m_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)))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3630,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : (m_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))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3629, 3628])).
% 35.69/23.51 tff(3631,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit1, s12) | (~node2(c_bit1, s12))),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3630, 3291, 3627])).
% 35.69/23.51 tff(3632,plain,
% 35.69/23.51 (~node2(c_bit1, s12)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3631, 3609])).
% 35.69/23.51 tff(3633,plain,
% 35.69/23.51 (((~![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))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3634,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit1, s12, s13))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3635,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit1, s12, s13)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3634, 3633])).
% 35.69/23.51 tff(3636,plain,
% 35.69/23.51 (node3(c_bit1, s12, s13)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3635, 81, 494])).
% 35.69/23.51 tff(3637,plain,
% 35.69/23.51 (((~![Y: $i, I0: $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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3638,plain,
% 35.69/23.51 ((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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3639,plain,
% 35.69/23.51 (((~![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))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3638])).
% 35.69/23.51 tff(3640,plain,
% 35.69/23.51 (((~![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)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3639, 3637])).
% 35.69/23.51 tff(3641,plain,
% 35.69/23.51 ((~![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)))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3642,plain,
% 35.69/23.51 ((~![Y: $i, I0: $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))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3641, 3640])).
% 35.69/23.51 tff(3643,plain,
% 35.69/23.51 ((~m_counter_cell_v_value(c_bit1, s13)) | node2(c_bit1, s12)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3642, 234, 3636])).
% 35.69/23.51 tff(3644,plain,
% 35.69/23.51 (~m_counter_cell_v_value(c_bit1, s13)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3643, 3632])).
% 35.69/23.51 tff(3645,plain,
% 35.69/23.51 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3646,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3647,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3646, 3645])).
% 35.69/23.51 tff(3648,plain,
% 35.69/23.51 ((~m_counter_cell_v_value(c_bit0, s13)) | m_counter_cell_v_carry_out(c_bit0, s13)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3647, 3031, 510])).
% 35.69/23.51 tff(3649,plain,
% 35.69/23.51 (m_counter_cell_v_carry_out(c_bit0, s13)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3648, 506])).
% 35.69/23.51 tff(3650,plain,
% 35.69/23.51 (((~![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))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3651,plain,
% 35.69/23.51 ((~![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))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3652,plain,
% 35.69/23.51 ((~![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)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 35.69/23.51 tff(3653,plain,
% 35.69/23.51 (m_counter_cell_v_carry_in(c_bit1, s13)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3652, 3046, 3649])).
% 35.69/23.51 tff(3654,plain,
% 35.69/23.51 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3655,plain,
% 35.69/23.51 (((~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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3656,plain,
% 35.69/23.51 (((~![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))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3655])).
% 35.69/23.51 tff(3657,plain,
% 35.69/23.51 (((~![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)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3656, 3654])).
% 35.69/23.51 tff(3658,plain,
% 35.69/23.51 ((~![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))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3659,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3658, 3657])).
% 35.69/23.51 tff(3660,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit1, s13) | (~node1(c_bit1, s13))),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3659, 170, 3653])).
% 35.69/23.51 tff(3661,plain,
% 35.69/23.51 (~node1(c_bit1, s13)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3660, 3644])).
% 35.69/23.51 tff(3662,plain,
% 35.69/23.51 (((~![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))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3663,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit1, s13, s14))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3664,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit1, s13, s14)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3663, 3662])).
% 35.69/23.51 tff(3665,plain,
% 35.69/23.51 (node3(c_bit1, s13, s14)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3664, 81, 522])).
% 35.69/23.51 tff(3666,plain,
% 35.69/23.51 (((~![Y: $i, I0: $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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3667,plain,
% 35.69/23.51 ((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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3668,plain,
% 35.69/23.51 (((~![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))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3667])).
% 35.69/23.51 tff(3669,plain,
% 35.69/23.51 (((~![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)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3668, 3666])).
% 35.69/23.51 tff(3670,plain,
% 35.69/23.51 ((~![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))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3671,plain,
% 35.69/23.51 ((~![Y: $i, I0: $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))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3670, 3669])).
% 35.69/23.51 tff(3672,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit1, s14) | node1(c_bit1, s13)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3671, 199, 3665])).
% 35.69/23.51 tff(3673,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit1, s14)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3672, 3661])).
% 35.69/23.51 tff(3674,assumption,(node1(c_bit1, s14)), introduced(assumption)).
% 35.69/23.51 tff(3675,plain,
% 35.69/23.51 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3676,plain,
% 35.69/23.51 (((~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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3677,plain,
% 35.69/23.51 (((~![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))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3676])).
% 35.69/23.51 tff(3678,plain,
% 35.69/23.51 (((~![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)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3677, 3675])).
% 35.69/23.51 tff(3679,plain,
% 35.69/23.51 ((~![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)))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3680,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~m_counter_cell_v_value(c_bit1, s14)) | (~node1(c_bit1, s14))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3679, 3678])).
% 35.69/23.51 tff(3681,plain,
% 35.69/23.51 ($false),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3680, 3359, 3674, 3673, 3208])).
% 35.69/23.51 tff(3682,plain,((~node1(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14)), inference(lemma,lemma(discharge,[]))).
% 35.69/23.51 tff(3683,plain,
% 35.69/23.51 (~node1(c_bit1, s14)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3682, 3207])).
% 35.69/23.51 tff(3684,plain,
% 35.69/23.51 (((~![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))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3685,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit1, s14, s15))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3686,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit1, s14, s15)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3685, 3684])).
% 35.69/23.51 tff(3687,plain,
% 35.69/23.51 (node3(c_bit1, s14, s15)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3686, 81, 553])).
% 35.69/23.51 tff(3688,plain,
% 35.69/23.51 (((~![Y: $i, I0: $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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3689,plain,
% 35.69/23.51 ((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)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3690,plain,
% 35.69/23.51 (((~![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))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3689])).
% 35.69/23.51 tff(3691,plain,
% 35.69/23.51 (((~![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)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3690, 3688])).
% 35.69/23.51 tff(3692,plain,
% 35.69/23.51 ((~![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))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3693,plain,
% 35.69/23.51 ((~![Y: $i, I0: $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))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3692, 3691])).
% 35.69/23.51 tff(3694,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit1, s15) | node1(c_bit1, s14)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3693, 199, 3687])).
% 35.69/23.51 tff(3695,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit1, s15)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3694, 3683])).
% 35.69/23.51 tff(3696,assumption,(m_counter_cell_v_value(c_bit0, s17)), introduced(assumption)).
% 35.69/23.51 tff(3697,plain,
% 35.69/23.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s17)) | node2(c_bit0, s16) | (~node3(c_bit0, 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_bit0, s17)) | node2(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3698,plain,
% 35.69/23.51 ((node2(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | (~m_counter_cell_v_value(c_bit0, s17))) <=> ((~m_counter_cell_v_value(c_bit0, s17)) | node2(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3699,plain,
% 35.69/23.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | (~m_counter_cell_v_value(c_bit0, 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_bit0, s17)) | node2(c_bit0, s16) | (~node3(c_bit0, s16, s17))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3698])).
% 35.69/23.51 tff(3700,plain,
% 35.69/23.51 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | (~m_counter_cell_v_value(c_bit0, 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_bit0, s17)) | node2(c_bit0, s16) | (~node3(c_bit0, s16, s17)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3699, 3697])).
% 35.69/23.51 tff(3701,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s16) | (~node3(c_bit0, s16, s17)) | (~m_counter_cell_v_value(c_bit0, s17)))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3702,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s17)) | node2(c_bit0, s16) | (~node3(c_bit0, s16, s17))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3701, 3700])).
% 35.69/23.51 tff(3703,plain,
% 35.69/23.51 ((~m_counter_cell_v_value(c_bit0, s17)) | node2(c_bit0, s16)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3702, 234, 614])).
% 35.69/23.51 tff(3704,plain,
% 35.69/23.51 (node2(c_bit0, s16)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3703, 3696])).
% 35.69/23.51 tff(3705,plain,
% 35.69/23.51 (((~![I0: $i, X: $i] : ((~m_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, s16)) | (~m_counter_cell_v_value(c_bit0, s16)) | (~node2(c_bit0, 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_bit0, s16)) | (~m_counter_cell_v_value(c_bit0, s16)) | (~node2(c_bit0, s16)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3706,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~m_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, s16)) | (~m_counter_cell_v_value(c_bit0, s16)) | (~node2(c_bit0, s16)))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3707,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~m_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, s16)) | (~m_counter_cell_v_value(c_bit0, s16)) | (~node2(c_bit0, s16))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3706, 3705])).
% 35.69/23.51 tff(3708,plain,
% 35.69/23.51 ((~m_counter_cell_v_value(c_bit0, s16)) | (~node2(c_bit0, s16))),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3707, 219, 595])).
% 35.69/23.51 tff(3709,plain,
% 35.69/23.51 (~m_counter_cell_v_value(c_bit0, s16)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3708, 3704])).
% 35.69/23.51 tff(3710,plain,
% 35.69/23.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s16) | node1(c_bit0, s15) | (~node3(c_bit0, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s16) | node1(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3711,plain,
% 35.69/23.51 ((node1(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | m_counter_cell_v_value(c_bit0, s16)) <=> (m_counter_cell_v_value(c_bit0, s16) | node1(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3712,plain,
% 35.69/23.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | m_counter_cell_v_value(c_bit0, s16))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s16) | node1(c_bit0, s15) | (~node3(c_bit0, s15, s16))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3711])).
% 35.69/23.51 tff(3713,plain,
% 35.69/23.51 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | m_counter_cell_v_value(c_bit0, s16))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s16) | node1(c_bit0, s15) | (~node3(c_bit0, s15, s16)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3712, 3710])).
% 35.69/23.51 tff(3714,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s15) | (~node3(c_bit0, s15, s16)) | m_counter_cell_v_value(c_bit0, s16))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3715,plain,
% 35.69/23.51 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s16) | node1(c_bit0, s15) | (~node3(c_bit0, s15, s16))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3714, 3713])).
% 35.69/23.51 tff(3716,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit0, s16) | node1(c_bit0, s15)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3715, 199, 585])).
% 35.69/23.51 tff(3717,plain,
% 35.69/23.51 (node1(c_bit0, s15)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3716, 3709])).
% 35.69/23.51 tff(3718,plain,
% 35.69/23.51 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15) | (~node1(c_bit0, s15)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15) | (~node1(c_bit0, s15)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3719,plain,
% 35.69/23.51 (((~node1(c_bit0, s15)) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15) | (~node1(c_bit0, s15)))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3720,plain,
% 35.69/23.51 (((~![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, s15)) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15) | (~node1(c_bit0, s15))))),
% 35.69/23.51 inference(monotonicity,[status(thm)],[3719])).
% 35.69/23.51 tff(3721,plain,
% 35.69/23.51 (((~![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, s15)) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15) | (~node1(c_bit0, s15)))),
% 35.69/23.51 inference(transitivity,[status(thm)],[3720, 3718])).
% 35.69/23.51 tff(3722,plain,
% 35.69/23.51 ((~![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, s15)) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3723,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s15)) | m_counter_cell_v_value(c_bit0, s15) | (~node1(c_bit0, s15))),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3722, 3721])).
% 35.69/23.51 tff(3724,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit0, s15) | (~node1(c_bit0, s15))),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3723, 170, 569])).
% 35.69/23.51 tff(3725,plain,
% 35.69/23.51 (m_counter_cell_v_value(c_bit0, s15)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3724, 3717])).
% 35.69/23.51 tff(3726,plain,
% 35.69/23.51 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.51 inference(rewrite,[status(thm)],[])).
% 35.69/23.51 tff(3727,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.51 inference(quant_inst,[status(thm)],[])).
% 35.69/23.51 tff(3728,plain,
% 35.69/23.51 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.69/23.51 inference(modus_ponens,[status(thm)],[3727, 3726])).
% 35.69/23.51 tff(3729,plain,
% 35.69/23.51 ((~m_counter_cell_v_value(c_bit0, s15)) | m_counter_cell_v_carry_out(c_bit0, s15)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3728, 3031, 569])).
% 35.69/23.51 tff(3730,plain,
% 35.69/23.51 (m_counter_cell_v_carry_out(c_bit0, s15)),
% 35.69/23.51 inference(unit_resolution,[status(thm)],[3729, 3725])).
% 35.69/23.52 tff(3731,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3732,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3733,plain,
% 35.69/23.52 ((~![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)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 35.69/23.52 tff(3734,plain,
% 35.69/23.52 (m_counter_cell_v_carry_in(c_bit1, s15)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3733, 3046, 3730])).
% 35.69/23.52 tff(3735,assumption,(m_counter_cell_v_value(c_bit1, s15)), introduced(assumption)).
% 35.69/23.52 tff(3736,plain,
% 35.69/23.52 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3737,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3738,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~m_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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3737, 3736])).
% 35.69/23.52 tff(3739,plain,
% 35.69/23.52 ((~m_counter_cell_v_carry_in(c_bit1, s15)) | (~node2(c_bit1, s15))),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3738, 219, 3735])).
% 35.69/23.52 tff(3740,plain,
% 35.69/23.52 (~node2(c_bit1, s15)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3739, 3734])).
% 35.69/23.52 tff(3741,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3742,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit1, s15, s16))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3743,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit1, s15, s16)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3742, 3741])).
% 35.69/23.52 tff(3744,plain,
% 35.69/23.52 (node3(c_bit1, s15, s16)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3743, 81, 581])).
% 35.69/23.52 tff(3745,plain,
% 35.69/23.52 (((~![Y: $i, I0: $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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3746,plain,
% 35.69/23.52 ((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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3747,plain,
% 35.69/23.52 (((~![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))))),
% 35.69/23.52 inference(monotonicity,[status(thm)],[3746])).
% 35.69/23.52 tff(3748,plain,
% 35.69/23.52 (((~![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)))),
% 35.69/23.52 inference(transitivity,[status(thm)],[3747, 3745])).
% 35.69/23.52 tff(3749,plain,
% 35.69/23.52 ((~![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)))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3750,plain,
% 35.69/23.52 ((~![Y: $i, I0: $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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3749, 3748])).
% 35.69/23.52 tff(3751,plain,
% 35.69/23.52 ((~m_counter_cell_v_value(c_bit1, s16)) | node2(c_bit1, s15)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3750, 234, 3744])).
% 35.69/23.52 tff(3752,plain,
% 35.69/23.52 (~m_counter_cell_v_value(c_bit1, s16)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3751, 3740])).
% 35.69/23.52 tff(3753,plain,
% 35.69/23.52 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3754,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3755,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3754, 3753])).
% 35.69/23.52 tff(3756,plain,
% 35.69/23.52 ((~m_counter_cell_v_value(c_bit0, s17)) | m_counter_cell_v_carry_out(c_bit0, s17)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3755, 3031, 626])).
% 35.69/23.52 tff(3757,plain,
% 35.69/23.52 (m_counter_cell_v_carry_out(c_bit0, s17)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3756, 3696])).
% 35.69/23.52 tff(3758,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3759,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3760,plain,
% 35.69/23.52 ((~![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)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3759, 3758])).
% 35.69/23.52 tff(3761,plain,
% 35.69/23.52 (m_counter_cell_v_carry_in(c_bit1, s17)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3760, 3046, 3757])).
% 35.69/23.52 tff(3762,assumption,(node1(c_bit1, s17)), introduced(assumption)).
% 35.69/23.52 tff(3763,plain,
% 35.69/23.52 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3764,plain,
% 35.69/23.52 (((~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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3765,plain,
% 35.69/23.52 (((~![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))))),
% 35.69/23.52 inference(monotonicity,[status(thm)],[3764])).
% 35.69/23.52 tff(3766,plain,
% 35.69/23.52 (((~![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)))),
% 35.69/23.52 inference(transitivity,[status(thm)],[3765, 3763])).
% 35.69/23.52 tff(3767,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3768,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3767, 3766])).
% 35.69/23.52 tff(3769,plain,
% 35.69/23.52 ((~m_counter_cell_v_carry_in(c_bit1, s17)) | m_counter_cell_v_value(c_bit1, s17)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3768, 170, 3762])).
% 35.69/23.52 tff(3770,plain,
% 35.69/23.52 (m_counter_cell_v_value(c_bit1, s17)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3769, 3761])).
% 35.69/23.52 tff(3771,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3772,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit1, s16, s17))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3773,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit1, s16, s17)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3772, 3771])).
% 35.69/23.52 tff(3774,plain,
% 35.69/23.52 (node3(c_bit1, s16, s17)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3773, 81, 610])).
% 35.69/23.52 tff(3775,plain,
% 35.69/23.52 (((~![Y: $i, I0: $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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3776,plain,
% 35.69/23.52 ((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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3777,plain,
% 35.69/23.52 (((~![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))))),
% 35.69/23.52 inference(monotonicity,[status(thm)],[3776])).
% 35.69/23.52 tff(3778,plain,
% 35.69/23.52 (((~![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)))),
% 35.69/23.52 inference(transitivity,[status(thm)],[3777, 3775])).
% 35.69/23.52 tff(3779,plain,
% 35.69/23.52 ((~![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)))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3780,plain,
% 35.69/23.52 ((~![Y: $i, I0: $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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3779, 3778])).
% 35.69/23.52 tff(3781,plain,
% 35.69/23.52 ((~m_counter_cell_v_value(c_bit1, s17)) | node2(c_bit1, s16)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3780, 234, 3774])).
% 35.69/23.52 tff(3782,plain,
% 35.69/23.52 (node2(c_bit1, s16)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3781, 3770])).
% 35.69/23.52 tff(3783,plain,
% 35.69/23.52 (((~![I0: $i, X: $i] : (m_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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3784,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : (m_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)))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3785,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : (m_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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3784, 3783])).
% 35.69/23.52 tff(3786,plain,
% 35.69/23.52 (m_counter_cell_v_carry_in(c_bit1, s16)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3785, 3291, 3782, 3752])).
% 35.69/23.52 tff(3787,plain,
% 35.69/23.52 (((~![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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3788,plain,
% 35.69/23.52 ((~![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)))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3789,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3788, 3787])).
% 35.69/23.52 tff(3790,plain,
% 35.69/23.52 (~node4(c_bit0, s16)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3789, 2875, 3709])).
% 35.69/23.52 tff(3791,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3792,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3793,plain,
% 35.69/23.52 ((~![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)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3792, 3791])).
% 35.69/23.52 tff(3794,plain,
% 35.69/23.52 (~m_counter_cell_v_carry_out(c_bit0, s16)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3793, 2887, 3790])).
% 35.69/23.52 tff(3795,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3796,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3797,plain,
% 35.69/23.52 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s16)) | m_counter_cell_v_carry_out(c_bit0, s16)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3796, 3795])).
% 35.69/23.52 tff(3798,plain,
% 35.69/23.52 ($false),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3797, 2901, 3794, 3786])).
% 35.69/23.52 tff(3799,plain,((~m_counter_cell_v_value(c_bit0, s17)) | (~m_counter_cell_v_value(c_bit1, s15)) | (~node1(c_bit1, s17))), inference(lemma,lemma(discharge,[]))).
% 35.69/23.52 tff(3800,plain,
% 35.69/23.52 ((~m_counter_cell_v_value(c_bit1, s15)) | (~node1(c_bit1, s17))),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3799, 622])).
% 35.69/23.52 tff(3801,plain,
% 35.69/23.52 (~node1(c_bit1, s17)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3800, 3695])).
% 35.69/23.52 tff(3802,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3803,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit1, s17, s18))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3804,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit1, s17, s18)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3803, 3802])).
% 35.69/23.52 tff(3805,plain,
% 35.69/23.52 (node3(c_bit1, s17, s18)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3804, 81, 638])).
% 35.69/23.52 tff(3806,plain,
% 35.69/23.52 (((~![Y: $i, I0: $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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3807,plain,
% 35.69/23.52 ((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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3808,plain,
% 35.69/23.52 (((~![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))))),
% 35.69/23.52 inference(monotonicity,[status(thm)],[3807])).
% 35.69/23.52 tff(3809,plain,
% 35.69/23.52 (((~![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)))),
% 35.69/23.52 inference(transitivity,[status(thm)],[3808, 3806])).
% 35.69/23.52 tff(3810,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3811,plain,
% 35.69/23.52 ((~![Y: $i, I0: $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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3810, 3809])).
% 35.69/23.52 tff(3812,plain,
% 35.69/23.52 (m_counter_cell_v_value(c_bit1, s18) | node1(c_bit1, s17)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3811, 199, 3805])).
% 35.69/23.52 tff(3813,plain,
% 35.69/23.52 (m_counter_cell_v_value(c_bit1, s18)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3812, 3801])).
% 35.69/23.52 tff(3814,plain,
% 35.69/23.52 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3815,plain,
% 35.69/23.52 (((~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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3816,plain,
% 35.69/23.52 (((~![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))))),
% 35.69/23.52 inference(monotonicity,[status(thm)],[3815])).
% 35.69/23.52 tff(3817,plain,
% 35.69/23.52 (((~![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)))),
% 35.69/23.52 inference(transitivity,[status(thm)],[3816, 3814])).
% 35.69/23.52 tff(3818,plain,
% 35.69/23.52 ((~![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)))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3819,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3818, 3817])).
% 35.69/23.52 tff(3820,plain,
% 35.69/23.52 (m_counter_cell_v_carry_in(c_bit1, s18) | (~node1(c_bit1, s18))),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3819, 3359, 3813])).
% 35.69/23.52 tff(3821,plain,
% 35.69/23.52 (~node1(c_bit1, s18)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3820, 3189])).
% 35.69/23.52 tff(3822,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3823,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit1, s18, s19))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3824,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit1, s18, s19)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3823, 3822])).
% 35.69/23.52 tff(3825,plain,
% 35.69/23.52 (node3(c_bit1, s18, s19)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3824, 81, 669])).
% 35.69/23.52 tff(3826,plain,
% 35.69/23.52 (((~![Y: $i, I0: $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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3827,plain,
% 35.69/23.52 ((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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3828,plain,
% 35.69/23.52 (((~![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))))),
% 35.69/23.52 inference(monotonicity,[status(thm)],[3827])).
% 35.69/23.52 tff(3829,plain,
% 35.69/23.52 (((~![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)))),
% 35.69/23.52 inference(transitivity,[status(thm)],[3828, 3826])).
% 35.69/23.52 tff(3830,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3831,plain,
% 35.69/23.52 ((~![Y: $i, I0: $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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3830, 3829])).
% 35.69/23.52 tff(3832,plain,
% 35.69/23.52 (m_counter_cell_v_value(c_bit1, s19) | node1(c_bit1, s18)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3831, 199, 3825])).
% 35.69/23.52 tff(3833,plain,
% 35.69/23.52 (m_counter_cell_v_value(c_bit1, s19)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3832, 3821])).
% 35.69/23.52 tff(3834,plain,
% 35.69/23.52 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3835,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3836,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3835, 3834])).
% 35.69/23.52 tff(3837,plain,
% 35.69/23.52 ((~m_counter_cell_v_value(c_bit0, s19)) | m_counter_cell_v_carry_out(c_bit0, s19)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3836, 3031, 685])).
% 35.69/23.52 tff(3838,plain,
% 35.69/23.52 (m_counter_cell_v_carry_out(c_bit0, s19)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3837, 681])).
% 35.69/23.52 tff(3839,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3840,plain,
% 35.69/23.52 ((~![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))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3841,plain,
% 35.69/23.52 ((~![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)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3840, 3839])).
% 35.69/23.52 tff(3842,plain,
% 35.69/23.52 (m_counter_cell_v_carry_in(c_bit1, s19)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3841, 3046, 3838])).
% 35.69/23.52 tff(3843,plain,
% 35.69/23.52 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3844,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3845,plain,
% 35.69/23.52 ((~![I0: $i, X: $i] : ((~m_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))),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3844, 3843])).
% 35.69/23.52 tff(3846,plain,
% 35.69/23.52 ((~m_counter_cell_v_value(c_bit1, s19)) | (~node2(c_bit1, s19))),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3845, 219, 3842])).
% 35.69/23.52 tff(3847,plain,
% 35.69/23.52 (~node2(c_bit1, s19)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3846, 3833])).
% 35.69/23.52 tff(3848,plain,
% 35.69/23.52 (((~![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))),
% 35.69/23.52 inference(rewrite,[status(thm)],[])).
% 35.69/23.52 tff(3849,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit1, s19, s20))),
% 35.69/23.52 inference(quant_inst,[status(thm)],[])).
% 35.69/23.52 tff(3850,plain,
% 35.69/23.52 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit1, s19, s20)),
% 35.69/23.52 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 35.69/23.52 tff(3851,plain,
% 35.69/23.52 (node3(c_bit1, s19, s20)),
% 35.69/23.52 inference(unit_resolution,[status(thm)],[3850, 81, 697])).
% 35.69/23.52 tff(3852,plain,
% 35.69/23.52 (((~![Y: $i, I0: $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)))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3853,plain,
% 35.69/23.53 ((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)))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3854,plain,
% 35.69/23.53 (((~![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))))),
% 35.69/23.53 inference(monotonicity,[status(thm)],[3853])).
% 35.69/23.53 tff(3855,plain,
% 35.69/23.53 (((~![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)))),
% 35.69/23.53 inference(transitivity,[status(thm)],[3854, 3852])).
% 35.69/23.53 tff(3856,plain,
% 35.69/23.53 ((~![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)))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3857,plain,
% 35.69/23.53 ((~![Y: $i, I0: $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))),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3856, 3855])).
% 35.69/23.53 tff(3858,plain,
% 35.69/23.53 ((~m_counter_cell_v_value(c_bit1, s20)) | node2(c_bit1, s19)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3857, 234, 3851])).
% 35.69/23.53 tff(3859,plain,
% 35.69/23.53 (~m_counter_cell_v_value(c_bit1, s20)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3858, 3847])).
% 35.69/23.53 tff(3860,plain,
% 35.69/23.53 (((~![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)))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3861,plain,
% 35.69/23.53 ((~![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)))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3862,plain,
% 35.69/23.53 ((~![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))),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3861, 3860])).
% 35.69/23.53 tff(3863,plain,
% 35.69/23.53 (~node4(c_bit0, s20)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3862, 2875, 709])).
% 35.69/23.53 tff(3864,plain,
% 35.69/23.53 (((~![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))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3865,plain,
% 35.69/23.53 ((~![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))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3866,plain,
% 35.69/23.53 ((~![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)),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3865, 3864])).
% 35.69/23.53 tff(3867,plain,
% 35.69/23.53 (~m_counter_cell_v_carry_out(c_bit0, s20)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3866, 2887, 3863])).
% 35.69/23.53 tff(3868,plain,
% 35.69/23.53 (((~![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))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3869,plain,
% 35.69/23.53 ((~![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))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3870,plain,
% 35.69/23.53 ((~![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)),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3869, 3868])).
% 35.69/23.53 tff(3871,plain,
% 35.69/23.53 (~m_counter_cell_v_carry_in(c_bit1, s20)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3870, 2901, 3867])).
% 35.69/23.53 tff(3872,plain,
% 35.69/23.53 (((~![I0: $i, X: $i] : (m_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)))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3873,plain,
% 35.69/23.53 ((~![I0: $i, X: $i] : (m_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)))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3874,plain,
% 35.69/23.53 ((~![I0: $i, X: $i] : (m_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))),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3873, 3872])).
% 35.69/23.53 tff(3875,plain,
% 35.69/23.53 (m_counter_cell_v_value(c_bit1, s20) | (~node2(c_bit1, s20))),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3874, 3291, 3871])).
% 35.69/23.53 tff(3876,plain,
% 35.69/23.53 (~node2(c_bit1, s20)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3875, 3859])).
% 35.69/23.53 tff(3877,plain,
% 35.69/23.53 (((~![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))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3878,plain,
% 35.69/23.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit1, s20, s21))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3879,plain,
% 35.69/23.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit1, s20, s21)),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3878, 3877])).
% 35.69/23.53 tff(3880,plain,
% 35.69/23.53 (node3(c_bit1, s20, s21)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3879, 81, 726])).
% 35.69/23.53 tff(3881,plain,
% 35.69/23.53 (((~![Y: $i, I0: $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)))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3882,plain,
% 35.69/23.53 ((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)))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3883,plain,
% 35.69/23.53 (((~![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))))),
% 35.69/23.53 inference(monotonicity,[status(thm)],[3882])).
% 35.69/23.53 tff(3884,plain,
% 35.69/23.53 (((~![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)))),
% 35.69/23.53 inference(transitivity,[status(thm)],[3883, 3881])).
% 35.69/23.53 tff(3885,plain,
% 35.69/23.53 ((~![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)))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3886,plain,
% 35.69/23.53 ((~![Y: $i, I0: $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))),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 35.69/23.53 tff(3887,plain,
% 35.69/23.53 ((~m_counter_cell_v_value(c_bit1, s21)) | node2(c_bit1, s20)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3886, 234, 3880])).
% 35.69/23.53 tff(3888,plain,
% 35.69/23.53 (~m_counter_cell_v_value(c_bit1, s21)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3887, 3876])).
% 35.69/23.53 tff(3889,assumption,(node1(c_bit1, s21)), introduced(assumption)).
% 35.69/23.53 tff(3890,plain,
% 35.69/23.53 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3891,plain,
% 35.69/23.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3892,plain,
% 35.69/23.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3891, 3890])).
% 35.69/23.53 tff(3893,plain,
% 35.69/23.53 ((~m_counter_cell_v_value(c_bit0, s21)) | m_counter_cell_v_carry_out(c_bit0, s21)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3892, 3031, 742])).
% 35.69/23.53 tff(3894,plain,
% 35.69/23.53 (m_counter_cell_v_carry_out(c_bit0, s21)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3893, 738])).
% 35.69/23.53 tff(3895,plain,
% 35.69/23.53 (((~![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))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3896,plain,
% 35.69/23.53 ((~![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))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3897,plain,
% 35.69/23.53 ((~![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)),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3896, 3895])).
% 35.69/23.53 tff(3898,plain,
% 35.69/23.53 (m_counter_cell_v_carry_in(c_bit1, s21)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3897, 3046, 3894])).
% 35.69/23.53 tff(3899,assumption,(~m_counter_cell_v_value(c_bit1, s21)), introduced(assumption)).
% 35.69/23.53 tff(3900,plain,
% 35.69/23.53 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3901,plain,
% 35.69/23.53 (((~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)))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3902,plain,
% 35.69/23.53 (((~![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))))),
% 35.69/23.53 inference(monotonicity,[status(thm)],[3901])).
% 35.69/23.53 tff(3903,plain,
% 35.69/23.53 (((~![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)))),
% 35.69/23.53 inference(transitivity,[status(thm)],[3902, 3900])).
% 35.69/23.53 tff(3904,plain,
% 35.69/23.53 ((~![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))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3905,plain,
% 35.69/23.53 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21) | (~node1(c_bit1, s21))),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3904, 3903])).
% 35.69/23.53 tff(3906,plain,
% 35.69/23.53 ($false),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3905, 170, 3899, 3898, 3889])).
% 35.69/23.53 tff(3907,plain,((~node1(c_bit1, s21)) | m_counter_cell_v_value(c_bit1, s21)), inference(lemma,lemma(discharge,[]))).
% 35.69/23.53 tff(3908,plain,
% 35.69/23.53 (~node1(c_bit1, s21)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3907, 3888])).
% 35.69/23.53 tff(3909,plain,
% 35.69/23.53 (((~![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))),
% 35.69/23.53 inference(rewrite,[status(thm)],[])).
% 35.69/23.53 tff(3910,plain,
% 35.69/23.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit1, s21, s22))),
% 35.69/23.53 inference(quant_inst,[status(thm)],[])).
% 35.69/23.53 tff(3911,plain,
% 35.69/23.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit1, s21, s22)),
% 35.69/23.53 inference(modus_ponens,[status(thm)],[3910, 3909])).
% 35.69/23.53 tff(3912,plain,
% 35.69/23.53 (node3(c_bit1, s21, s22)),
% 35.69/23.53 inference(unit_resolution,[status(thm)],[3911, 81, 754])).
% 35.69/23.53 tff(3913,plain,
% 35.69/23.53 (((~![Y: $i, I0: $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)))),
% 35.72/23.53 inference(rewrite,[status(thm)],[])).
% 35.72/23.53 tff(3914,plain,
% 35.72/23.53 ((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)))),
% 35.72/23.53 inference(rewrite,[status(thm)],[])).
% 35.72/23.53 tff(3915,plain,
% 35.72/23.53 (((~![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))))),
% 35.72/23.53 inference(monotonicity,[status(thm)],[3914])).
% 35.72/23.53 tff(3916,plain,
% 35.72/23.53 (((~![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)))),
% 35.72/23.53 inference(transitivity,[status(thm)],[3915, 3913])).
% 35.72/23.53 tff(3917,plain,
% 35.72/23.53 ((~![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))),
% 35.72/23.53 inference(quant_inst,[status(thm)],[])).
% 35.72/23.53 tff(3918,plain,
% 35.72/23.53 ((~![Y: $i, I0: $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))),
% 35.72/23.53 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 35.72/23.53 tff(3919,plain,
% 35.72/23.53 (m_counter_cell_v_value(c_bit1, s22) | node1(c_bit1, s21)),
% 35.72/23.53 inference(unit_resolution,[status(thm)],[3918, 199, 3912])).
% 35.72/23.53 tff(3920,plain,
% 35.72/23.53 (m_counter_cell_v_value(c_bit1, s22)),
% 35.72/23.53 inference(unit_resolution,[status(thm)],[3919, 3908])).
% 35.72/23.53 tff(3921,assumption,(node1(c_bit1, s22)), introduced(assumption)).
% 35.72/23.53 tff(3922,plain,
% 35.72/23.53 (((~![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)))),
% 35.72/23.53 inference(rewrite,[status(thm)],[])).
% 35.72/23.53 tff(3923,plain,
% 35.72/23.53 ((~![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)))),
% 35.72/23.53 inference(quant_inst,[status(thm)],[])).
% 35.72/23.53 tff(3924,plain,
% 35.72/23.53 ((~![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))),
% 35.72/23.53 inference(modus_ponens,[status(thm)],[3923, 3922])).
% 35.72/23.53 tff(3925,plain,
% 35.72/23.53 (~node4(c_bit0, s22)),
% 35.72/23.53 inference(unit_resolution,[status(thm)],[3924, 2875, 766])).
% 35.72/23.53 tff(3926,assumption,(m_counter_cell_v_carry_out(c_bit0, s22)), introduced(assumption)).
% 35.72/23.53 tff(3927,plain,
% 35.72/23.53 (((~![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))),
% 35.72/23.53 inference(rewrite,[status(thm)],[])).
% 35.72/23.53 tff(3928,plain,
% 35.72/23.53 ((~![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))),
% 35.72/23.53 inference(quant_inst,[status(thm)],[])).
% 35.72/23.53 tff(3929,plain,
% 35.72/23.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s22)) | node4(c_bit0, s22)),
% 35.72/23.53 inference(modus_ponens,[status(thm)],[3928, 3927])).
% 35.72/23.53 tff(3930,plain,
% 35.72/23.53 ($false),
% 35.72/23.53 inference(unit_resolution,[status(thm)],[3929, 2887, 3926, 3925])).
% 35.72/23.53 tff(3931,plain,(~m_counter_cell_v_carry_out(c_bit0, s22)), inference(lemma,lemma(discharge,[]))).
% 35.72/23.53 tff(3932,assumption,(m_counter_cell_v_carry_in(c_bit1, s22)), introduced(assumption)).
% 35.72/23.53 tff(3933,assumption,(~m_counter_cell_v_carry_out(c_bit0, s22)), introduced(assumption)).
% 35.72/23.53 tff(3934,plain,
% 35.72/23.53 (((~![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))),
% 35.72/23.53 inference(rewrite,[status(thm)],[])).
% 35.72/23.53 tff(3935,plain,
% 35.72/23.53 ((~![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))),
% 35.72/23.53 inference(quant_inst,[status(thm)],[])).
% 35.72/23.53 tff(3936,plain,
% 35.72/23.53 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s22)) | m_counter_cell_v_carry_out(c_bit0, s22)),
% 35.72/23.53 inference(modus_ponens,[status(thm)],[3935, 3934])).
% 35.72/23.53 tff(3937,plain,
% 35.72/23.53 ($false),
% 35.72/23.53 inference(unit_resolution,[status(thm)],[3936, 2901, 3933, 3932])).
% 35.72/23.53 tff(3938,plain,(m_counter_cell_v_carry_out(c_bit0, s22) | (~m_counter_cell_v_carry_in(c_bit1, s22))), inference(lemma,lemma(discharge,[]))).
% 35.72/23.53 tff(3939,plain,
% 35.72/23.53 (~m_counter_cell_v_carry_in(c_bit1, s22)),
% 35.72/23.53 inference(unit_resolution,[status(thm)],[3938, 3931])).
% 35.72/23.53 tff(3940,assumption,(m_counter_cell_v_value(c_bit1, s22)), introduced(assumption)).
% 35.72/23.53 tff(3941,plain,
% 35.72/23.53 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.72/23.53 inference(rewrite,[status(thm)],[])).
% 35.72/23.53 tff(3942,plain,
% 35.72/23.53 (((~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)))),
% 35.72/23.53 inference(rewrite,[status(thm)],[])).
% 35.72/23.53 tff(3943,plain,
% 35.72/23.53 (((~![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))))),
% 35.72/23.53 inference(monotonicity,[status(thm)],[3942])).
% 35.72/23.53 tff(3944,plain,
% 35.72/23.53 (((~![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)))),
% 35.72/23.53 inference(transitivity,[status(thm)],[3943, 3941])).
% 35.72/23.53 tff(3945,plain,
% 35.72/23.53 ((~![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)))),
% 35.72/23.53 inference(quant_inst,[status(thm)],[])).
% 35.72/23.53 tff(3946,plain,
% 35.72/23.53 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22))),
% 35.72/23.53 inference(modus_ponens,[status(thm)],[3945, 3944])).
% 35.72/23.53 tff(3947,plain,
% 35.72/23.53 ($false),
% 35.72/23.53 inference(unit_resolution,[status(thm)],[3946, 3359, 3940, 3939, 3921])).
% 35.72/23.53 tff(3948,plain,((~m_counter_cell_v_value(c_bit1, s22)) | (~node1(c_bit1, s22))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.53 tff(3949,plain,
% 35.73/23.53 (~node1(c_bit1, s22)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3948, 3920])).
% 35.73/23.53 tff(3950,plain,
% 35.73/23.53 (((~![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))),
% 35.73/23.53 inference(rewrite,[status(thm)],[])).
% 35.73/23.53 tff(3951,plain,
% 35.73/23.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit1, s22, s23))),
% 35.73/23.53 inference(quant_inst,[status(thm)],[])).
% 35.73/23.53 tff(3952,plain,
% 35.73/23.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit1, s22, s23)),
% 35.73/23.53 inference(modus_ponens,[status(thm)],[3951, 3950])).
% 35.73/23.53 tff(3953,plain,
% 35.73/23.53 (node3(c_bit1, s22, s23)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3952, 81, 785])).
% 35.73/23.53 tff(3954,plain,
% 35.73/23.53 (((~![Y: $i, I0: $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)))),
% 35.73/23.53 inference(rewrite,[status(thm)],[])).
% 35.73/23.53 tff(3955,plain,
% 35.73/23.53 ((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)))),
% 35.73/23.53 inference(rewrite,[status(thm)],[])).
% 35.73/23.53 tff(3956,plain,
% 35.73/23.53 (((~![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))))),
% 35.73/23.53 inference(monotonicity,[status(thm)],[3955])).
% 35.73/23.53 tff(3957,plain,
% 35.73/23.53 (((~![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)))),
% 35.73/23.53 inference(transitivity,[status(thm)],[3956, 3954])).
% 35.73/23.53 tff(3958,plain,
% 35.73/23.53 ((~![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))),
% 35.73/23.53 inference(quant_inst,[status(thm)],[])).
% 35.73/23.53 tff(3959,plain,
% 35.73/23.53 ((~![Y: $i, I0: $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))),
% 35.73/23.53 inference(modus_ponens,[status(thm)],[3958, 3957])).
% 35.73/23.53 tff(3960,plain,
% 35.73/23.53 (m_counter_cell_v_value(c_bit1, s23) | node1(c_bit1, s22)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3959, 199, 3953])).
% 35.73/23.53 tff(3961,plain,
% 35.73/23.53 (m_counter_cell_v_value(c_bit1, s23)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3960, 3949])).
% 35.73/23.53 tff(3962,plain,
% 35.73/23.53 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.53 inference(rewrite,[status(thm)],[])).
% 35.73/23.53 tff(3963,plain,
% 35.73/23.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.53 inference(quant_inst,[status(thm)],[])).
% 35.73/23.53 tff(3964,plain,
% 35.73/23.53 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.73/23.53 inference(modus_ponens,[status(thm)],[3963, 3962])).
% 35.73/23.53 tff(3965,plain,
% 35.73/23.53 ((~m_counter_cell_v_value(c_bit0, s23)) | m_counter_cell_v_carry_out(c_bit0, s23)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3964, 3031, 801])).
% 35.73/23.53 tff(3966,plain,
% 35.73/23.53 (m_counter_cell_v_carry_out(c_bit0, s23)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3965, 797])).
% 35.73/23.53 tff(3967,plain,
% 35.73/23.53 (((~![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))),
% 35.73/23.53 inference(rewrite,[status(thm)],[])).
% 35.73/23.53 tff(3968,plain,
% 35.73/23.53 ((~![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))),
% 35.73/23.53 inference(quant_inst,[status(thm)],[])).
% 35.73/23.53 tff(3969,plain,
% 35.73/23.53 ((~![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)),
% 35.73/23.53 inference(modus_ponens,[status(thm)],[3968, 3967])).
% 35.73/23.53 tff(3970,plain,
% 35.73/23.53 (m_counter_cell_v_carry_in(c_bit1, s23)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3969, 3046, 3966])).
% 35.73/23.53 tff(3971,plain,
% 35.73/23.53 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.73/23.53 inference(rewrite,[status(thm)],[])).
% 35.73/23.53 tff(3972,plain,
% 35.73/23.53 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.73/23.53 inference(quant_inst,[status(thm)],[])).
% 35.73/23.53 tff(3973,plain,
% 35.73/23.53 ((~![I0: $i, X: $i] : ((~m_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))),
% 35.73/23.53 inference(modus_ponens,[status(thm)],[3972, 3971])).
% 35.73/23.53 tff(3974,plain,
% 35.73/23.53 ((~m_counter_cell_v_value(c_bit1, s23)) | (~node2(c_bit1, s23))),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3973, 219, 3970])).
% 35.73/23.53 tff(3975,plain,
% 35.73/23.53 (~node2(c_bit1, s23)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3974, 3961])).
% 35.73/23.53 tff(3976,plain,
% 35.73/23.53 (((~![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))),
% 35.73/23.53 inference(rewrite,[status(thm)],[])).
% 35.73/23.53 tff(3977,plain,
% 35.73/23.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit1, s23, s24))),
% 35.73/23.53 inference(quant_inst,[status(thm)],[])).
% 35.73/23.53 tff(3978,plain,
% 35.73/23.53 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit1, s23, s24)),
% 35.73/23.53 inference(modus_ponens,[status(thm)],[3977, 3976])).
% 35.73/23.53 tff(3979,plain,
% 35.73/23.53 (node3(c_bit1, s23, s24)),
% 35.73/23.53 inference(unit_resolution,[status(thm)],[3978, 81, 813])).
% 35.73/23.53 tff(3980,plain,
% 35.73/23.53 (((~![Y: $i, I0: $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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(3981,plain,
% 35.73/23.54 ((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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(3982,plain,
% 35.73/23.54 (((~![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))))),
% 35.73/23.54 inference(monotonicity,[status(thm)],[3981])).
% 35.73/23.54 tff(3983,plain,
% 35.73/23.54 (((~![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)))),
% 35.73/23.54 inference(transitivity,[status(thm)],[3982, 3980])).
% 35.73/23.54 tff(3984,plain,
% 35.73/23.54 ((~![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)))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(3985,plain,
% 35.73/23.54 ((~![Y: $i, I0: $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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[3984, 3983])).
% 35.73/23.54 tff(3986,plain,
% 35.73/23.54 ((~m_counter_cell_v_value(c_bit1, s24)) | node2(c_bit1, s23)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[3985, 234, 3979])).
% 35.73/23.54 tff(3987,plain,
% 35.73/23.54 (~m_counter_cell_v_value(c_bit1, s24)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[3986, 3975])).
% 35.73/23.54 tff(3988,plain,
% 35.73/23.54 (((~![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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(3989,plain,
% 35.73/23.54 ((~![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)))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(3990,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[3989, 3988])).
% 35.73/23.54 tff(3991,plain,
% 35.73/23.54 (~node4(c_bit0, s24)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[3990, 2875, 825])).
% 35.73/23.54 tff(3992,assumption,(m_counter_cell_v_carry_out(c_bit0, s24)), introduced(assumption)).
% 35.73/23.54 tff(3993,plain,
% 35.73/23.54 (((~![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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(3994,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(3995,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s24)) | node4(c_bit0, s24)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[3994, 3993])).
% 35.73/23.54 tff(3996,plain,
% 35.73/23.54 ($false),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[3995, 2887, 3992, 3991])).
% 35.73/23.54 tff(3997,plain,(~m_counter_cell_v_carry_out(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.54 tff(3998,assumption,(m_counter_cell_v_carry_in(c_bit1, s24)), introduced(assumption)).
% 35.73/23.54 tff(3999,assumption,(~m_counter_cell_v_carry_out(c_bit0, s24)), introduced(assumption)).
% 35.73/23.54 tff(4000,plain,
% 35.73/23.54 (((~![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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4001,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4002,plain,
% 35.73/23.54 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4001, 4000])).
% 35.73/23.54 tff(4003,plain,
% 35.73/23.54 ($false),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4002, 2901, 3999, 3998])).
% 35.73/23.54 tff(4004,plain,((~m_counter_cell_v_carry_in(c_bit1, s24)) | m_counter_cell_v_carry_out(c_bit0, s24)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.54 tff(4005,plain,
% 35.73/23.54 (~m_counter_cell_v_carry_in(c_bit1, s24)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4004, 3997])).
% 35.73/23.54 tff(4006,plain,
% 35.73/23.54 (((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4007,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4008,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : (m_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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4007, 4006])).
% 35.73/23.54 tff(4009,plain,
% 35.73/23.54 (m_counter_cell_v_value(c_bit1, s24) | (~node2(c_bit1, s24))),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4008, 3291, 4005])).
% 35.73/23.54 tff(4010,plain,
% 35.73/23.54 (~node2(c_bit1, s24)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4009, 3987])).
% 35.73/23.54 tff(4011,plain,
% 35.73/23.54 (((~![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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4012,plain,
% 35.73/23.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit1, s24, s25))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4013,plain,
% 35.73/23.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit1, s24, s25)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4012, 4011])).
% 35.73/23.54 tff(4014,plain,
% 35.73/23.54 (node3(c_bit1, s24, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4013, 81, 844])).
% 35.73/23.54 tff(4015,plain,
% 35.73/23.54 (((~![Y: $i, I0: $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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4016,plain,
% 35.73/23.54 ((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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4017,plain,
% 35.73/23.54 (((~![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))))),
% 35.73/23.54 inference(monotonicity,[status(thm)],[4016])).
% 35.73/23.54 tff(4018,plain,
% 35.73/23.54 (((~![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)))),
% 35.73/23.54 inference(transitivity,[status(thm)],[4017, 4015])).
% 35.73/23.54 tff(4019,plain,
% 35.73/23.54 ((~![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)))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4020,plain,
% 35.73/23.54 ((~![Y: $i, I0: $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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4019, 4018])).
% 35.73/23.54 tff(4021,plain,
% 35.73/23.54 ((~m_counter_cell_v_value(c_bit1, s25)) | node2(c_bit1, s24)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4020, 234, 4014])).
% 35.73/23.54 tff(4022,plain,
% 35.73/23.54 (~m_counter_cell_v_value(c_bit1, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4021, 4010])).
% 35.73/23.54 tff(4023,plain,
% 35.73/23.54 (((~![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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4024,plain,
% 35.73/23.54 ((~![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)))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4025,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4024, 4023])).
% 35.73/23.54 tff(4026,plain,
% 35.73/23.54 (~node4(c_bit0, s26)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4025, 2875, 882])).
% 35.73/23.54 tff(4027,assumption,(m_counter_cell_v_carry_out(c_bit0, s26)), introduced(assumption)).
% 35.73/23.54 tff(4028,plain,
% 35.73/23.54 (((~![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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4029,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4030,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s26)) | node4(c_bit0, s26)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 35.73/23.54 tff(4031,plain,
% 35.73/23.54 ($false),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4030, 2887, 4027, 4026])).
% 35.73/23.54 tff(4032,plain,(~m_counter_cell_v_carry_out(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.54 tff(4033,assumption,(~m_counter_cell_v_carry_out(c_bit0, s26)), introduced(assumption)).
% 35.73/23.54 tff(4034,assumption,(m_counter_cell_v_carry_in(c_bit1, s26)), introduced(assumption)).
% 35.73/23.54 tff(4035,plain,
% 35.73/23.54 (((~![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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4036,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4037,plain,
% 35.73/23.54 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 35.73/23.54 tff(4038,plain,
% 35.73/23.54 ($false),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4037, 2901, 4033, 4034])).
% 35.73/23.54 tff(4039,plain,((~m_counter_cell_v_carry_in(c_bit1, s26)) | m_counter_cell_v_carry_out(c_bit0, s26)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.54 tff(4040,plain,
% 35.73/23.54 (~m_counter_cell_v_carry_in(c_bit1, s26)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4039, 4033])).
% 35.73/23.54 tff(4041,assumption,(node1(c_bit1, s26)), introduced(assumption)).
% 35.73/23.54 tff(4042,plain,
% 35.73/23.54 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4043,plain,
% 35.73/23.54 (((~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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4044,plain,
% 35.73/23.54 (((~![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))))),
% 35.73/23.54 inference(monotonicity,[status(thm)],[4043])).
% 35.73/23.54 tff(4045,plain,
% 35.73/23.54 (((~![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)))),
% 35.73/23.54 inference(transitivity,[status(thm)],[4044, 4042])).
% 35.73/23.54 tff(4046,plain,
% 35.73/23.54 ((~![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)))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4047,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4046, 4045])).
% 35.73/23.54 tff(4048,plain,
% 35.73/23.54 (m_counter_cell_v_carry_in(c_bit1, s26) | (~m_counter_cell_v_value(c_bit1, s26))),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4047, 3359, 4041])).
% 35.73/23.54 tff(4049,plain,
% 35.73/23.54 (~m_counter_cell_v_value(c_bit1, s26)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4048, 4040])).
% 35.73/23.54 tff(4050,plain,
% 35.73/23.54 (((~![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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4051,plain,
% 35.73/23.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit1, s25, s26))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4052,plain,
% 35.73/23.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit1, s25, s26)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4051, 4050])).
% 35.73/23.54 tff(4053,plain,
% 35.73/23.54 (node3(c_bit1, s25, s26)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4052, 81, 870])).
% 35.73/23.54 tff(4054,plain,
% 35.73/23.54 (((~![Y: $i, I0: $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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4055,plain,
% 35.73/23.54 ((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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4056,plain,
% 35.73/23.54 (((~![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))))),
% 35.73/23.54 inference(monotonicity,[status(thm)],[4055])).
% 35.73/23.54 tff(4057,plain,
% 35.73/23.54 (((~![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)))),
% 35.73/23.54 inference(transitivity,[status(thm)],[4056, 4054])).
% 35.73/23.54 tff(4058,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4059,plain,
% 35.73/23.54 ((~![Y: $i, I0: $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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4058, 4057])).
% 35.73/23.54 tff(4060,plain,
% 35.73/23.54 (m_counter_cell_v_value(c_bit1, s26) | node1(c_bit1, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4059, 199, 4053])).
% 35.73/23.54 tff(4061,plain,
% 35.73/23.54 (node1(c_bit1, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4060, 4049])).
% 35.73/23.54 tff(4062,assumption,(~m_counter_cell_v_value(c_bit1, s25)), introduced(assumption)).
% 35.73/23.54 tff(4063,plain,
% 35.73/23.54 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4064,plain,
% 35.73/23.54 (((~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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4065,plain,
% 35.73/23.54 (((~![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))))),
% 35.73/23.54 inference(monotonicity,[status(thm)],[4064])).
% 35.73/23.54 tff(4066,plain,
% 35.73/23.54 (((~![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)))),
% 35.73/23.54 inference(transitivity,[status(thm)],[4065, 4063])).
% 35.73/23.54 tff(4067,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4068,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4067, 4066])).
% 35.73/23.54 tff(4069,plain,
% 35.73/23.54 ((~m_counter_cell_v_carry_in(c_bit1, s25)) | (~node1(c_bit1, s25))),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4068, 170, 4062])).
% 35.73/23.54 tff(4070,plain,
% 35.73/23.54 (~m_counter_cell_v_carry_in(c_bit1, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4069, 4061])).
% 35.73/23.54 tff(4071,plain,
% 35.73/23.54 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s26)) | (~m_counter_cell_v_value(c_bit0, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s26)) | (~m_counter_cell_v_value(c_bit0, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4072,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s26)) | (~m_counter_cell_v_value(c_bit0, s26)) | m_counter_cell_v_carry_out(c_bit0, s26))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4073,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s26)) | (~m_counter_cell_v_value(c_bit0, s26)) | m_counter_cell_v_carry_out(c_bit0, s26)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4072, 4071])).
% 35.73/23.54 tff(4074,plain,
% 35.73/23.54 ((~m_counter_cell_v_value(c_bit0, s26)) | m_counter_cell_v_carry_out(c_bit0, s26)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4073, 3031, 886])).
% 35.73/23.54 tff(4075,plain,
% 35.73/23.54 (~m_counter_cell_v_value(c_bit0, s26)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4074, 4033])).
% 35.73/23.54 tff(4076,plain,
% 35.73/23.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s26) | node1(c_bit0, s25) | (~node3(c_bit0, 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_bit0, s26) | node1(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4077,plain,
% 35.73/23.54 ((node1(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | m_counter_cell_v_value(c_bit0, s26)) <=> (m_counter_cell_v_value(c_bit0, s26) | node1(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4078,plain,
% 35.73/23.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | m_counter_cell_v_value(c_bit0, 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_bit0, s26) | node1(c_bit0, s25) | (~node3(c_bit0, s25, s26))))),
% 35.73/23.54 inference(monotonicity,[status(thm)],[4077])).
% 35.73/23.54 tff(4079,plain,
% 35.73/23.54 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | m_counter_cell_v_value(c_bit0, 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_bit0, s26) | node1(c_bit0, s25) | (~node3(c_bit0, s25, s26)))),
% 35.73/23.54 inference(transitivity,[status(thm)],[4078, 4076])).
% 35.73/23.54 tff(4080,plain,
% 35.73/23.54 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s25) | (~node3(c_bit0, s25, s26)) | m_counter_cell_v_value(c_bit0, s26))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4081,plain,
% 35.73/23.54 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s26) | node1(c_bit0, s25) | (~node3(c_bit0, s25, s26))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4080, 4079])).
% 35.73/23.54 tff(4082,plain,
% 35.73/23.54 (m_counter_cell_v_value(c_bit0, s26) | node1(c_bit0, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4081, 199, 874])).
% 35.73/23.54 tff(4083,plain,
% 35.73/23.54 (node1(c_bit0, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4082, 4075])).
% 35.73/23.54 tff(4084,plain,
% 35.73/23.54 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s25)) | m_counter_cell_v_value(c_bit0, s25) | (~node1(c_bit0, 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_bit0, s25)) | m_counter_cell_v_value(c_bit0, s25) | (~node1(c_bit0, s25)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4085,plain,
% 35.73/23.54 (((~node1(c_bit0, s25)) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | m_counter_cell_v_value(c_bit0, s25)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s25)) | m_counter_cell_v_value(c_bit0, s25) | (~node1(c_bit0, s25)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4086,plain,
% 35.73/23.54 (((~![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, s25)) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | m_counter_cell_v_value(c_bit0, 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_bit0, s25)) | m_counter_cell_v_value(c_bit0, s25) | (~node1(c_bit0, s25))))),
% 35.73/23.54 inference(monotonicity,[status(thm)],[4085])).
% 35.73/23.54 tff(4087,plain,
% 35.73/23.54 (((~![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, s25)) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | m_counter_cell_v_value(c_bit0, 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_bit0, s25)) | m_counter_cell_v_value(c_bit0, s25) | (~node1(c_bit0, s25)))),
% 35.73/23.54 inference(transitivity,[status(thm)],[4086, 4084])).
% 35.73/23.54 tff(4088,plain,
% 35.73/23.54 ((~![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, s25)) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | m_counter_cell_v_value(c_bit0, s25))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4089,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s25)) | m_counter_cell_v_value(c_bit0, s25) | (~node1(c_bit0, s25))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4088, 4087])).
% 35.73/23.54 tff(4090,plain,
% 35.73/23.54 (m_counter_cell_v_value(c_bit0, s25) | (~node1(c_bit0, s25))),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4089, 170, 858])).
% 35.73/23.54 tff(4091,plain,
% 35.73/23.54 (m_counter_cell_v_value(c_bit0, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4090, 4083])).
% 35.73/23.54 tff(4092,plain,
% 35.73/23.54 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4093,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4094,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4093, 4092])).
% 35.73/23.54 tff(4095,plain,
% 35.73/23.54 ((~m_counter_cell_v_value(c_bit0, s25)) | m_counter_cell_v_carry_out(c_bit0, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4094, 3031, 858])).
% 35.73/23.54 tff(4096,plain,
% 35.73/23.54 (m_counter_cell_v_carry_out(c_bit0, s25)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4095, 4091])).
% 35.73/23.54 tff(4097,plain,
% 35.73/23.54 (((~![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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4098,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4099,plain,
% 35.73/23.54 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s25)) | m_counter_cell_v_carry_in(c_bit1, s25)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4098, 4097])).
% 35.73/23.54 tff(4100,plain,
% 35.73/23.54 ($false),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4099, 3046, 4096, 4070])).
% 35.73/23.54 tff(4101,plain,(m_counter_cell_v_carry_out(c_bit0, s26) | m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s26))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.54 tff(4102,plain,
% 35.73/23.54 (m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s26))),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4101, 4032])).
% 35.73/23.54 tff(4103,plain,
% 35.73/23.54 (~node1(c_bit1, s26)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4102, 4022])).
% 35.73/23.54 tff(4104,plain,
% 35.73/23.54 (((~![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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4105,plain,
% 35.73/23.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit1, s26, s27))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4106,plain,
% 35.73/23.54 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit1, s26, s27)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4105, 4104])).
% 35.73/23.54 tff(4107,plain,
% 35.73/23.54 (node3(c_bit1, s26, s27)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4106, 81, 901])).
% 35.73/23.54 tff(4108,plain,
% 35.73/23.54 (((~![Y: $i, I0: $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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4109,plain,
% 35.73/23.54 ((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)))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4110,plain,
% 35.73/23.54 (((~![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))))),
% 35.73/23.54 inference(monotonicity,[status(thm)],[4109])).
% 35.73/23.54 tff(4111,plain,
% 35.73/23.54 (((~![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)))),
% 35.73/23.54 inference(transitivity,[status(thm)],[4110, 4108])).
% 35.73/23.54 tff(4112,plain,
% 35.73/23.54 ((~![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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4113,plain,
% 35.73/23.54 ((~![Y: $i, I0: $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))),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4112, 4111])).
% 35.73/23.54 tff(4114,plain,
% 35.73/23.54 (m_counter_cell_v_value(c_bit1, s27) | node1(c_bit1, s26)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4113, 199, 4107])).
% 35.73/23.54 tff(4115,plain,
% 35.73/23.54 (m_counter_cell_v_value(c_bit1, s27)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4114, 4103])).
% 35.73/23.54 tff(4116,assumption,(node2(c_bit1, s27)), introduced(assumption)).
% 35.73/23.54 tff(4117,plain,
% 35.73/23.54 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.54 inference(rewrite,[status(thm)],[])).
% 35.73/23.54 tff(4118,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.54 inference(quant_inst,[status(thm)],[])).
% 35.73/23.54 tff(4119,plain,
% 35.73/23.54 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.73/23.54 inference(modus_ponens,[status(thm)],[4118, 4117])).
% 35.73/23.54 tff(4120,plain,
% 35.73/23.54 ((~m_counter_cell_v_value(c_bit0, s27)) | m_counter_cell_v_carry_out(c_bit0, s27)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4119, 3031, 917])).
% 35.73/23.54 tff(4121,plain,
% 35.73/23.54 (m_counter_cell_v_carry_out(c_bit0, s27)),
% 35.73/23.54 inference(unit_resolution,[status(thm)],[4120, 913])).
% 35.73/23.55 tff(4122,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4123,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4124,plain,
% 35.73/23.55 ((~![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)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4123, 4122])).
% 35.73/23.55 tff(4125,plain,
% 35.73/23.55 (m_counter_cell_v_carry_in(c_bit1, s27)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4124, 3046, 4121])).
% 35.73/23.55 tff(4126,assumption,(m_counter_cell_v_value(c_bit1, s27)), introduced(assumption)).
% 35.73/23.55 tff(4127,plain,
% 35.73/23.55 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4128,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4129,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | (~node2(c_bit1, s27))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4128, 4127])).
% 35.73/23.55 tff(4130,plain,
% 35.73/23.55 ($false),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4129, 219, 4126, 4125, 4116])).
% 35.73/23.55 tff(4131,plain,((~node2(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.55 tff(4132,plain,
% 35.73/23.55 (~node2(c_bit1, s27)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4131, 4115])).
% 35.73/23.55 tff(4133,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4134,plain,
% 35.73/23.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit1, s27, s28))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4135,plain,
% 35.73/23.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit1, s27, s28)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4134, 4133])).
% 35.73/23.55 tff(4136,plain,
% 35.73/23.55 (node3(c_bit1, s27, s28)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4135, 81, 929])).
% 35.73/23.55 tff(4137,plain,
% 35.73/23.55 (((~![Y: $i, I0: $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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4138,plain,
% 35.73/23.55 ((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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4139,plain,
% 35.73/23.55 (((~![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))))),
% 35.73/23.55 inference(monotonicity,[status(thm)],[4138])).
% 35.73/23.55 tff(4140,plain,
% 35.73/23.55 (((~![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)))),
% 35.73/23.55 inference(transitivity,[status(thm)],[4139, 4137])).
% 35.73/23.55 tff(4141,plain,
% 35.73/23.55 ((~![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)))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4142,plain,
% 35.73/23.55 ((~![Y: $i, I0: $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))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4141, 4140])).
% 35.73/23.55 tff(4143,plain,
% 35.73/23.55 ((~m_counter_cell_v_value(c_bit1, s28)) | node2(c_bit1, s27)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4142, 234, 4136])).
% 35.73/23.55 tff(4144,plain,
% 35.73/23.55 (~m_counter_cell_v_value(c_bit1, s28)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4143, 4132])).
% 35.73/23.55 tff(4145,plain,
% 35.73/23.55 (((~![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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4146,plain,
% 35.73/23.55 ((~![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)))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4147,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4146, 4145])).
% 35.73/23.55 tff(4148,plain,
% 35.73/23.55 (~node4(c_bit0, s28)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4147, 2875, 941])).
% 35.73/23.55 tff(4149,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4150,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4151,plain,
% 35.73/23.55 ((~![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)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4150, 4149])).
% 35.73/23.55 tff(4152,plain,
% 35.73/23.55 (~m_counter_cell_v_carry_out(c_bit0, s28)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4151, 2887, 4148])).
% 35.73/23.55 tff(4153,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4154,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4155,plain,
% 35.73/23.55 ((~![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)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4154, 4153])).
% 35.73/23.55 tff(4156,plain,
% 35.73/23.55 (~m_counter_cell_v_carry_in(c_bit1, s28)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4155, 2901, 4152])).
% 35.73/23.55 tff(4157,plain,
% 35.73/23.55 (((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4158,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4159,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : (m_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))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4158, 4157])).
% 35.73/23.55 tff(4160,plain,
% 35.73/23.55 (m_counter_cell_v_value(c_bit1, s28) | (~node2(c_bit1, s28))),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4159, 3291, 4156])).
% 35.73/23.55 tff(4161,plain,
% 35.73/23.55 (~node2(c_bit1, s28)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4160, 4144])).
% 35.73/23.55 tff(4162,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4163,plain,
% 35.73/23.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit1, s28, s29))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4164,plain,
% 35.73/23.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit1, s28, s29)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4163, 4162])).
% 35.73/23.55 tff(4165,plain,
% 35.73/23.55 (node3(c_bit1, s28, s29)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4164, 81, 958])).
% 35.73/23.55 tff(4166,plain,
% 35.73/23.55 (((~![Y: $i, I0: $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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4167,plain,
% 35.73/23.55 ((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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4168,plain,
% 35.73/23.55 (((~![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))))),
% 35.73/23.55 inference(monotonicity,[status(thm)],[4167])).
% 35.73/23.55 tff(4169,plain,
% 35.73/23.55 (((~![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)))),
% 35.73/23.55 inference(transitivity,[status(thm)],[4168, 4166])).
% 35.73/23.55 tff(4170,plain,
% 35.73/23.55 ((~![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)))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4171,plain,
% 35.73/23.55 ((~![Y: $i, I0: $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))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4170, 4169])).
% 35.73/23.55 tff(4172,plain,
% 35.73/23.55 ((~m_counter_cell_v_value(c_bit1, s29)) | node2(c_bit1, s28)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4171, 234, 4165])).
% 35.73/23.55 tff(4173,plain,
% 35.73/23.55 (~m_counter_cell_v_value(c_bit1, s29)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4172, 4161])).
% 35.73/23.55 tff(4174,plain,
% 35.73/23.55 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4175,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4176,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4175, 4174])).
% 35.73/23.55 tff(4177,plain,
% 35.73/23.55 ((~m_counter_cell_v_value(c_bit0, s29)) | m_counter_cell_v_carry_out(c_bit0, s29)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4176, 3031, 974])).
% 35.73/23.55 tff(4178,plain,
% 35.73/23.55 (m_counter_cell_v_carry_out(c_bit0, s29)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4177, 970])).
% 35.73/23.55 tff(4179,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4180,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4181,plain,
% 35.73/23.55 ((~![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)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4180, 4179])).
% 35.73/23.55 tff(4182,plain,
% 35.73/23.55 (m_counter_cell_v_carry_in(c_bit1, s29)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4181, 3046, 4178])).
% 35.73/23.55 tff(4183,assumption,(node1(c_bit1, s29)), introduced(assumption)).
% 35.73/23.55 tff(4184,assumption,(~m_counter_cell_v_value(c_bit1, s29)), introduced(assumption)).
% 35.73/23.55 tff(4185,plain,
% 35.73/23.55 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4186,plain,
% 35.73/23.55 (((~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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4187,plain,
% 35.73/23.55 (((~![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))))),
% 35.73/23.55 inference(monotonicity,[status(thm)],[4186])).
% 35.73/23.55 tff(4188,plain,
% 35.73/23.55 (((~![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)))),
% 35.73/23.55 inference(transitivity,[status(thm)],[4187, 4185])).
% 35.73/23.55 tff(4189,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4190,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29) | (~node1(c_bit1, s29))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4189, 4188])).
% 35.73/23.55 tff(4191,plain,
% 35.73/23.55 ($false),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4190, 170, 4184, 4183, 4182])).
% 35.73/23.55 tff(4192,plain,((~node1(c_bit1, s29)) | m_counter_cell_v_value(c_bit1, s29)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.55 tff(4193,plain,
% 35.73/23.55 (~node1(c_bit1, s29)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4192, 4173])).
% 35.73/23.55 tff(4194,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4195,plain,
% 35.73/23.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit1, s29, s30))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4196,plain,
% 35.73/23.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit1, s29, s30)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4195, 4194])).
% 35.73/23.55 tff(4197,plain,
% 35.73/23.55 (node3(c_bit1, s29, s30)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4196, 81, 986])).
% 35.73/23.55 tff(4198,plain,
% 35.73/23.55 (((~![Y: $i, I0: $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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4199,plain,
% 35.73/23.55 ((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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4200,plain,
% 35.73/23.55 (((~![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))))),
% 35.73/23.55 inference(monotonicity,[status(thm)],[4199])).
% 35.73/23.55 tff(4201,plain,
% 35.73/23.55 (((~![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)))),
% 35.73/23.55 inference(transitivity,[status(thm)],[4200, 4198])).
% 35.73/23.55 tff(4202,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4203,plain,
% 35.73/23.55 ((~![Y: $i, I0: $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))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4202, 4201])).
% 35.73/23.55 tff(4204,plain,
% 35.73/23.55 (m_counter_cell_v_value(c_bit1, s30) | node1(c_bit1, s29)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4203, 199, 4197])).
% 35.73/23.55 tff(4205,plain,
% 35.73/23.55 (m_counter_cell_v_value(c_bit1, s30)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4204, 4193])).
% 35.73/23.55 tff(4206,plain,
% 35.73/23.55 (((~![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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4207,plain,
% 35.73/23.55 ((~![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)))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4208,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4207, 4206])).
% 35.73/23.55 tff(4209,plain,
% 35.73/23.55 (~node4(c_bit0, s30)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4208, 2875, 998])).
% 35.73/23.55 tff(4210,assumption,(m_counter_cell_v_carry_out(c_bit0, s30)), introduced(assumption)).
% 35.73/23.55 tff(4211,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4212,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4213,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s30)) | node4(c_bit0, s30)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4212, 4211])).
% 35.73/23.55 tff(4214,plain,
% 35.73/23.55 ($false),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4213, 2887, 4210, 4209])).
% 35.73/23.55 tff(4215,plain,(~m_counter_cell_v_carry_out(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.55 tff(4216,assumption,(m_counter_cell_v_carry_in(c_bit1, s30)), introduced(assumption)).
% 35.73/23.55 tff(4217,assumption,(~m_counter_cell_v_carry_out(c_bit0, s30)), introduced(assumption)).
% 35.73/23.55 tff(4218,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4219,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4220,plain,
% 35.73/23.55 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4219, 4218])).
% 35.73/23.55 tff(4221,plain,
% 35.73/23.55 ($false),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4220, 2901, 4217, 4216])).
% 35.73/23.55 tff(4222,plain,((~m_counter_cell_v_carry_in(c_bit1, s30)) | m_counter_cell_v_carry_out(c_bit0, s30)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.55 tff(4223,plain,
% 35.73/23.55 (~m_counter_cell_v_carry_in(c_bit1, s30)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4222, 4215])).
% 35.73/23.55 tff(4224,plain,
% 35.73/23.55 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4225,plain,
% 35.73/23.55 (((~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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4226,plain,
% 35.73/23.55 (((~![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))))),
% 35.73/23.55 inference(monotonicity,[status(thm)],[4225])).
% 35.73/23.55 tff(4227,plain,
% 35.73/23.55 (((~![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)))),
% 35.73/23.55 inference(transitivity,[status(thm)],[4226, 4224])).
% 35.73/23.55 tff(4228,plain,
% 35.73/23.55 ((~![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)))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4229,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4228, 4227])).
% 35.73/23.55 tff(4230,plain,
% 35.73/23.55 ((~m_counter_cell_v_value(c_bit1, s30)) | (~node1(c_bit1, s30))),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4229, 3359, 4223])).
% 35.73/23.55 tff(4231,plain,
% 35.73/23.55 (~node1(c_bit1, s30)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4230, 4205])).
% 35.73/23.55 tff(4232,plain,
% 35.73/23.55 (((~![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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4233,plain,
% 35.73/23.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit1, s30, s31))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4234,plain,
% 35.73/23.55 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit1, s30, s31)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4233, 4232])).
% 35.73/23.55 tff(4235,plain,
% 35.73/23.55 (node3(c_bit1, s30, s31)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4234, 81, 1017])).
% 35.73/23.55 tff(4236,plain,
% 35.73/23.55 (((~![Y: $i, I0: $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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4237,plain,
% 35.73/23.55 ((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)))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4238,plain,
% 35.73/23.55 (((~![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))))),
% 35.73/23.55 inference(monotonicity,[status(thm)],[4237])).
% 35.73/23.55 tff(4239,plain,
% 35.73/23.55 (((~![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)))),
% 35.73/23.55 inference(transitivity,[status(thm)],[4238, 4236])).
% 35.73/23.55 tff(4240,plain,
% 35.73/23.55 ((~![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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4241,plain,
% 35.73/23.55 ((~![Y: $i, I0: $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))),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4240, 4239])).
% 35.73/23.55 tff(4242,plain,
% 35.73/23.55 (m_counter_cell_v_value(c_bit1, s31) | node1(c_bit1, s30)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4241, 199, 4235])).
% 35.73/23.55 tff(4243,plain,
% 35.73/23.55 (m_counter_cell_v_value(c_bit1, s31)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4242, 4231])).
% 35.73/23.55 tff(4244,plain,
% 35.73/23.55 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.55 inference(rewrite,[status(thm)],[])).
% 35.73/23.55 tff(4245,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.55 inference(quant_inst,[status(thm)],[])).
% 35.73/23.55 tff(4246,plain,
% 35.73/23.55 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.73/23.55 inference(modus_ponens,[status(thm)],[4245, 4244])).
% 35.73/23.55 tff(4247,plain,
% 35.73/23.55 ((~m_counter_cell_v_value(c_bit0, s31)) | m_counter_cell_v_carry_out(c_bit0, s31)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4246, 3031, 1033])).
% 35.73/23.55 tff(4248,plain,
% 35.73/23.55 (m_counter_cell_v_carry_out(c_bit0, s31)),
% 35.73/23.55 inference(unit_resolution,[status(thm)],[4247, 1029])).
% 35.73/23.56 tff(4249,assumption,(~m_counter_cell_v_carry_in(c_bit1, s31)), introduced(assumption)).
% 35.73/23.56 tff(4250,assumption,(m_counter_cell_v_carry_out(c_bit0, s31)), introduced(assumption)).
% 35.73/23.56 tff(4251,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4252,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4253,plain,
% 35.73/23.56 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4252, 4251])).
% 35.73/23.56 tff(4254,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4253, 3046, 4250, 4249])).
% 35.73/23.56 tff(4255,plain,((~m_counter_cell_v_carry_out(c_bit0, s31)) | m_counter_cell_v_carry_in(c_bit1, s31)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4256,plain,
% 35.73/23.56 (m_counter_cell_v_carry_in(c_bit1, s31)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4255, 4248])).
% 35.73/23.56 tff(4257,assumption,(m_counter_cell_v_value(c_bit1, s31)), introduced(assumption)).
% 35.73/23.56 tff(4258,assumption,(node2(c_bit1, s31)), introduced(assumption)).
% 35.73/23.56 tff(4259,plain,
% 35.73/23.56 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4260,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4261,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | (~node2(c_bit1, s31))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4260, 4259])).
% 35.73/23.56 tff(4262,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4261, 219, 4258, 4257, 4256])).
% 35.73/23.56 tff(4263,plain,((~node2(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4264,plain,
% 35.73/23.56 (~node2(c_bit1, s31)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4263, 4243])).
% 35.73/23.56 tff(4265,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4266,plain,
% 35.73/23.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit1, s31, s32))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4267,plain,
% 35.73/23.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit1, s31, s32)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4266, 4265])).
% 35.73/23.56 tff(4268,plain,
% 35.73/23.56 (node3(c_bit1, s31, s32)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4267, 81, 1045])).
% 35.73/23.56 tff(4269,plain,
% 35.73/23.56 (((~![Y: $i, I0: $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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4270,plain,
% 35.73/23.56 ((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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4271,plain,
% 35.73/23.56 (((~![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))))),
% 35.73/23.56 inference(monotonicity,[status(thm)],[4270])).
% 35.73/23.56 tff(4272,plain,
% 35.73/23.56 (((~![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)))),
% 35.73/23.56 inference(transitivity,[status(thm)],[4271, 4269])).
% 35.73/23.56 tff(4273,plain,
% 35.73/23.56 ((~![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)))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4274,plain,
% 35.73/23.56 ((~![Y: $i, I0: $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))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4273, 4272])).
% 35.73/23.56 tff(4275,plain,
% 35.73/23.56 ((~m_counter_cell_v_value(c_bit1, s32)) | node2(c_bit1, s31)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4274, 234, 4268])).
% 35.73/23.56 tff(4276,plain,
% 35.73/23.56 (~m_counter_cell_v_value(c_bit1, s32)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4275, 4264])).
% 35.73/23.56 tff(4277,plain,
% 35.73/23.56 (((~![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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4278,plain,
% 35.73/23.56 ((~![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)))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4279,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4278, 4277])).
% 35.73/23.56 tff(4280,plain,
% 35.73/23.56 (~node4(c_bit0, s32)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4279, 2875, 1057])).
% 35.73/23.56 tff(4281,assumption,(m_counter_cell_v_carry_out(c_bit0, s32)), introduced(assumption)).
% 35.73/23.56 tff(4282,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4283,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4284,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s32)) | node4(c_bit0, s32)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4283, 4282])).
% 35.73/23.56 tff(4285,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4284, 2887, 4281, 4280])).
% 35.73/23.56 tff(4286,plain,(~m_counter_cell_v_carry_out(c_bit0, s32)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4287,assumption,(m_counter_cell_v_carry_in(c_bit1, s32)), introduced(assumption)).
% 35.73/23.56 tff(4288,assumption,(~m_counter_cell_v_carry_out(c_bit0, s32)), introduced(assumption)).
% 35.73/23.56 tff(4289,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4290,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4291,plain,
% 35.73/23.56 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s32)) | m_counter_cell_v_carry_out(c_bit0, s32)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4290, 4289])).
% 35.73/23.56 tff(4292,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4291, 2901, 4288, 4287])).
% 35.73/23.56 tff(4293,plain,(m_counter_cell_v_carry_out(c_bit0, s32) | (~m_counter_cell_v_carry_in(c_bit1, s32))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4294,plain,
% 35.73/23.56 (~m_counter_cell_v_carry_in(c_bit1, s32)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4293, 4286])).
% 35.73/23.56 tff(4295,assumption,(~m_counter_cell_v_value(c_bit1, s32)), introduced(assumption)).
% 35.73/23.56 tff(4296,assumption,(node2(c_bit1, s32)), introduced(assumption)).
% 35.73/23.56 tff(4297,plain,
% 35.73/23.56 (((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4298,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4299,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s32) | m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4298, 4297])).
% 35.73/23.56 tff(4300,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4299, 3291, 4296, 4295, 4294])).
% 35.73/23.56 tff(4301,plain,(m_counter_cell_v_value(c_bit1, s32) | (~node2(c_bit1, s32))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4302,plain,
% 35.73/23.56 (~node2(c_bit1, s32)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4301, 4276])).
% 35.73/23.56 tff(4303,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4304,plain,
% 35.73/23.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit1, s32, s33))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4305,plain,
% 35.73/23.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit1, s32, s33)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4304, 4303])).
% 35.73/23.56 tff(4306,plain,
% 35.73/23.56 (node3(c_bit1, s32, s33)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4305, 81, 1076])).
% 35.73/23.56 tff(4307,plain,
% 35.73/23.56 (((~![Y: $i, I0: $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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4308,plain,
% 35.73/23.56 ((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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4309,plain,
% 35.73/23.56 (((~![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))))),
% 35.73/23.56 inference(monotonicity,[status(thm)],[4308])).
% 35.73/23.56 tff(4310,plain,
% 35.73/23.56 (((~![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)))),
% 35.73/23.56 inference(transitivity,[status(thm)],[4309, 4307])).
% 35.73/23.56 tff(4311,plain,
% 35.73/23.56 ((~![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)))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4312,plain,
% 35.73/23.56 ((~![Y: $i, I0: $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))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4311, 4310])).
% 35.73/23.56 tff(4313,plain,
% 35.73/23.56 ((~m_counter_cell_v_value(c_bit1, s33)) | node2(c_bit1, s32)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4312, 234, 4306])).
% 35.73/23.56 tff(4314,plain,
% 35.73/23.56 (~m_counter_cell_v_value(c_bit1, s33)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4313, 4302])).
% 35.73/23.56 tff(4315,plain,
% 35.73/23.56 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4316,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4317,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4316, 4315])).
% 35.73/23.56 tff(4318,plain,
% 35.73/23.56 ((~m_counter_cell_v_value(c_bit0, s33)) | m_counter_cell_v_carry_out(c_bit0, s33)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4317, 3031, 1092])).
% 35.73/23.56 tff(4319,plain,
% 35.73/23.56 (m_counter_cell_v_carry_out(c_bit0, s33)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4318, 1088])).
% 35.73/23.56 tff(4320,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4321,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4322,plain,
% 35.73/23.56 ((~![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)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4321, 4320])).
% 35.73/23.56 tff(4323,plain,
% 35.73/23.56 (m_counter_cell_v_carry_in(c_bit1, s33)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4322, 3046, 4319])).
% 35.73/23.56 tff(4324,assumption,(m_counter_cell_v_carry_in(c_bit1, s33)), introduced(assumption)).
% 35.73/23.56 tff(4325,assumption,(node1(c_bit1, s33)), introduced(assumption)).
% 35.73/23.56 tff(4326,assumption,(~m_counter_cell_v_value(c_bit1, s33)), introduced(assumption)).
% 35.73/23.56 tff(4327,plain,
% 35.73/23.56 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4328,plain,
% 35.73/23.56 (((~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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4329,plain,
% 35.73/23.56 (((~![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))))),
% 35.73/23.56 inference(monotonicity,[status(thm)],[4328])).
% 35.73/23.56 tff(4330,plain,
% 35.73/23.56 (((~![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)))),
% 35.73/23.56 inference(transitivity,[status(thm)],[4329, 4327])).
% 35.73/23.56 tff(4331,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4332,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~node1(c_bit1, s33))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4331, 4330])).
% 35.73/23.56 tff(4333,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4332, 170, 4326, 4325, 4324])).
% 35.73/23.56 tff(4334,plain,((~node1(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33) | (~m_counter_cell_v_carry_in(c_bit1, s33))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4335,plain,
% 35.73/23.56 ((~node1(c_bit1, s33)) | m_counter_cell_v_value(c_bit1, s33)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4334, 4323])).
% 35.73/23.56 tff(4336,plain,
% 35.73/23.56 (~node1(c_bit1, s33)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4335, 4314])).
% 35.73/23.56 tff(4337,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4338,plain,
% 35.73/23.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit1, s33, s34))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4339,plain,
% 35.73/23.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit1, s33, s34)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4338, 4337])).
% 35.73/23.56 tff(4340,plain,
% 35.73/23.56 (node3(c_bit1, s33, s34)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4339, 81, 1104])).
% 35.73/23.56 tff(4341,plain,
% 35.73/23.56 (((~![Y: $i, I0: $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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4342,plain,
% 35.73/23.56 ((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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4343,plain,
% 35.73/23.56 (((~![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))))),
% 35.73/23.56 inference(monotonicity,[status(thm)],[4342])).
% 35.73/23.56 tff(4344,plain,
% 35.73/23.56 (((~![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)))),
% 35.73/23.56 inference(transitivity,[status(thm)],[4343, 4341])).
% 35.73/23.56 tff(4345,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4346,plain,
% 35.73/23.56 ((~![Y: $i, I0: $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))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4345, 4344])).
% 35.73/23.56 tff(4347,plain,
% 35.73/23.56 (m_counter_cell_v_value(c_bit1, s34) | node1(c_bit1, s33)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4346, 199, 4340])).
% 35.73/23.56 tff(4348,plain,
% 35.73/23.56 (m_counter_cell_v_value(c_bit1, s34)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4347, 4336])).
% 35.73/23.56 tff(4349,plain,
% 35.73/23.56 (((~![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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4350,plain,
% 35.73/23.56 ((~![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)))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4351,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4350, 4349])).
% 35.73/23.56 tff(4352,plain,
% 35.73/23.56 (~node4(c_bit0, s34)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4351, 2875, 1116])).
% 35.73/23.56 tff(4353,assumption,(m_counter_cell_v_carry_out(c_bit0, s34)), introduced(assumption)).
% 35.73/23.56 tff(4354,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4355,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4356,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s34)) | node4(c_bit0, s34)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4355, 4354])).
% 35.73/23.56 tff(4357,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4356, 2887, 4353, 4352])).
% 35.73/23.56 tff(4358,plain,(~m_counter_cell_v_carry_out(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4359,assumption,(m_counter_cell_v_carry_in(c_bit1, s34)), introduced(assumption)).
% 35.73/23.56 tff(4360,assumption,(~m_counter_cell_v_carry_out(c_bit0, s34)), introduced(assumption)).
% 35.73/23.56 tff(4361,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4362,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4363,plain,
% 35.73/23.56 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4362, 4361])).
% 35.73/23.56 tff(4364,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4363, 2901, 4360, 4359])).
% 35.73/23.56 tff(4365,plain,((~m_counter_cell_v_carry_in(c_bit1, s34)) | m_counter_cell_v_carry_out(c_bit0, s34)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4366,plain,
% 35.73/23.56 (~m_counter_cell_v_carry_in(c_bit1, s34)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4365, 4358])).
% 35.73/23.56 tff(4367,plain,
% 35.73/23.56 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4368,plain,
% 35.73/23.56 (((~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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4369,plain,
% 35.73/23.56 (((~![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))))),
% 35.73/23.56 inference(monotonicity,[status(thm)],[4368])).
% 35.73/23.56 tff(4370,plain,
% 35.73/23.56 (((~![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)))),
% 35.73/23.56 inference(transitivity,[status(thm)],[4369, 4367])).
% 35.73/23.56 tff(4371,plain,
% 35.73/23.56 ((~![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)))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4372,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4371, 4370])).
% 35.73/23.56 tff(4373,plain,
% 35.73/23.56 ((~m_counter_cell_v_value(c_bit1, s34)) | (~node1(c_bit1, s34))),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4372, 3359, 4366])).
% 35.73/23.56 tff(4374,plain,
% 35.73/23.56 (~node1(c_bit1, s34)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4373, 4348])).
% 35.73/23.56 tff(4375,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4376,plain,
% 35.73/23.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit1, s34, s35))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4377,plain,
% 35.73/23.56 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit1, s34, s35)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4376, 4375])).
% 35.73/23.56 tff(4378,plain,
% 35.73/23.56 (node3(c_bit1, s34, s35)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4377, 81, 1135])).
% 35.73/23.56 tff(4379,plain,
% 35.73/23.56 (((~![Y: $i, I0: $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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4380,plain,
% 35.73/23.56 ((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)))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4381,plain,
% 35.73/23.56 (((~![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))))),
% 35.73/23.56 inference(monotonicity,[status(thm)],[4380])).
% 35.73/23.56 tff(4382,plain,
% 35.73/23.56 (((~![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)))),
% 35.73/23.56 inference(transitivity,[status(thm)],[4381, 4379])).
% 35.73/23.56 tff(4383,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4384,plain,
% 35.73/23.56 ((~![Y: $i, I0: $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))),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4383, 4382])).
% 35.73/23.56 tff(4385,plain,
% 35.73/23.56 (m_counter_cell_v_value(c_bit1, s35) | node1(c_bit1, s34)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4384, 199, 4378])).
% 35.73/23.56 tff(4386,plain,
% 35.73/23.56 (m_counter_cell_v_value(c_bit1, s35)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4385, 4374])).
% 35.73/23.56 tff(4387,plain,
% 35.73/23.56 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4388,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4389,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4388, 4387])).
% 35.73/23.56 tff(4390,plain,
% 35.73/23.56 ((~m_counter_cell_v_value(c_bit0, s35)) | m_counter_cell_v_carry_out(c_bit0, s35)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4389, 3031, 1151])).
% 35.73/23.56 tff(4391,plain,
% 35.73/23.56 (m_counter_cell_v_carry_out(c_bit0, s35)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4390, 1147])).
% 35.73/23.56 tff(4392,plain,
% 35.73/23.56 (((~![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))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4393,plain,
% 35.73/23.56 ((~![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))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4394,plain,
% 35.73/23.56 ((~![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)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4393, 4392])).
% 35.73/23.56 tff(4395,plain,
% 35.73/23.56 (m_counter_cell_v_carry_in(c_bit1, s35)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4394, 3046, 4391])).
% 35.73/23.56 tff(4396,assumption,(~m_counter_cell_v_carry_out(c_bit1, s35)), introduced(assumption)).
% 35.73/23.56 tff(4397,assumption,(m_counter_cell_v_carry_in(c_bit1, s35)), introduced(assumption)).
% 35.73/23.56 tff(4398,assumption,(m_counter_cell_v_value(c_bit1, s35)), introduced(assumption)).
% 35.73/23.56 tff(4399,plain,
% 35.73/23.56 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | m_counter_cell_v_carry_out(c_bit1, 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_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | m_counter_cell_v_carry_out(c_bit1, s35))),
% 35.73/23.56 inference(rewrite,[status(thm)],[])).
% 35.73/23.56 tff(4400,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | m_counter_cell_v_carry_out(c_bit1, s35))),
% 35.73/23.56 inference(quant_inst,[status(thm)],[])).
% 35.73/23.56 tff(4401,plain,
% 35.73/23.56 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | m_counter_cell_v_carry_out(c_bit1, s35)),
% 35.73/23.56 inference(modus_ponens,[status(thm)],[4400, 4399])).
% 35.73/23.56 tff(4402,plain,
% 35.73/23.56 ($false),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4401, 3031, 4398, 4397, 4396])).
% 35.73/23.56 tff(4403,plain,(m_counter_cell_v_carry_out(c_bit1, s35) | (~m_counter_cell_v_value(c_bit1, s35)) | (~m_counter_cell_v_carry_in(c_bit1, s35))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.56 tff(4404,plain,
% 35.73/23.56 (m_counter_cell_v_carry_out(c_bit1, s35) | (~m_counter_cell_v_value(c_bit1, s35))),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4403, 4395])).
% 35.73/23.56 tff(4405,plain,
% 35.73/23.56 (m_counter_cell_v_carry_out(c_bit1, s35)),
% 35.73/23.56 inference(unit_resolution,[status(thm)],[4404, 4386])).
% 35.73/23.56 tff(4406,assumption,(~m_counter_cell_v_carry_in(c_bit2, s35)), introduced(assumption)).
% 35.73/23.56 tff(4407,assumption,(m_counter_cell_v_carry_out(c_bit1, s35)), introduced(assumption)).
% 35.73/23.56 tff(4408,plain,
% 35.73/23.56 (^[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)))),
% 35.73/23.57 inference(bind,[status(th)],[])).
% 35.73/23.57 tff(4409,plain,
% 35.73/23.57 (![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))),
% 35.73/23.57 inference(quant_intro,[status(thm)],[4408])).
% 35.73/23.57 tff(4410,plain,
% 35.73/23.57 (![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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4411,plain,
% 35.73/23.57 (^[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)))),
% 35.73/23.57 inference(bind,[status(th)],[])).
% 35.73/23.57 tff(4412,plain,
% 35.73/23.57 (![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))),
% 35.73/23.57 inference(quant_intro,[status(thm)],[4411])).
% 35.73/23.57 tff(4413,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')).
% 35.73/23.57 tff(4414,plain,
% 35.73/23.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4413, 4412])).
% 35.73/23.57 tff(4415,plain,
% 35.73/23.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4414, 4410])).
% 35.73/23.57 tff(4416,plain,(
% 35.73/23.57 ![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 35.73/23.57 inference(skolemize,[status(sab)],[4415])).
% 35.73/23.57 tff(4417,plain,
% 35.73/23.57 (![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4416, 4409])).
% 35.73/23.57 tff(4418,plain,
% 35.73/23.57 (((~![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, s35)) | m_counter_cell_v_carry_in(c_bit2, s35))) <=> ((~![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, s35)) | m_counter_cell_v_carry_in(c_bit2, s35))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4419,plain,
% 35.73/23.57 ((~![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, s35)) | m_counter_cell_v_carry_in(c_bit2, s35))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4420,plain,
% 35.73/23.57 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s35)) | m_counter_cell_v_carry_in(c_bit2, s35)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4419, 4418])).
% 35.73/23.57 tff(4421,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4420, 4417, 4407, 4406])).
% 35.73/23.57 tff(4422,plain,(m_counter_cell_v_carry_in(c_bit2, s35) | (~m_counter_cell_v_carry_out(c_bit1, s35))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4423,plain,
% 35.73/23.57 (m_counter_cell_v_carry_in(c_bit2, s35)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4422, 4405])).
% 35.73/23.57 tff(4424,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s29) | (~node4(c_bit1, s29)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s29) | (~node4(c_bit1, s29)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4425,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s29) | (~node4(c_bit1, s29)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4426,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s29) | (~node4(c_bit1, s29))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4425, 4424])).
% 35.73/23.57 tff(4427,plain,
% 35.73/23.57 (~node4(c_bit1, s29)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4426, 2875, 4173])).
% 35.73/23.57 tff(4428,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s29)) | node4(c_bit1, s29))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s29)) | node4(c_bit1, s29))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4429,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s29)) | node4(c_bit1, s29))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4430,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s29)) | node4(c_bit1, s29)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4429, 4428])).
% 35.73/23.57 tff(4431,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_out(c_bit1, s29)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4430, 2887, 4427])).
% 35.73/23.57 tff(4432,plain,
% 35.73/23.57 (((~![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, s29)) | m_counter_cell_v_carry_out(c_bit1, s29))) <=> ((~![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, s29)) | m_counter_cell_v_carry_out(c_bit1, s29))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4433,plain,
% 35.73/23.57 ((~![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, s29)) | m_counter_cell_v_carry_out(c_bit1, s29))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4434,plain,
% 35.73/23.57 ((~![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, s29)) | m_counter_cell_v_carry_out(c_bit1, s29)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4433, 4432])).
% 35.73/23.57 tff(4435,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_in(c_bit2, s29)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4434, 3167, 4431])).
% 35.73/23.57 tff(4436,assumption,(~m_counter_cell_v_carry_out(c_bit1, s27)), introduced(assumption)).
% 35.73/23.57 tff(4437,assumption,(m_counter_cell_v_carry_in(c_bit1, s27)), introduced(assumption)).
% 35.73/23.57 tff(4438,plain,
% 35.73/23.57 (((~![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, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | m_counter_cell_v_carry_out(c_bit1, 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_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | m_counter_cell_v_carry_out(c_bit1, s27))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4439,plain,
% 35.73/23.57 ((~![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, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | m_counter_cell_v_carry_out(c_bit1, s27))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4440,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s27)) | (~m_counter_cell_v_value(c_bit1, s27)) | m_counter_cell_v_carry_out(c_bit1, s27)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4439, 4438])).
% 35.73/23.57 tff(4441,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4440, 3031, 4126, 4437, 4436])).
% 35.73/23.57 tff(4442,plain,(m_counter_cell_v_carry_out(c_bit1, s27) | (~m_counter_cell_v_value(c_bit1, s27)) | (~m_counter_cell_v_carry_in(c_bit1, s27))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4443,plain,
% 35.73/23.57 (m_counter_cell_v_carry_out(c_bit1, s27) | (~m_counter_cell_v_value(c_bit1, s27))),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4442, 4125])).
% 35.73/23.57 tff(4444,plain,
% 35.73/23.57 (m_counter_cell_v_carry_out(c_bit1, s27)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4443, 4115])).
% 35.73/23.57 tff(4445,assumption,(m_counter_cell_v_carry_out(c_bit1, s27)), introduced(assumption)).
% 35.73/23.57 tff(4446,assumption,(~m_counter_cell_v_carry_in(c_bit2, s27)), introduced(assumption)).
% 35.73/23.57 tff(4447,plain,
% 35.73/23.57 (((~![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, s27)) | m_counter_cell_v_carry_in(c_bit2, s27))) <=> ((~![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, s27)) | m_counter_cell_v_carry_in(c_bit2, s27))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4448,plain,
% 35.73/23.57 ((~![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, s27)) | m_counter_cell_v_carry_in(c_bit2, s27))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4449,plain,
% 35.73/23.57 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s27)) | m_counter_cell_v_carry_in(c_bit2, s27)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4448, 4447])).
% 35.73/23.57 tff(4450,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4449, 4417, 4446, 4445])).
% 35.73/23.57 tff(4451,plain,((~m_counter_cell_v_carry_out(c_bit1, s27)) | m_counter_cell_v_carry_in(c_bit2, s27)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4452,plain,
% 35.73/23.57 (m_counter_cell_v_carry_in(c_bit2, s27)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4451, 4444])).
% 35.73/23.57 tff(4453,assumption,(node4(c_bit1, s18)), introduced(assumption)).
% 35.73/23.57 tff(4454,assumption,(~m_counter_cell_v_carry_in(c_bit1, s18)), introduced(assumption)).
% 35.73/23.57 tff(4455,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s18) | (~node4(c_bit1, s18)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~node4(c_bit1, s18)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4456,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s18) | (~node4(c_bit1, s18)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4457,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s18) | (~node4(c_bit1, s18))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4456, 4455])).
% 35.73/23.57 tff(4458,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4457, 3076, 4454, 4453])).
% 35.73/23.57 tff(4459,plain,((~node4(c_bit1, s18)) | m_counter_cell_v_carry_in(c_bit1, s18)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4460,plain,
% 35.73/23.57 (~node4(c_bit1, s18)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4459, 3189])).
% 35.73/23.57 tff(4461,assumption,(~node4(c_bit1, s18)), introduced(assumption)).
% 35.73/23.57 tff(4462,assumption,(m_counter_cell_v_carry_out(c_bit1, s18)), introduced(assumption)).
% 35.73/23.57 tff(4463,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4464,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4465,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4464, 4463])).
% 35.73/23.57 tff(4466,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4465, 2887, 4462, 4461])).
% 35.73/23.57 tff(4467,plain,((~m_counter_cell_v_carry_out(c_bit1, s18)) | node4(c_bit1, s18)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4468,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_out(c_bit1, s18)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4467, 4460])).
% 35.73/23.57 tff(4469,assumption,(~m_counter_cell_v_carry_out(c_bit1, s18)), introduced(assumption)).
% 35.73/23.57 tff(4470,assumption,(m_counter_cell_v_carry_in(c_bit2, s18)), introduced(assumption)).
% 35.73/23.57 tff(4471,plain,
% 35.73/23.57 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4472,plain,
% 35.73/23.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4473,plain,
% 35.73/23.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4472, 4471])).
% 35.73/23.57 tff(4474,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4473, 3167, 4469, 4470])).
% 35.73/23.57 tff(4475,plain,((~m_counter_cell_v_carry_in(c_bit2, s18)) | m_counter_cell_v_carry_out(c_bit1, s18)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4476,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_in(c_bit2, s18)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4475, 4469])).
% 35.73/23.57 tff(4477,plain,
% 35.73/23.57 (~node1(c_bit1, s14)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[3682, 3208])).
% 35.73/23.57 tff(4478,plain,
% 35.73/23.57 (m_counter_cell_v_value(c_bit1, s15)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[3694, 4477])).
% 35.73/23.57 tff(4479,plain,
% 35.73/23.57 (~node1(c_bit1, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[3800, 4478])).
% 35.73/23.57 tff(4480,plain,
% 35.73/23.57 (m_counter_cell_v_value(c_bit1, s18)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[3812, 4479])).
% 35.73/23.57 tff(4481,plain,
% 35.73/23.57 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s18)) | node2(c_bit1, s17) | (~node3(c_bit1, 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_bit1, s18)) | node2(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4482,plain,
% 35.73/23.57 ((node2(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | (~m_counter_cell_v_value(c_bit1, s18))) <=> ((~m_counter_cell_v_value(c_bit1, s18)) | node2(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4483,plain,
% 35.73/23.57 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s18)) | node2(c_bit1, s17) | (~node3(c_bit1, s17, s18))))),
% 35.73/23.57 inference(monotonicity,[status(thm)],[4482])).
% 35.73/23.57 tff(4484,plain,
% 35.73/23.57 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s18)) | node2(c_bit1, s17) | (~node3(c_bit1, s17, s18)))),
% 35.73/23.57 inference(transitivity,[status(thm)],[4483, 4481])).
% 35.73/23.57 tff(4485,plain,
% 35.73/23.57 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s17) | (~node3(c_bit1, s17, s18)) | (~m_counter_cell_v_value(c_bit1, s18)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4486,plain,
% 35.73/23.57 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s18)) | node2(c_bit1, s17) | (~node3(c_bit1, s17, s18))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4485, 4484])).
% 35.73/23.57 tff(4487,plain,
% 35.73/23.57 ((~m_counter_cell_v_value(c_bit1, s18)) | node2(c_bit1, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4486, 234, 3805])).
% 35.73/23.57 tff(4488,plain,
% 35.73/23.57 (node2(c_bit1, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4487, 4480])).
% 35.73/23.57 tff(4489,plain,
% 35.73/23.57 (m_counter_cell_v_carry_out(c_bit0, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[3756, 622])).
% 35.73/23.57 tff(4490,plain,
% 35.73/23.57 (m_counter_cell_v_carry_in(c_bit1, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[3760, 3046, 4489])).
% 35.73/23.57 tff(4491,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : ((~m_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, s17)) | (~m_counter_cell_v_value(c_bit1, s17)) | (~node2(c_bit1, 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_bit1, s17)) | (~m_counter_cell_v_value(c_bit1, s17)) | (~node2(c_bit1, s17)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4492,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_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, s17)) | (~m_counter_cell_v_value(c_bit1, s17)) | (~node2(c_bit1, s17)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4493,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_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, s17)) | (~m_counter_cell_v_value(c_bit1, s17)) | (~node2(c_bit1, s17))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4492, 4491])).
% 35.73/23.57 tff(4494,plain,
% 35.73/23.57 ((~m_counter_cell_v_value(c_bit1, s17)) | (~node2(c_bit1, s17))),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4493, 219, 4490])).
% 35.73/23.57 tff(4495,plain,
% 35.73/23.57 (~m_counter_cell_v_value(c_bit1, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4494, 4488])).
% 35.73/23.57 tff(4496,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s17) | (~node4(c_bit1, s17)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s17) | (~node4(c_bit1, s17)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4497,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s17) | (~node4(c_bit1, s17)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4498,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s17) | (~node4(c_bit1, s17))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4497, 4496])).
% 35.73/23.57 tff(4499,plain,
% 35.73/23.57 (~node4(c_bit1, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4498, 2875, 4495])).
% 35.73/23.57 tff(4500,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s17)) | node4(c_bit1, s17))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s17)) | node4(c_bit1, s17))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4501,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s17)) | node4(c_bit1, s17))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4502,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s17)) | node4(c_bit1, s17)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4501, 4500])).
% 35.73/23.57 tff(4503,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_out(c_bit1, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4502, 2887, 4499])).
% 35.73/23.57 tff(4504,plain,
% 35.73/23.57 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s17)) | m_counter_cell_v_carry_out(c_bit1, s17))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s17)) | m_counter_cell_v_carry_out(c_bit1, s17))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4505,plain,
% 35.73/23.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s17)) | m_counter_cell_v_carry_out(c_bit1, s17))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4506,plain,
% 35.73/23.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s17)) | m_counter_cell_v_carry_out(c_bit1, s17)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4505, 4504])).
% 35.73/23.57 tff(4507,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_in(c_bit2, s17)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4506, 3167, 4503])).
% 35.73/23.57 tff(4508,plain,
% 35.73/23.57 (m_counter_cell_v_carry_out(c_bit0, s15)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[3729, 565])).
% 35.73/23.57 tff(4509,plain,
% 35.73/23.57 (m_counter_cell_v_carry_in(c_bit1, s15)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[3733, 3046, 4508])).
% 35.73/23.57 tff(4510,plain,
% 35.73/23.57 (((~![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, 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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4511,plain,
% 35.73/23.57 ((~![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, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4512,plain,
% 35.73/23.57 ((~![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, s15)) | (~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4511, 4510])).
% 35.73/23.57 tff(4513,plain,
% 35.73/23.57 ((~m_counter_cell_v_value(c_bit1, s15)) | m_counter_cell_v_carry_out(c_bit1, s15)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4512, 3031, 4509])).
% 35.73/23.57 tff(4514,plain,
% 35.73/23.57 (m_counter_cell_v_carry_out(c_bit1, s15)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4513, 4478])).
% 35.73/23.57 tff(4515,plain,
% 35.73/23.57 (((~![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, 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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4516,plain,
% 35.73/23.57 ((~![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, s15)) | m_counter_cell_v_carry_in(c_bit2, s15))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4517,plain,
% 35.73/23.57 ((~![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, s15)) | m_counter_cell_v_carry_in(c_bit2, s15)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4516, 4515])).
% 35.73/23.57 tff(4518,plain,
% 35.73/23.57 (m_counter_cell_v_carry_in(c_bit2, s15)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4517, 4417, 4514])).
% 35.73/23.57 tff(4519,assumption,(node4(c_bit1, s14)), introduced(assumption)).
% 35.73/23.57 tff(4520,plain,
% 35.73/23.57 (((~![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)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4521,plain,
% 35.73/23.57 ((~![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)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4522,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s14) | (~node4(c_bit1, s14))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4521, 4520])).
% 35.73/23.57 tff(4523,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4522, 3076, 3208, 4519])).
% 35.73/23.57 tff(4524,plain,((~node4(c_bit1, s14)) | m_counter_cell_v_carry_in(c_bit1, s14)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4525,plain,
% 35.73/23.57 (~node4(c_bit1, s14)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4524, 3208])).
% 35.73/23.57 tff(4526,assumption,(~node4(c_bit1, s14)), introduced(assumption)).
% 35.73/23.57 tff(4527,assumption,(m_counter_cell_v_carry_out(c_bit1, s14)), introduced(assumption)).
% 35.73/23.57 tff(4528,plain,
% 35.73/23.57 (((~![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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4529,plain,
% 35.73/23.57 ((~![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))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4530,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s14)) | node4(c_bit1, s14)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4529, 4528])).
% 35.73/23.57 tff(4531,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4530, 2887, 4527, 4526])).
% 35.73/23.57 tff(4532,plain,((~m_counter_cell_v_carry_out(c_bit1, s14)) | node4(c_bit1, s14)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4533,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_out(c_bit1, s14)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4532, 4525])).
% 35.73/23.57 tff(4534,assumption,(m_counter_cell_v_carry_in(c_bit2, s14)), introduced(assumption)).
% 35.73/23.57 tff(4535,assumption,(~m_counter_cell_v_carry_out(c_bit1, s14)), introduced(assumption)).
% 35.73/23.57 tff(4536,plain,
% 35.73/23.57 (((~![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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4537,plain,
% 35.73/23.57 ((~![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))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4538,plain,
% 35.73/23.57 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s14)) | m_counter_cell_v_carry_out(c_bit1, s14)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4537, 4536])).
% 35.73/23.57 tff(4539,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4538, 3167, 4535, 4534])).
% 35.73/23.57 tff(4540,plain,((~m_counter_cell_v_carry_in(c_bit2, s14)) | m_counter_cell_v_carry_out(c_bit1, s14)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4541,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_in(c_bit2, s14)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4540, 4533])).
% 35.73/23.57 tff(4542,assumption,(~m_counter_cell_v_carry_out(c_bit1, s7)), introduced(assumption)).
% 35.73/23.57 tff(4543,plain,
% 35.73/23.57 (((~![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, 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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4544,plain,
% 35.73/23.57 ((~![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, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | m_counter_cell_v_carry_out(c_bit1, s7))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4545,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s7)) | (~m_counter_cell_v_value(c_bit1, s7)) | m_counter_cell_v_carry_out(c_bit1, s7)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4544, 4543])).
% 35.73/23.57 tff(4546,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4545, 3031, 3474, 3235, 4542])).
% 35.73/23.57 tff(4547,plain,(m_counter_cell_v_carry_out(c_bit1, s7)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4548,plain,
% 35.73/23.57 (((~![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, 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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4549,plain,
% 35.73/23.57 ((~![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, s7)) | m_counter_cell_v_carry_in(c_bit2, s7))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4550,plain,
% 35.73/23.57 ((~![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, s7)) | m_counter_cell_v_carry_in(c_bit2, s7)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4549, 4548])).
% 35.73/23.57 tff(4551,plain,
% 35.73/23.57 (m_counter_cell_v_carry_in(c_bit2, s7)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4550, 4417, 4547])).
% 35.73/23.57 tff(4552,assumption,(node4(c_bit1, s6)), introduced(assumption)).
% 35.73/23.57 tff(4553,plain,
% 35.73/23.57 (((~![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)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~node4(c_bit1, s6)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4554,plain,
% 35.73/23.57 ((~![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)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4555,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s6) | (~node4(c_bit1, s6))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4554, 4553])).
% 35.73/23.57 tff(4556,plain,
% 35.73/23.57 ($false),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4555, 3076, 3254, 4552])).
% 35.73/23.57 tff(4557,plain,(~node4(c_bit1, s6)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.57 tff(4558,plain,
% 35.73/23.57 (((~![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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4559,plain,
% 35.73/23.57 ((~![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))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4560,plain,
% 35.73/23.57 ((~![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)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4559, 4558])).
% 35.73/23.57 tff(4561,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_out(c_bit1, s6)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4560, 2887, 4557])).
% 35.73/23.57 tff(4562,plain,
% 35.73/23.57 (((~![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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4563,plain,
% 35.73/23.57 ((~![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))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4564,plain,
% 35.73/23.57 ((~![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)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4563, 4562])).
% 35.73/23.57 tff(4565,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_in(c_bit2, s6)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4564, 3167, 4561])).
% 35.73/23.57 tff(4566,assumption,(~m_counter_cell_v_value(c_bit1, s5)), introduced(assumption)).
% 35.73/23.57 tff(4567,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s5) | (~node4(c_bit1, s5)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s5) | (~node4(c_bit1, s5)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4568,plain,
% 35.73/23.57 ((~![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)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4569,plain,
% 35.73/23.57 ((~![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))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4568, 4567])).
% 35.73/23.57 tff(4570,plain,
% 35.73/23.57 (~node4(c_bit1, s5)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4569, 2875, 4566])).
% 35.73/23.57 tff(4571,plain,
% 35.73/23.57 (((~![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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4572,plain,
% 35.73/23.57 ((~![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))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4573,plain,
% 35.73/23.57 ((~![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)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4572, 4571])).
% 35.73/23.57 tff(4574,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_out(c_bit1, s5)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4573, 2887, 4570])).
% 35.73/23.57 tff(4575,plain,
% 35.73/23.57 (((~![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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4576,plain,
% 35.73/23.57 ((~![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))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4577,plain,
% 35.73/23.57 ((~![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)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4576, 4575])).
% 35.73/23.57 tff(4578,plain,
% 35.73/23.57 (~m_counter_cell_v_carry_in(c_bit2, s5)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4577, 3167, 4574])).
% 35.73/23.57 tff(4579,assumption,(node1(c_bit2, s5)), introduced(assumption)).
% 35.73/23.57 tff(4580,plain,
% 35.73/23.57 (((~![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_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4581,plain,
% 35.73/23.57 (((~node1(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5))) <=> (m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5)))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4582,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5))))),
% 35.73/23.57 inference(monotonicity,[status(thm)],[4581])).
% 35.73/23.57 tff(4583,plain,
% 35.73/23.57 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5)))),
% 35.73/23.57 inference(transitivity,[status(thm)],[4582, 4580])).
% 35.73/23.57 tff(4584,plain,
% 35.73/23.57 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s5)) | m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4585,plain,
% 35.73/23.57 ((~![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_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5)) | (~node1(c_bit2, s5))),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4584, 4583])).
% 35.73/23.57 tff(4586,plain,
% 35.73/23.57 (m_counter_cell_v_carry_in(c_bit2, s5) | (~m_counter_cell_v_value(c_bit2, s5))),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4585, 3359, 4579])).
% 35.73/23.57 tff(4587,plain,
% 35.73/23.57 (~m_counter_cell_v_value(c_bit2, s5)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4586, 4578])).
% 35.73/23.57 tff(4588,plain,
% 35.73/23.57 (((~![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))),
% 35.73/23.57 inference(rewrite,[status(thm)],[])).
% 35.73/23.57 tff(4589,plain,
% 35.73/23.57 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s4, s5)) | node3(c_bit2, s4, s5))),
% 35.73/23.57 inference(quant_inst,[status(thm)],[])).
% 35.73/23.57 tff(4590,plain,
% 35.73/23.57 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s4, s5)) | node3(c_bit2, s4, s5)),
% 35.73/23.57 inference(modus_ponens,[status(thm)],[4589, 4588])).
% 35.73/23.57 tff(4591,plain,
% 35.73/23.57 (node3(c_bit2, s4, s5)),
% 35.73/23.57 inference(unit_resolution,[status(thm)],[4590, 81, 103])).
% 35.73/23.58 tff(4592,plain,
% 35.73/23.58 (((~![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, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4593,plain,
% 35.73/23.58 ((node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)) | m_counter_cell_v_value(c_bit2, s5)) <=> (m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4594,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)) | m_counter_cell_v_value(c_bit2, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5))))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4593])).
% 35.73/23.58 tff(4595,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)) | m_counter_cell_v_value(c_bit2, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5)))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4594, 4592])).
% 35.73/23.58 tff(4596,plain,
% 35.73/23.58 ((~![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))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4597,plain,
% 35.73/23.58 ((~![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, s5) | node1(c_bit2, s4) | (~node3(c_bit2, s4, s5))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4596, 4595])).
% 35.73/23.58 tff(4598,plain,
% 35.73/23.58 (m_counter_cell_v_value(c_bit2, s5) | node1(c_bit2, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4597, 199, 4591])).
% 35.73/23.58 tff(4599,plain,
% 35.73/23.58 (node1(c_bit2, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4598, 4587])).
% 35.73/23.58 tff(4600,plain,
% 35.73/23.58 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s4) | (~node4(c_bit1, s4)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node4(c_bit1, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4601,plain,
% 35.73/23.58 ((~![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)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4602,plain,
% 35.73/23.58 ((~![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))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4601, 4600])).
% 35.73/23.58 tff(4603,plain,
% 35.73/23.58 (~node4(c_bit1, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4602, 3076, 3417])).
% 35.73/23.58 tff(4604,plain,
% 35.73/23.58 (((~![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))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4605,plain,
% 35.73/23.58 ((~![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))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4606,plain,
% 35.73/23.58 ((~![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)),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4605, 4604])).
% 35.73/23.58 tff(4607,plain,
% 35.73/23.58 (~m_counter_cell_v_carry_out(c_bit1, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4606, 2887, 4603])).
% 35.73/23.58 tff(4608,plain,
% 35.73/23.58 (((~![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))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4609,plain,
% 35.73/23.58 ((~![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))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4610,plain,
% 35.73/23.58 ((~![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)),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4609, 4608])).
% 35.73/23.58 tff(4611,plain,
% 35.73/23.58 (~m_counter_cell_v_carry_in(c_bit2, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4610, 3167, 4607])).
% 35.73/23.58 tff(4612,plain,
% 35.73/23.58 (((~![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, s4) | (~node1(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) | (~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4613,plain,
% 35.73/23.58 (((~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) | (~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4614,plain,
% 35.73/23.58 (((~![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, 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) | (~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4))))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4613])).
% 35.73/23.58 tff(4615,plain,
% 35.73/23.58 (((~![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, 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) | (~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4)))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4614, 4612])).
% 35.73/23.58 tff(4616,plain,
% 35.73/23.58 ((~![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, s4)) | m_counter_cell_v_carry_in(c_bit2, s4) | (~m_counter_cell_v_value(c_bit2, s4)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4617,plain,
% 35.73/23.58 ((~![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, s4) | (~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4616, 4615])).
% 35.73/23.58 tff(4618,plain,
% 35.73/23.58 ((~node1(c_bit2, s4)) | (~m_counter_cell_v_value(c_bit2, s4))),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4617, 3359, 4611])).
% 35.73/23.58 tff(4619,plain,
% 35.73/23.58 (~m_counter_cell_v_value(c_bit2, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4618, 4599])).
% 35.73/23.58 tff(4620,plain,
% 35.73/23.58 (((~![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))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4621,plain,
% 35.73/23.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s3, s4)) | node3(c_bit2, s3, s4))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4622,plain,
% 35.73/23.58 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s3, s4)) | node3(c_bit2, s3, s4)),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4621, 4620])).
% 35.73/23.58 tff(4623,plain,
% 35.73/23.58 (node3(c_bit2, s3, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4622, 81, 114])).
% 35.73/23.58 tff(4624,plain,
% 35.73/23.58 (((~![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, s4) | node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4625,plain,
% 35.73/23.58 ((node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)) | m_counter_cell_v_value(c_bit2, s4)) <=> (m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4626,plain,
% 35.73/23.58 (((~![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))) | (m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3) | (~node3(c_bit2, s3, s4))))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4625])).
% 35.73/23.58 tff(4627,plain,
% 35.73/23.58 (((~![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))) | m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3) | (~node3(c_bit2, s3, s4)))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4626, 4624])).
% 35.73/23.58 tff(4628,plain,
% 35.73/23.58 ((~![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))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4629,plain,
% 35.73/23.58 ((~![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, s4) | node1(c_bit2, s3) | (~node3(c_bit2, s3, s4))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4628, 4627])).
% 35.73/23.58 tff(4630,plain,
% 35.73/23.58 (m_counter_cell_v_value(c_bit2, s4) | node1(c_bit2, s3)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4629, 199, 4623])).
% 35.73/23.58 tff(4631,plain,
% 35.73/23.58 (node1(c_bit2, s3)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4630, 4619])).
% 35.73/23.58 tff(4632,plain,
% 35.73/23.58 (((~![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, s5) | node1(c_bit1, s4) | (~node3(c_bit1, s4, s5)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s5) | node1(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4633,plain,
% 35.73/23.58 ((node1(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | m_counter_cell_v_value(c_bit1, s5)) <=> (m_counter_cell_v_value(c_bit1, s5) | node1(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4634,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | m_counter_cell_v_value(c_bit1, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s5) | node1(c_bit1, s4) | (~node3(c_bit1, s4, s5))))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4633])).
% 35.73/23.58 tff(4635,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | m_counter_cell_v_value(c_bit1, s5))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s5) | node1(c_bit1, s4) | (~node3(c_bit1, s4, s5)))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4634, 4632])).
% 35.73/23.58 tff(4636,plain,
% 35.73/23.58 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s4) | (~node3(c_bit1, s4, s5)) | m_counter_cell_v_value(c_bit1, s5))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4637,plain,
% 35.73/23.58 ((~![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, s5) | node1(c_bit1, s4) | (~node3(c_bit1, s4, s5))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4636, 4635])).
% 35.73/23.58 tff(4638,plain,
% 35.73/23.58 (m_counter_cell_v_value(c_bit1, s5) | node1(c_bit1, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4637, 199, 3426])).
% 35.73/23.58 tff(4639,plain,
% 35.73/23.58 (node1(c_bit1, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4638, 4566])).
% 35.73/23.58 tff(4640,plain,
% 35.73/23.58 (((~![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_value(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node1(c_bit1, 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_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node1(c_bit1, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4641,plain,
% 35.73/23.58 (((~node1(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, s4))) <=> ((~m_counter_cell_v_value(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node1(c_bit1, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4642,plain,
% 35.73/23.58 (((~![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, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node1(c_bit1, s4))))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4641])).
% 35.73/23.58 tff(4643,plain,
% 35.73/23.58 (((~![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, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node1(c_bit1, s4)))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4642, 4640])).
% 35.73/23.58 tff(4644,plain,
% 35.73/23.58 ((~![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, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~m_counter_cell_v_value(c_bit1, s4)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4645,plain,
% 35.73/23.58 ((~![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_value(c_bit1, s4)) | m_counter_cell_v_carry_in(c_bit1, s4) | (~node1(c_bit1, s4))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4644, 4643])).
% 35.73/23.58 tff(4646,plain,
% 35.73/23.58 ((~m_counter_cell_v_value(c_bit1, s4)) | (~node1(c_bit1, s4))),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4645, 3359, 3417])).
% 35.73/23.58 tff(4647,plain,
% 35.73/23.58 (~m_counter_cell_v_value(c_bit1, s4)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4646, 4639])).
% 35.73/23.58 tff(4648,plain,
% 35.73/23.58 (((~![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, s4) | node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s4) | node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4649,plain,
% 35.73/23.58 ((node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | m_counter_cell_v_value(c_bit1, s4)) <=> (m_counter_cell_v_value(c_bit1, s4) | node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4650,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | m_counter_cell_v_value(c_bit1, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s4) | node1(c_bit1, s3) | (~node3(c_bit1, s3, s4))))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4649])).
% 35.73/23.58 tff(4651,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | m_counter_cell_v_value(c_bit1, s4))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s4) | node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4650, 4648])).
% 35.73/23.58 tff(4652,plain,
% 35.73/23.58 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s3) | (~node3(c_bit1, s3, s4)) | m_counter_cell_v_value(c_bit1, s4))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4653,plain,
% 35.73/23.58 ((~![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, s4) | node1(c_bit1, s3) | (~node3(c_bit1, s3, s4))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4652, 4651])).
% 35.73/23.58 tff(4654,plain,
% 35.73/23.58 (m_counter_cell_v_value(c_bit1, s4) | node1(c_bit1, s3)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4653, 199, 3397])).
% 35.73/23.58 tff(4655,plain,
% 35.73/23.58 (node1(c_bit1, s3)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4654, 4647])).
% 35.73/23.58 tff(4656,plain,
% 35.73/23.58 (((~![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, s3)) | m_counter_cell_v_value(c_bit1, s3) | (~node1(c_bit1, s3)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3) | (~node1(c_bit1, s3)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4657,plain,
% 35.73/23.58 (((~node1(c_bit1, s3)) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3) | (~node1(c_bit1, s3)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4658,plain,
% 35.73/23.58 (((~![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, s3)) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3) | (~node1(c_bit1, s3))))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4657])).
% 35.73/23.58 tff(4659,plain,
% 35.73/23.58 (((~![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, s3)) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3) | (~node1(c_bit1, s3)))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4658, 4656])).
% 35.73/23.58 tff(4660,plain,
% 35.73/23.58 ((~![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, s3)) | (~m_counter_cell_v_carry_in(c_bit1, s3)) | m_counter_cell_v_value(c_bit1, s3))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4661,plain,
% 35.73/23.58 ((~![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, s3)) | m_counter_cell_v_value(c_bit1, s3) | (~node1(c_bit1, s3))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4660, 4659])).
% 35.73/23.58 tff(4662,plain,
% 35.73/23.58 (m_counter_cell_v_value(c_bit1, s3) | (~node1(c_bit1, s3))),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4661, 170, 3388])).
% 35.73/23.58 tff(4663,plain,
% 35.73/23.58 (m_counter_cell_v_value(c_bit1, s3)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4662, 4655])).
% 35.73/23.58 tff(4664,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node3(c_bit1, s2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node3(c_bit1, s2, s3)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4665,plain,
% 35.73/23.58 ((node2(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | (~m_counter_cell_v_value(c_bit1, s3))) <=> (node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node3(c_bit1, s2, s3)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4666,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | (~m_counter_cell_v_value(c_bit1, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node3(c_bit1, s2, s3))))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4665])).
% 35.73/23.58 tff(4667,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | (~m_counter_cell_v_value(c_bit1, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node3(c_bit1, s2, s3)))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4666, 4664])).
% 35.73/23.58 tff(4668,plain,
% 35.73/23.58 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s2) | (~node3(c_bit1, s2, s3)) | (~m_counter_cell_v_value(c_bit1, s3)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4669,plain,
% 35.73/23.58 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3)) | (~node3(c_bit1, s2, s3))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4668, 4667])).
% 35.73/23.58 tff(4670,plain,
% 35.73/23.58 (node2(c_bit1, s2) | (~m_counter_cell_v_value(c_bit1, s3))),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4669, 234, 3371])).
% 35.73/23.58 tff(4671,plain,
% 35.73/23.58 (node2(c_bit1, s2)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4670, 4663])).
% 35.73/23.58 tff(4672,plain,
% 35.73/23.58 (((~![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_bit1, s2) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s2) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4673,plain,
% 35.73/23.58 ((~![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_bit1, s2) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4674,plain,
% 35.73/23.58 ((~![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_bit1, s2) | m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4673, 4672])).
% 35.73/23.58 tff(4675,plain,
% 35.73/23.58 (m_counter_cell_v_value(c_bit1, s2) | (~node2(c_bit1, s2))),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4674, 3291, 3349])).
% 35.73/23.58 tff(4676,plain,
% 35.73/23.58 (m_counter_cell_v_value(c_bit1, s2)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4675, 4671])).
% 35.73/23.58 tff(4677,plain,
% 35.73/23.58 (((~![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_bit1, s2)) | (~node3(c_bit1, s1, s2)) | node2(c_bit1, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node3(c_bit1, s1, s2)) | node2(c_bit1, s1))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4678,plain,
% 35.73/23.58 ((node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | (~m_counter_cell_v_value(c_bit1, s2))) <=> ((~m_counter_cell_v_value(c_bit1, s2)) | (~node3(c_bit1, s1, s2)) | node2(c_bit1, s1))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4679,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s2)) | (~node3(c_bit1, s1, s2)) | node2(c_bit1, s1)))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4678])).
% 35.73/23.58 tff(4680,plain,
% 35.73/23.58 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s2)) | (~node3(c_bit1, s1, s2)) | node2(c_bit1, s1))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4679, 4677])).
% 35.73/23.58 tff(4681,plain,
% 35.73/23.58 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s1) | (~node3(c_bit1, s1, s2)) | (~m_counter_cell_v_value(c_bit1, s2)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4682,plain,
% 35.73/23.58 ((~![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_bit1, s2)) | (~node3(c_bit1, s1, s2)) | node2(c_bit1, s1)),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4681, 4680])).
% 35.73/23.58 tff(4683,plain,
% 35.73/23.58 ((~m_counter_cell_v_value(c_bit1, s2)) | node2(c_bit1, s1)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4682, 234, 3329])).
% 35.73/23.58 tff(4684,plain,
% 35.73/23.58 (node2(c_bit1, s1)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4683, 4676])).
% 35.73/23.58 tff(4685,plain,
% 35.73/23.58 (((~![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_bit1, s1)) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s1)) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4686,plain,
% 35.73/23.58 ((~![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_bit1, s1)) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4687,plain,
% 35.73/23.58 ((~![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_bit1, s1)) | (~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4686, 4685])).
% 35.73/23.58 tff(4688,plain,
% 35.73/23.58 ((~m_counter_cell_v_value(c_bit1, s1)) | (~node2(c_bit1, s1))),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4687, 219, 3317])).
% 35.73/23.58 tff(4689,plain,
% 35.73/23.58 (~m_counter_cell_v_value(c_bit1, s1)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4688, 4684])).
% 35.73/23.58 tff(4690,plain,
% 35.73/23.58 (((~![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)))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4691,plain,
% 35.73/23.58 ((~![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)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4692,plain,
% 35.73/23.58 ((~![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))),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4691, 4690])).
% 35.73/23.58 tff(4693,plain,
% 35.73/23.58 (~node4(c_bit1, s1)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4692, 2875, 4689])).
% 35.73/23.58 tff(4694,plain,
% 35.73/23.58 (((~![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))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4695,plain,
% 35.73/23.58 ((~![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))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4696,plain,
% 35.73/23.58 ((~![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)),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4695, 4694])).
% 35.73/23.58 tff(4697,plain,
% 35.73/23.58 (~m_counter_cell_v_carry_out(c_bit1, s1)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4696, 2887, 4693])).
% 35.73/23.58 tff(4698,plain,
% 35.73/23.58 (((~![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))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4699,plain,
% 35.73/23.58 ((~![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))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4700,plain,
% 35.73/23.58 ((~![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)),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4699, 4698])).
% 35.73/23.58 tff(4701,plain,
% 35.73/23.58 (~m_counter_cell_v_carry_in(c_bit2, s1)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4700, 3167, 4697])).
% 35.73/23.58 tff(4702,assumption,(m_counter_cell_v_value(c_bit2, s0)), introduced(assumption)).
% 35.73/23.58 tff(4703,plain,
% 35.73/23.58 ((~![I0: $i] : (~m_counter_cell_v_value(I0, s0))) | (~m_counter_cell_v_value(c_bit2, s0))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4704,plain,
% 35.73/23.58 ($false),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4703, 148, 4702])).
% 35.73/23.58 tff(4705,plain,(~m_counter_cell_v_value(c_bit2, s0)), inference(lemma,lemma(discharge,[]))).
% 35.73/23.58 tff(4706,plain,
% 35.73/23.58 (((~![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))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4707,plain,
% 35.73/23.58 ((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))),
% 35.73/23.58 inference(rewrite,[status(thm)],[])).
% 35.73/23.58 tff(4708,plain,
% 35.73/23.58 (((~![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)))),
% 35.73/23.58 inference(monotonicity,[status(thm)],[4707])).
% 35.73/23.58 tff(4709,plain,
% 35.73/23.58 (((~![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))),
% 35.73/23.58 inference(transitivity,[status(thm)],[4708, 4706])).
% 35.73/23.58 tff(4710,plain,
% 35.73/23.58 ((~![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)))),
% 35.73/23.58 inference(quant_inst,[status(thm)],[])).
% 35.73/23.58 tff(4711,plain,
% 35.73/23.58 ((~![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)),
% 35.73/23.58 inference(modus_ponens,[status(thm)],[4710, 4709])).
% 35.73/23.58 tff(4712,plain,
% 35.73/23.58 (~node4(c_bit1, s0)),
% 35.73/23.58 inference(unit_resolution,[status(thm)],[4711, 3076, 3281])).
% 35.73/23.58 tff(4713,plain,
% 35.73/23.58 (((~![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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4714,plain,
% 35.73/23.59 ((~![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))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4715,plain,
% 35.73/23.59 ((~![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)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4714, 4713])).
% 35.73/23.59 tff(4716,plain,
% 35.73/23.59 (~m_counter_cell_v_carry_out(c_bit1, s0)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4715, 2887, 4712])).
% 35.73/23.59 tff(4717,plain,
% 35.73/23.59 (((~![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, 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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4718,plain,
% 35.73/23.59 ((~![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, s0)) | m_counter_cell_v_carry_out(c_bit1, s0))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4719,plain,
% 35.73/23.59 ((~![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, s0)) | m_counter_cell_v_carry_out(c_bit1, s0)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4718, 4717])).
% 35.73/23.59 tff(4720,plain,
% 35.73/23.59 (~m_counter_cell_v_carry_in(c_bit2, s0)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4719, 3167, 4716])).
% 35.73/23.59 tff(4721,plain,
% 35.73/23.59 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit2, s0)) | m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s0)) | m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4722,plain,
% 35.73/23.59 ((m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0))) <=> ((~node2(c_bit2, s0)) | m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4723,plain,
% 35.73/23.59 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | ((~node2(c_bit2, s0)) | m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0)))),
% 35.73/23.59 inference(monotonicity,[status(thm)],[4722])).
% 35.73/23.59 tff(4724,plain,
% 35.73/23.59 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0) | (~node2(c_bit2, s0)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s0)) | m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0))),
% 35.73/23.59 inference(transitivity,[status(thm)],[4723, 4721])).
% 35.73/23.59 tff(4725,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4726,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (~node2(c_bit2, s0)) | m_counter_cell_v_carry_in(c_bit2, s0) | m_counter_cell_v_value(c_bit2, s0)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4725, 4724])).
% 35.73/23.59 tff(4727,plain,
% 35.73/23.59 ((~node2(c_bit2, s0)) | m_counter_cell_v_value(c_bit2, s0)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4726, 3291, 4720])).
% 35.73/23.59 tff(4728,plain,
% 35.73/23.59 (~node2(c_bit2, s0)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4727, 4705])).
% 35.73/23.59 tff(4729,plain,
% 35.73/23.59 (((~![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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4730,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s0, s1)) | node3(c_bit2, s0, s1))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4731,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s0, s1)) | node3(c_bit2, s0, s1)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4730, 4729])).
% 35.73/23.59 tff(4732,plain,
% 35.73/23.59 (node3(c_bit2, s0, s1)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4731, 81, 185])).
% 35.73/23.59 tff(4733,plain,
% 35.73/23.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s0) | (~node3(c_bit2, s0, s1)) | (~m_counter_cell_v_value(c_bit2, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s0) | (~node3(c_bit2, s0, s1)) | (~m_counter_cell_v_value(c_bit2, s1)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4734,plain,
% 35.73/23.59 ((~![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)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4735,plain,
% 35.73/23.59 ((~![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))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4734, 4733])).
% 35.73/23.59 tff(4736,plain,
% 35.73/23.59 (node2(c_bit2, s0) | (~m_counter_cell_v_value(c_bit2, s1))),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4735, 234, 4732])).
% 35.73/23.59 tff(4737,plain,
% 35.73/23.59 (~m_counter_cell_v_value(c_bit2, s1)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4736, 4728])).
% 35.73/23.59 tff(4738,plain,
% 35.73/23.59 (((~![I0: $i, X: $i] : (m_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_carry_in(c_bit2, s1) | m_counter_cell_v_value(c_bit2, s1) | (~node2(c_bit2, s1)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4739,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4740,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : (m_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))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4739, 4738])).
% 35.73/23.59 tff(4741,plain,
% 35.73/23.59 (m_counter_cell_v_carry_in(c_bit2, s1) | (~node2(c_bit2, s1))),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4740, 3291, 4737])).
% 35.73/23.59 tff(4742,plain,
% 35.73/23.59 (~node2(c_bit2, s1)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4741, 4701])).
% 35.73/23.59 tff(4743,plain,
% 35.73/23.59 (((~![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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4744,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s1, s2)) | node3(c_bit2, s1, s2))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4745,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s1, s2)) | node3(c_bit2, s1, s2)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4744, 4743])).
% 35.73/23.59 tff(4746,plain,
% 35.73/23.59 (node3(c_bit2, s1, s2)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4745, 81, 136])).
% 35.73/23.59 tff(4747,plain,
% 35.73/23.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4748,plain,
% 35.73/23.59 ((node2(c_bit2, s1) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2))) <=> ((~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4749,plain,
% 35.73/23.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s1) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1)))),
% 35.73/23.59 inference(monotonicity,[status(thm)],[4748])).
% 35.73/23.59 tff(4750,plain,
% 35.73/23.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s1) | (~node3(c_bit2, s1, s2)) | (~m_counter_cell_v_value(c_bit2, s2)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1))),
% 35.73/23.59 inference(transitivity,[status(thm)],[4749, 4747])).
% 35.73/23.59 tff(4751,plain,
% 35.73/23.59 ((~![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)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4752,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s2)) | (~node3(c_bit2, s1, s2)) | node2(c_bit2, s1)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4751, 4750])).
% 35.73/23.59 tff(4753,plain,
% 35.73/23.59 ((~m_counter_cell_v_value(c_bit2, s2)) | node2(c_bit2, s1)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4752, 234, 4746])).
% 35.73/23.59 tff(4754,plain,
% 35.73/23.59 (~m_counter_cell_v_value(c_bit2, s2)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4753, 4742])).
% 35.73/23.59 tff(4755,plain,
% 35.73/23.59 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | ((~node4(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4756,plain,
% 35.73/23.59 ((m_counter_cell_v_carry_in(c_bit1, s2) | (~node4(c_bit1, s2))) <=> ((~node4(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4757,plain,
% 35.73/23.59 (((~![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)))) | ((~node4(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2)))),
% 35.73/23.59 inference(monotonicity,[status(thm)],[4756])).
% 35.73/23.59 tff(4758,plain,
% 35.73/23.59 (((~![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)))) | (~node4(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2))),
% 35.73/23.59 inference(transitivity,[status(thm)],[4757, 4755])).
% 35.73/23.59 tff(4759,plain,
% 35.73/23.59 ((~![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)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4760,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (~node4(c_bit1, s2)) | m_counter_cell_v_carry_in(c_bit1, s2)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 35.73/23.59 tff(4761,plain,
% 35.73/23.59 (~node4(c_bit1, s2)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4760, 3076, 3349])).
% 35.73/23.59 tff(4762,plain,
% 35.73/23.59 (((~![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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4763,plain,
% 35.73/23.59 ((~![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))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4764,plain,
% 35.73/23.59 ((~![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)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4763, 4762])).
% 35.73/23.59 tff(4765,plain,
% 35.73/23.59 (~m_counter_cell_v_carry_out(c_bit1, s2)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4764, 2887, 4761])).
% 35.73/23.59 tff(4766,plain,
% 35.73/23.59 (((~![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, 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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4767,plain,
% 35.73/23.59 ((~![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, s2)) | m_counter_cell_v_carry_out(c_bit1, s2))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4768,plain,
% 35.73/23.59 ((~![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, s2)) | m_counter_cell_v_carry_out(c_bit1, s2)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4767, 4766])).
% 35.73/23.59 tff(4769,plain,
% 35.73/23.59 (~m_counter_cell_v_carry_in(c_bit2, s2)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4768, 3167, 4765])).
% 35.73/23.59 tff(4770,plain,
% 35.73/23.59 (((~![I0: $i, 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, s2) | m_counter_cell_v_carry_in(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_value(c_bit2, s2) | m_counter_cell_v_carry_in(c_bit2, s2) | (~node2(c_bit2, s2)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4771,plain,
% 35.73/23.59 ((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_value(c_bit2, s2) | m_counter_cell_v_carry_in(c_bit2, s2) | (~node2(c_bit2, s2)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4772,plain,
% 35.73/23.59 (((~![I0: $i, X: $i] : (m_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_value(c_bit2, s2) | m_counter_cell_v_carry_in(c_bit2, s2) | (~node2(c_bit2, s2))))),
% 35.73/23.59 inference(monotonicity,[status(thm)],[4771])).
% 35.73/23.59 tff(4773,plain,
% 35.73/23.59 (((~![I0: $i, X: $i] : (m_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_value(c_bit2, s2) | m_counter_cell_v_carry_in(c_bit2, s2) | (~node2(c_bit2, s2)))),
% 35.73/23.59 inference(transitivity,[status(thm)],[4772, 4770])).
% 35.73/23.59 tff(4774,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4775,plain,
% 35.73/23.59 ((~![I0: $i, 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, s2) | m_counter_cell_v_carry_in(c_bit2, s2) | (~node2(c_bit2, s2))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4774, 4773])).
% 35.73/23.59 tff(4776,plain,
% 35.73/23.59 (m_counter_cell_v_value(c_bit2, s2) | (~node2(c_bit2, s2))),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4775, 3291, 4769])).
% 35.73/23.59 tff(4777,plain,
% 35.73/23.59 (~node2(c_bit2, s2)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4776, 4754])).
% 35.73/23.59 tff(4778,plain,
% 35.73/23.59 (((~![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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4779,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s2, s3)) | node3(c_bit2, s2, s3))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4780,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s2, s3)) | node3(c_bit2, s2, s3)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4779, 4778])).
% 35.73/23.59 tff(4781,plain,
% 35.73/23.59 (node3(c_bit2, s2, s3)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4780, 81, 125])).
% 35.73/23.59 tff(4782,plain,
% 35.73/23.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s2) | (~node3(c_bit2, s2, s3)) | (~m_counter_cell_v_value(c_bit2, s3)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | node2(c_bit2, s2) | (~node3(c_bit2, s2, s3)) | (~m_counter_cell_v_value(c_bit2, s3)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4783,plain,
% 35.73/23.59 ((~![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)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4784,plain,
% 35.73/23.59 ((~![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))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4783, 4782])).
% 35.73/23.59 tff(4785,plain,
% 35.73/23.59 (node2(c_bit2, s2) | (~m_counter_cell_v_value(c_bit2, s3))),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4784, 234, 4781])).
% 35.73/23.59 tff(4786,plain,
% 35.73/23.59 (~m_counter_cell_v_value(c_bit2, s3)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4785, 4777])).
% 35.73/23.59 tff(4787,plain,
% 35.73/23.59 (((~![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, 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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4788,plain,
% 35.73/23.59 ((~![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, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4789,plain,
% 35.73/23.59 ((~![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, s3)) | (~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4788, 4787])).
% 35.73/23.59 tff(4790,plain,
% 35.73/23.59 ((~m_counter_cell_v_value(c_bit1, s3)) | m_counter_cell_v_carry_out(c_bit1, s3)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4789, 3031, 3388])).
% 35.73/23.59 tff(4791,plain,
% 35.73/23.59 (m_counter_cell_v_carry_out(c_bit1, s3)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4790, 4663])).
% 35.73/23.59 tff(4792,plain,
% 35.73/23.59 (((~![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, 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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4793,plain,
% 35.73/23.59 ((~![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, s3)) | m_counter_cell_v_carry_in(c_bit2, s3))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4794,plain,
% 35.73/23.59 ((~![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, s3)) | m_counter_cell_v_carry_in(c_bit2, s3)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4793, 4792])).
% 35.73/23.59 tff(4795,plain,
% 35.73/23.59 (m_counter_cell_v_carry_in(c_bit2, s3)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4794, 4417, 4791])).
% 35.73/23.59 tff(4796,plain,
% 35.73/23.59 (((~![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, 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)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4797,plain,
% 35.73/23.59 (((~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)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4798,plain,
% 35.73/23.59 (((~![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, 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))))),
% 35.73/23.59 inference(monotonicity,[status(thm)],[4797])).
% 35.73/23.59 tff(4799,plain,
% 35.73/23.59 (((~![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, 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)))),
% 35.73/23.59 inference(transitivity,[status(thm)],[4798, 4796])).
% 35.73/23.59 tff(4800,plain,
% 35.73/23.59 ((~![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, s3)) | (~m_counter_cell_v_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4801,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s3)) | m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4800, 4799])).
% 35.73/23.59 tff(4802,plain,
% 35.73/23.59 (m_counter_cell_v_value(c_bit2, s3) | (~node1(c_bit2, s3))),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4801, 170, 4795])).
% 35.73/23.59 tff(4803,plain,
% 35.73/23.59 ($false),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4802, 4786, 4631])).
% 35.73/23.59 tff(4804,plain,(m_counter_cell_v_value(c_bit1, s5) | (~node1(c_bit2, s5))), inference(lemma,lemma(discharge,[]))).
% 35.73/23.59 tff(4805,plain,
% 35.73/23.59 (~node1(c_bit2, s5)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4804, 3434])).
% 35.73/23.59 tff(4806,plain,
% 35.73/23.59 (((~![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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4807,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s5, s6)) | node3(c_bit2, s5, s6))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4808,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s5, s6)) | node3(c_bit2, s5, s6)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4807, 4806])).
% 35.73/23.59 tff(4809,plain,
% 35.73/23.59 (node3(c_bit2, s5, s6)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4808, 81, 92])).
% 35.73/23.59 tff(4810,plain,
% 35.73/23.59 (((~![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, 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)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4811,plain,
% 35.73/23.59 ((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)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4812,plain,
% 35.73/23.59 (((~![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))))),
% 35.73/23.59 inference(monotonicity,[status(thm)],[4811])).
% 35.73/23.59 tff(4813,plain,
% 35.73/23.59 (((~![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)))),
% 35.73/23.59 inference(transitivity,[status(thm)],[4812, 4810])).
% 35.73/23.59 tff(4814,plain,
% 35.73/23.59 ((~![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))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4815,plain,
% 35.73/23.59 ((~![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, s6) | node1(c_bit2, s5) | (~node3(c_bit2, s5, s6))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4814, 4813])).
% 35.73/23.59 tff(4816,plain,
% 35.73/23.59 (m_counter_cell_v_value(c_bit2, s6) | node1(c_bit2, s5)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4815, 199, 4809])).
% 35.73/23.59 tff(4817,plain,
% 35.73/23.59 (m_counter_cell_v_value(c_bit2, s6)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4816, 4805])).
% 35.73/23.59 tff(4818,plain,
% 35.73/23.59 (((~![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, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4819,plain,
% 35.73/23.59 (((~node1(c_bit2, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6))) <=> (m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4820,plain,
% 35.73/23.59 (((~![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, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6))))),
% 35.73/23.59 inference(monotonicity,[status(thm)],[4819])).
% 35.73/23.59 tff(4821,plain,
% 35.73/23.59 (((~![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, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6)))),
% 35.73/23.59 inference(transitivity,[status(thm)],[4820, 4818])).
% 35.73/23.59 tff(4822,plain,
% 35.73/23.59 ((~![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, s6)) | m_counter_cell_v_carry_in(c_bit2, s6) | (~m_counter_cell_v_value(c_bit2, s6)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4823,plain,
% 35.73/23.59 ((~![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, s6) | (~m_counter_cell_v_value(c_bit2, s6)) | (~node1(c_bit2, s6))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4822, 4821])).
% 35.73/23.59 tff(4824,plain,
% 35.73/23.59 (m_counter_cell_v_carry_in(c_bit2, s6) | (~node1(c_bit2, s6))),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4823, 3359, 4817])).
% 35.73/23.59 tff(4825,plain,
% 35.73/23.59 (~node1(c_bit2, s6)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4824, 4565])).
% 35.73/23.59 tff(4826,plain,
% 35.73/23.59 (((~![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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4827,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s6, s7)) | node3(c_bit2, s6, s7))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4828,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s6, s7)) | node3(c_bit2, s6, s7)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4827, 4826])).
% 35.73/23.59 tff(4829,plain,
% 35.73/23.59 (node3(c_bit2, s6, s7)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4828, 81, 321])).
% 35.73/23.59 tff(4830,plain,
% 35.73/23.59 (((~![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, s7) | node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s7) | node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4831,plain,
% 35.73/23.59 ((node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)) | m_counter_cell_v_value(c_bit2, s7)) <=> (m_counter_cell_v_value(c_bit2, s7) | node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4832,plain,
% 35.73/23.59 (((~![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))) | (m_counter_cell_v_value(c_bit2, s7) | node1(c_bit2, s6) | (~node3(c_bit2, s6, s7))))),
% 35.73/23.59 inference(monotonicity,[status(thm)],[4831])).
% 35.73/23.59 tff(4833,plain,
% 35.73/23.59 (((~![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))) | m_counter_cell_v_value(c_bit2, s7) | node1(c_bit2, s6) | (~node3(c_bit2, s6, s7)))),
% 35.73/23.59 inference(transitivity,[status(thm)],[4832, 4830])).
% 35.73/23.59 tff(4834,plain,
% 35.73/23.59 ((~![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))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4835,plain,
% 35.73/23.59 ((~![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, s7) | node1(c_bit2, s6) | (~node3(c_bit2, s6, s7))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4834, 4833])).
% 35.73/23.59 tff(4836,plain,
% 35.73/23.59 (m_counter_cell_v_value(c_bit2, s7) | node1(c_bit2, s6)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4835, 199, 4829])).
% 35.73/23.59 tff(4837,plain,
% 35.73/23.59 (m_counter_cell_v_value(c_bit2, s7)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4836, 4825])).
% 35.73/23.59 tff(4838,plain,
% 35.73/23.59 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4839,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4840,plain,
% 35.73/23.59 ((~![I0: $i, X: $i] : ((~m_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))),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4839, 4838])).
% 35.73/23.59 tff(4841,plain,
% 35.73/23.59 ((~m_counter_cell_v_carry_in(c_bit2, s7)) | (~node2(c_bit2, s7))),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4840, 219, 4837])).
% 35.73/23.59 tff(4842,plain,
% 35.73/23.59 (~node2(c_bit2, s7)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4841, 4551])).
% 35.73/23.59 tff(4843,plain,
% 35.73/23.59 (((~![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))),
% 35.73/23.59 inference(rewrite,[status(thm)],[])).
% 35.73/23.59 tff(4844,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s7, s8)) | node3(c_bit2, s7, s8))),
% 35.73/23.59 inference(quant_inst,[status(thm)],[])).
% 35.73/23.59 tff(4845,plain,
% 35.73/23.59 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s7, s8)) | node3(c_bit2, s7, s8)),
% 35.73/23.59 inference(modus_ponens,[status(thm)],[4844, 4843])).
% 35.73/23.59 tff(4846,plain,
% 35.73/23.59 (node3(c_bit2, s7, s8)),
% 35.73/23.59 inference(unit_resolution,[status(thm)],[4845, 81, 349])).
% 35.73/23.59 tff(4847,plain,
% 35.73/23.59 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s8)) | node2(c_bit2, s7) | (~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)))) | (~m_counter_cell_v_value(c_bit2, s8)) | node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4848,plain,
% 35.73/23.60 ((node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | (~m_counter_cell_v_value(c_bit2, s8))) <=> ((~m_counter_cell_v_value(c_bit2, s8)) | node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4849,plain,
% 35.73/23.60 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | (~m_counter_cell_v_value(c_bit2, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s8)) | node2(c_bit2, s7) | (~node3(c_bit2, s7, s8))))),
% 35.73/23.60 inference(monotonicity,[status(thm)],[4848])).
% 35.73/23.60 tff(4850,plain,
% 35.73/23.60 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)) | (~m_counter_cell_v_value(c_bit2, s8)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s8)) | node2(c_bit2, s7) | (~node3(c_bit2, s7, s8)))),
% 35.73/23.60 inference(transitivity,[status(thm)],[4849, 4847])).
% 35.73/23.60 tff(4851,plain,
% 35.73/23.60 ((~![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)))),
% 35.73/23.60 inference(quant_inst,[status(thm)],[])).
% 35.73/23.60 tff(4852,plain,
% 35.73/23.60 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s8)) | node2(c_bit2, s7) | (~node3(c_bit2, s7, s8))),
% 35.73/23.60 inference(modus_ponens,[status(thm)],[4851, 4850])).
% 35.73/23.60 tff(4853,plain,
% 35.73/23.60 ((~m_counter_cell_v_value(c_bit2, s8)) | node2(c_bit2, s7)),
% 35.73/23.60 inference(unit_resolution,[status(thm)],[4852, 234, 4846])).
% 35.73/23.60 tff(4854,plain,
% 35.73/23.60 (~m_counter_cell_v_value(c_bit2, s8)),
% 35.73/23.60 inference(unit_resolution,[status(thm)],[4853, 4842])).
% 35.73/23.60 tff(4855,plain,
% 35.73/23.60 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | (~node4(c_bit1, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s8) | (~node4(c_bit1, s8)))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4856,plain,
% 35.73/23.60 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s8) | (~node4(c_bit1, s8)))),
% 35.73/23.60 inference(quant_inst,[status(thm)],[])).
% 35.73/23.60 tff(4857,plain,
% 35.73/23.60 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s8) | (~node4(c_bit1, s8))),
% 35.73/23.60 inference(modus_ponens,[status(thm)],[4856, 4855])).
% 35.73/23.60 tff(4858,plain,
% 35.73/23.60 (~node4(c_bit1, s8)),
% 35.73/23.60 inference(unit_resolution,[status(thm)],[4857, 3076, 3503])).
% 35.73/23.60 tff(4859,plain,
% 35.73/23.60 (((~![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))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4860,plain,
% 35.73/23.60 ((~![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))),
% 35.73/23.60 inference(quant_inst,[status(thm)],[])).
% 35.73/23.60 tff(4861,plain,
% 35.73/23.60 ((~![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)),
% 35.73/23.60 inference(modus_ponens,[status(thm)],[4860, 4859])).
% 35.73/23.60 tff(4862,plain,
% 35.73/23.60 (~m_counter_cell_v_carry_out(c_bit1, s8)),
% 35.73/23.60 inference(unit_resolution,[status(thm)],[4861, 2887, 4858])).
% 35.73/23.60 tff(4863,plain,
% 35.73/23.60 (((~![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))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4864,plain,
% 35.73/23.60 ((~![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))),
% 35.73/23.60 inference(quant_inst,[status(thm)],[])).
% 35.73/23.60 tff(4865,plain,
% 35.73/23.60 ((~![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)),
% 35.73/23.60 inference(modus_ponens,[status(thm)],[4864, 4863])).
% 35.73/23.60 tff(4866,plain,
% 35.73/23.60 (~m_counter_cell_v_carry_in(c_bit2, s8)),
% 35.73/23.60 inference(unit_resolution,[status(thm)],[4865, 3167, 4862])).
% 35.73/23.60 tff(4867,plain,
% 35.73/23.60 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s8) | m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s8) | m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8)))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4868,plain,
% 35.73/23.60 ((~![I0: $i, X: $i] : (m_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)))),
% 35.73/23.60 inference(quant_inst,[status(thm)],[])).
% 35.73/23.60 tff(4869,plain,
% 35.73/23.60 ((~![I0: $i, X: $i] : (m_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))),
% 35.73/23.60 inference(modus_ponens,[status(thm)],[4868, 4867])).
% 35.73/23.60 tff(4870,plain,
% 35.73/23.60 (m_counter_cell_v_value(c_bit2, s8) | (~node2(c_bit2, s8))),
% 35.73/23.60 inference(unit_resolution,[status(thm)],[4869, 3291, 4866])).
% 35.73/23.60 tff(4871,plain,
% 35.73/23.60 (~node2(c_bit2, s8)),
% 35.73/23.60 inference(unit_resolution,[status(thm)],[4870, 4854])).
% 35.73/23.60 tff(4872,plain,
% 35.73/23.60 (((~![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))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4873,plain,
% 35.73/23.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s8, s9)) | node3(c_bit2, s8, s9))),
% 35.73/23.60 inference(quant_inst,[status(thm)],[])).
% 35.73/23.60 tff(4874,plain,
% 35.73/23.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s8, s9)) | node3(c_bit2, s8, s9)),
% 35.73/23.60 inference(modus_ponens,[status(thm)],[4873, 4872])).
% 35.73/23.60 tff(4875,plain,
% 35.73/23.60 (node3(c_bit2, s8, s9)),
% 35.73/23.60 inference(unit_resolution,[status(thm)],[4874, 81, 378])).
% 35.73/23.60 tff(4876,plain,
% 35.73/23.60 (((~![Y: $i, 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)))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4877,plain,
% 35.73/23.60 ((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)))),
% 35.73/23.60 inference(rewrite,[status(thm)],[])).
% 35.73/23.60 tff(4878,plain,
% 35.73/23.60 (((~![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))))),
% 35.73/23.60 inference(monotonicity,[status(thm)],[4877])).
% 35.73/23.60 tff(4879,plain,
% 35.73/23.60 (((~![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)))),
% 35.79/23.60 inference(transitivity,[status(thm)],[4878, 4876])).
% 35.79/23.60 tff(4880,plain,
% 35.79/23.60 ((~![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)))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4881,plain,
% 35.79/23.60 ((~![Y: $i, 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))),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4880, 4879])).
% 35.79/23.60 tff(4882,plain,
% 35.79/23.60 ((~m_counter_cell_v_value(c_bit2, s9)) | node2(c_bit2, s8)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4881, 234, 4875])).
% 35.79/23.60 tff(4883,plain,
% 35.79/23.60 (~m_counter_cell_v_value(c_bit2, s9)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4882, 4871])).
% 35.79/23.60 tff(4884,plain,
% 35.79/23.60 (((~![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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4885,plain,
% 35.79/23.60 ((~![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)))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4886,plain,
% 35.79/23.60 ((~![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))),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4885, 4884])).
% 35.79/23.60 tff(4887,plain,
% 35.79/23.60 (~node4(c_bit1, s9)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4886, 2875, 3520])).
% 35.79/23.60 tff(4888,plain,
% 35.79/23.60 (((~![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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4889,plain,
% 35.79/23.60 ((~![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))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4890,plain,
% 35.79/23.60 ((~![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)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4889, 4888])).
% 35.79/23.60 tff(4891,plain,
% 35.79/23.60 (~m_counter_cell_v_carry_out(c_bit1, s9)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4890, 2887, 4887])).
% 35.79/23.60 tff(4892,plain,
% 35.79/23.60 (((~![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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4893,plain,
% 35.79/23.60 ((~![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))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4894,plain,
% 35.79/23.60 ((~![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)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4893, 4892])).
% 35.79/23.60 tff(4895,plain,
% 35.79/23.60 (~m_counter_cell_v_carry_in(c_bit2, s9)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4894, 3167, 4891])).
% 35.79/23.60 tff(4896,plain,
% 35.79/23.60 (((~![I0: $i, X: $i] : (m_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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4897,plain,
% 35.79/23.60 ((~![I0: $i, X: $i] : (m_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)))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4898,plain,
% 35.79/23.60 ((~![I0: $i, X: $i] : (m_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))),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4897, 4896])).
% 35.79/23.60 tff(4899,plain,
% 35.79/23.60 (m_counter_cell_v_value(c_bit2, s9) | (~node2(c_bit2, s9))),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4898, 3291, 4895])).
% 35.79/23.60 tff(4900,plain,
% 35.79/23.60 (~node2(c_bit2, s9)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4899, 4883])).
% 35.79/23.60 tff(4901,plain,
% 35.79/23.60 (((~![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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4902,plain,
% 35.79/23.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s9, s10)) | node3(c_bit2, s9, s10))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4903,plain,
% 35.79/23.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s9, s10)) | node3(c_bit2, s9, s10)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 35.79/23.60 tff(4904,plain,
% 35.79/23.60 (node3(c_bit2, s9, s10)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4903, 81, 404])).
% 35.79/23.60 tff(4905,plain,
% 35.79/23.60 (((~![Y: $i, 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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4906,plain,
% 35.79/23.60 ((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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4907,plain,
% 35.79/23.60 (((~![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))))),
% 35.79/23.60 inference(monotonicity,[status(thm)],[4906])).
% 35.79/23.60 tff(4908,plain,
% 35.79/23.60 (((~![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)))),
% 35.79/23.60 inference(transitivity,[status(thm)],[4907, 4905])).
% 35.79/23.60 tff(4909,plain,
% 35.79/23.60 ((~![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)))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4910,plain,
% 35.79/23.60 ((~![Y: $i, 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))),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4909, 4908])).
% 35.79/23.60 tff(4911,plain,
% 35.79/23.60 ((~m_counter_cell_v_value(c_bit2, s10)) | node2(c_bit2, s9)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4910, 234, 4904])).
% 35.79/23.60 tff(4912,plain,
% 35.79/23.60 (~m_counter_cell_v_value(c_bit2, s10)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4911, 4900])).
% 35.79/23.60 tff(4913,assumption,(node4(c_bit1, s10)), introduced(assumption)).
% 35.79/23.60 tff(4914,plain,
% 35.79/23.60 (((~![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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4915,plain,
% 35.79/23.60 ((~![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)))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4916,plain,
% 35.79/23.60 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s10) | (~node4(c_bit1, s10))),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4915, 4914])).
% 35.79/23.60 tff(4917,plain,
% 35.79/23.60 ($false),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4916, 3076, 3226, 4913])).
% 35.79/23.60 tff(4918,plain,(~node4(c_bit1, s10)), inference(lemma,lemma(discharge,[]))).
% 35.79/23.60 tff(4919,plain,
% 35.79/23.60 (((~![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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4920,plain,
% 35.79/23.60 ((~![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))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4921,plain,
% 35.79/23.60 ((~![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)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4920, 4919])).
% 35.79/23.60 tff(4922,plain,
% 35.79/23.60 (~m_counter_cell_v_carry_out(c_bit1, s10)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4921, 2887, 4918])).
% 35.79/23.60 tff(4923,assumption,(m_counter_cell_v_carry_in(c_bit2, s10)), introduced(assumption)).
% 35.79/23.60 tff(4924,assumption,(~m_counter_cell_v_carry_out(c_bit1, s10)), introduced(assumption)).
% 35.79/23.60 tff(4925,plain,
% 35.79/23.60 (((~![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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4926,plain,
% 35.79/23.60 ((~![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))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4927,plain,
% 35.79/23.60 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s10)) | m_counter_cell_v_carry_out(c_bit1, s10)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4926, 4925])).
% 35.79/23.60 tff(4928,plain,
% 35.79/23.60 ($false),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4927, 3167, 4924, 4923])).
% 35.79/23.60 tff(4929,plain,((~m_counter_cell_v_carry_in(c_bit2, s10)) | m_counter_cell_v_carry_out(c_bit1, s10)), inference(lemma,lemma(discharge,[]))).
% 35.79/23.60 tff(4930,plain,
% 35.79/23.60 (~m_counter_cell_v_carry_in(c_bit2, s10)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4929, 4922])).
% 35.79/23.60 tff(4931,plain,
% 35.79/23.60 (((~![I0: $i, X: $i] : (m_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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4932,plain,
% 35.79/23.60 ((~![I0: $i, X: $i] : (m_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)))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4933,plain,
% 35.79/23.60 ((~![I0: $i, X: $i] : (m_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))),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4932, 4931])).
% 35.79/23.60 tff(4934,plain,
% 35.79/23.60 (m_counter_cell_v_value(c_bit2, s10) | (~node2(c_bit2, s10))),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4933, 3291, 4930])).
% 35.79/23.60 tff(4935,plain,
% 35.79/23.60 (~node2(c_bit2, s10)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4934, 4912])).
% 35.79/23.60 tff(4936,plain,
% 35.79/23.60 (((~![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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4937,plain,
% 35.79/23.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s10, s11)) | node3(c_bit2, s10, s11))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4938,plain,
% 35.79/23.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s10, s11)) | node3(c_bit2, s10, s11)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4937, 4936])).
% 35.79/23.60 tff(4939,plain,
% 35.79/23.60 (node3(c_bit2, s10, s11)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4938, 81, 435])).
% 35.79/23.60 tff(4940,plain,
% 35.79/23.60 (((~![Y: $i, 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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4941,plain,
% 35.79/23.60 ((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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4942,plain,
% 35.79/23.60 (((~![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))))),
% 35.79/23.60 inference(monotonicity,[status(thm)],[4941])).
% 35.79/23.60 tff(4943,plain,
% 35.79/23.60 (((~![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)))),
% 35.79/23.60 inference(transitivity,[status(thm)],[4942, 4940])).
% 35.79/23.60 tff(4944,plain,
% 35.79/23.60 ((~![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)))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4945,plain,
% 35.79/23.60 ((~![Y: $i, 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))),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4944, 4943])).
% 35.79/23.60 tff(4946,plain,
% 35.79/23.60 ((~m_counter_cell_v_value(c_bit2, s11)) | node2(c_bit2, s10)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4945, 234, 4939])).
% 35.79/23.60 tff(4947,plain,
% 35.79/23.60 (~m_counter_cell_v_value(c_bit2, s11)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4946, 4935])).
% 35.79/23.60 tff(4948,assumption,(~m_counter_cell_v_carry_in(c_bit2, s11)), introduced(assumption)).
% 35.79/23.60 tff(4949,assumption,(~m_counter_cell_v_carry_out(c_bit1, s11)), introduced(assumption)).
% 35.79/23.60 tff(4950,plain,
% 35.79/23.60 (((~![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_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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4951,plain,
% 35.79/23.60 ((~![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_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | m_counter_cell_v_carry_out(c_bit1, s11))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4952,plain,
% 35.79/23.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s11)) | (~m_counter_cell_v_value(c_bit1, s11)) | m_counter_cell_v_carry_out(c_bit1, s11)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4951, 4950])).
% 35.79/23.60 tff(4953,plain,
% 35.79/23.60 ($false),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4952, 3031, 3590, 3588, 4949])).
% 35.79/23.60 tff(4954,plain,(m_counter_cell_v_carry_out(c_bit1, s11) | (~m_counter_cell_v_value(c_bit1, s11)) | (~m_counter_cell_v_carry_in(c_bit1, s11))), inference(lemma,lemma(discharge,[]))).
% 35.79/23.60 tff(4955,plain,
% 35.79/23.60 (m_counter_cell_v_carry_out(c_bit1, s11) | (~m_counter_cell_v_value(c_bit1, s11))),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4954, 3587])).
% 35.79/23.60 tff(4956,plain,
% 35.79/23.60 (m_counter_cell_v_carry_out(c_bit1, s11)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4955, 3574])).
% 35.79/23.60 tff(4957,plain,
% 35.79/23.60 (((~![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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4958,plain,
% 35.79/23.60 ((~![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))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4959,plain,
% 35.79/23.60 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s11)) | m_counter_cell_v_carry_in(c_bit2, s11)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4958, 4957])).
% 35.79/23.60 tff(4960,plain,
% 35.79/23.60 ($false),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4959, 4417, 4956, 4948])).
% 35.79/23.60 tff(4961,plain,(m_counter_cell_v_carry_in(c_bit2, s11)), inference(lemma,lemma(discharge,[]))).
% 35.79/23.60 tff(4962,plain,
% 35.79/23.60 (((~![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, 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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4963,plain,
% 35.79/23.60 (((~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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4964,plain,
% 35.79/23.60 (((~![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, 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))))),
% 35.79/23.60 inference(monotonicity,[status(thm)],[4963])).
% 35.79/23.60 tff(4965,plain,
% 35.79/23.60 (((~![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, 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)))),
% 35.79/23.60 inference(transitivity,[status(thm)],[4964, 4962])).
% 35.79/23.60 tff(4966,plain,
% 35.79/23.60 ((~![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, s11)) | (~m_counter_cell_v_carry_in(c_bit2, s11)) | m_counter_cell_v_value(c_bit2, s11))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4967,plain,
% 35.79/23.60 ((~![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, s11)) | m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11))),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4966, 4965])).
% 35.79/23.60 tff(4968,plain,
% 35.79/23.60 (m_counter_cell_v_value(c_bit2, s11) | (~node1(c_bit2, s11))),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4967, 170, 4961])).
% 35.79/23.60 tff(4969,plain,
% 35.79/23.60 (~node1(c_bit2, s11)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4968, 4947])).
% 35.79/23.60 tff(4970,plain,
% 35.79/23.60 (((~![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))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4971,plain,
% 35.79/23.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s11, s12)) | node3(c_bit2, s11, s12))),
% 35.79/23.60 inference(quant_inst,[status(thm)],[])).
% 35.79/23.60 tff(4972,plain,
% 35.79/23.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s11, s12)) | node3(c_bit2, s11, s12)),
% 35.79/23.60 inference(modus_ponens,[status(thm)],[4971, 4970])).
% 35.79/23.60 tff(4973,plain,
% 35.79/23.60 (node3(c_bit2, s11, s12)),
% 35.79/23.60 inference(unit_resolution,[status(thm)],[4972, 81, 463])).
% 35.79/23.60 tff(4974,plain,
% 35.79/23.60 (((~![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, 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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4975,plain,
% 35.79/23.60 ((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)))),
% 35.79/23.60 inference(rewrite,[status(thm)],[])).
% 35.79/23.60 tff(4976,plain,
% 35.79/23.60 (((~![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))))),
% 35.79/23.60 inference(monotonicity,[status(thm)],[4975])).
% 35.79/23.60 tff(4977,plain,
% 35.79/23.60 (((~![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)))),
% 35.79/23.61 inference(transitivity,[status(thm)],[4976, 4974])).
% 35.79/23.61 tff(4978,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(4979,plain,
% 35.79/23.61 ((~![Y: $i, 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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[4978, 4977])).
% 35.79/23.61 tff(4980,plain,
% 35.79/23.61 (m_counter_cell_v_value(c_bit2, s12) | node1(c_bit2, s11)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[4979, 199, 4973])).
% 35.79/23.61 tff(4981,plain,
% 35.79/23.61 (m_counter_cell_v_value(c_bit2, s12)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[4980, 4969])).
% 35.79/23.61 tff(4982,plain,
% 35.79/23.61 (((~![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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(4983,plain,
% 35.79/23.61 ((~![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)))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(4984,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[4983, 4982])).
% 35.79/23.61 tff(4985,plain,
% 35.79/23.61 (~node4(c_bit1, s12)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[4984, 3076, 3627])).
% 35.79/23.61 tff(4986,plain,
% 35.79/23.61 (((~![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))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(4987,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(4988,plain,
% 35.79/23.61 ((~![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)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[4987, 4986])).
% 35.79/23.61 tff(4989,plain,
% 35.79/23.61 (~m_counter_cell_v_carry_out(c_bit1, s12)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[4988, 2887, 4985])).
% 35.79/23.61 tff(4990,plain,
% 35.79/23.61 (((~![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))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(4991,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(4992,plain,
% 35.79/23.61 ((~![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)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[4991, 4990])).
% 35.79/23.61 tff(4993,plain,
% 35.79/23.61 (~m_counter_cell_v_carry_in(c_bit2, s12)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[4992, 3167, 4989])).
% 35.79/23.61 tff(4994,plain,
% 35.79/23.61 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(4995,plain,
% 35.79/23.61 (((~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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(4996,plain,
% 35.79/23.61 (((~![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))))),
% 35.79/23.61 inference(monotonicity,[status(thm)],[4995])).
% 35.79/23.61 tff(4997,plain,
% 35.79/23.61 (((~![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)))),
% 35.79/23.61 inference(transitivity,[status(thm)],[4996, 4994])).
% 35.79/23.61 tff(4998,plain,
% 35.79/23.61 ((~![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)))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(4999,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : ((~node1(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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 35.79/23.61 tff(5000,plain,
% 35.79/23.61 ((~m_counter_cell_v_value(c_bit2, s12)) | (~node1(c_bit2, s12))),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[4999, 3359, 4993])).
% 35.79/23.61 tff(5001,plain,
% 35.79/23.61 (~node1(c_bit2, s12)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5000, 4981])).
% 35.79/23.61 tff(5002,plain,
% 35.79/23.61 (((~![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))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5003,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s12, s13)) | node3(c_bit2, s12, s13))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5004,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s12, s13)) | node3(c_bit2, s12, s13)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5003, 5002])).
% 35.79/23.61 tff(5005,plain,
% 35.79/23.61 (node3(c_bit2, s12, s13)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5004, 81, 494])).
% 35.79/23.61 tff(5006,plain,
% 35.79/23.61 (((~![Y: $i, 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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5007,plain,
% 35.79/23.61 ((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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5008,plain,
% 35.79/23.61 (((~![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))))),
% 35.79/23.61 inference(monotonicity,[status(thm)],[5007])).
% 35.79/23.61 tff(5009,plain,
% 35.79/23.61 (((~![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)))),
% 35.79/23.61 inference(transitivity,[status(thm)],[5008, 5006])).
% 35.79/23.61 tff(5010,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5011,plain,
% 35.79/23.61 ((~![Y: $i, 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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5010, 5009])).
% 35.79/23.61 tff(5012,plain,
% 35.79/23.61 (m_counter_cell_v_value(c_bit2, s13) | node1(c_bit2, s12)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5011, 199, 5005])).
% 35.79/23.61 tff(5013,plain,
% 35.79/23.61 (m_counter_cell_v_value(c_bit2, s13)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5012, 5001])).
% 35.79/23.61 tff(5014,plain,
% 35.79/23.61 (((~![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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5015,plain,
% 35.79/23.61 ((~![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)))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5016,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5015, 5014])).
% 35.79/23.61 tff(5017,plain,
% 35.79/23.61 (~node4(c_bit1, s13)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5016, 2875, 3644])).
% 35.79/23.61 tff(5018,plain,
% 35.79/23.61 (((~![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))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5019,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5020,plain,
% 35.79/23.61 ((~![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)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5019, 5018])).
% 35.79/23.61 tff(5021,plain,
% 35.79/23.61 (~m_counter_cell_v_carry_out(c_bit1, s13)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5020, 2887, 5017])).
% 35.79/23.61 tff(5022,plain,
% 35.79/23.61 (((~![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))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5023,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5024,plain,
% 35.79/23.61 ((~![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)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5023, 5022])).
% 35.79/23.61 tff(5025,plain,
% 35.79/23.61 (~m_counter_cell_v_carry_in(c_bit2, s13)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5024, 3167, 5021])).
% 35.79/23.61 tff(5026,plain,
% 35.79/23.61 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5027,plain,
% 35.79/23.61 (((~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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5028,plain,
% 35.79/23.61 (((~![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))))),
% 35.79/23.61 inference(monotonicity,[status(thm)],[5027])).
% 35.79/23.61 tff(5029,plain,
% 35.79/23.61 (((~![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)))),
% 35.79/23.61 inference(transitivity,[status(thm)],[5028, 5026])).
% 35.79/23.61 tff(5030,plain,
% 35.79/23.61 ((~![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)))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5031,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : ((~node1(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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5030, 5029])).
% 35.79/23.61 tff(5032,plain,
% 35.79/23.61 ((~m_counter_cell_v_value(c_bit2, s13)) | (~node1(c_bit2, s13))),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5031, 3359, 5025])).
% 35.79/23.61 tff(5033,plain,
% 35.79/23.61 (~node1(c_bit2, s13)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5032, 5013])).
% 35.79/23.61 tff(5034,plain,
% 35.79/23.61 (((~![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))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5035,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s13, s14)) | node3(c_bit2, s13, s14))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5036,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s13, s14)) | node3(c_bit2, s13, s14)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5035, 5034])).
% 35.79/23.61 tff(5037,plain,
% 35.79/23.61 (node3(c_bit2, s13, s14)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5036, 81, 522])).
% 35.79/23.61 tff(5038,plain,
% 35.79/23.61 (((~![Y: $i, 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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5039,plain,
% 35.79/23.61 ((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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5040,plain,
% 35.79/23.61 (((~![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))))),
% 35.79/23.61 inference(monotonicity,[status(thm)],[5039])).
% 35.79/23.61 tff(5041,plain,
% 35.79/23.61 (((~![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)))),
% 35.79/23.61 inference(transitivity,[status(thm)],[5040, 5038])).
% 35.79/23.61 tff(5042,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5043,plain,
% 35.79/23.61 ((~![Y: $i, 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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5042, 5041])).
% 35.79/23.61 tff(5044,plain,
% 35.79/23.61 (m_counter_cell_v_value(c_bit2, s14) | node1(c_bit2, s13)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5043, 199, 5037])).
% 35.79/23.61 tff(5045,plain,
% 35.79/23.61 (m_counter_cell_v_value(c_bit2, s14)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5044, 5033])).
% 35.79/23.61 tff(5046,plain,
% 35.79/23.61 (((~![I0: $i, X: $i] : ((~node1(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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5047,plain,
% 35.79/23.61 (((~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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5048,plain,
% 35.79/23.61 (((~![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))))),
% 35.79/23.61 inference(monotonicity,[status(thm)],[5047])).
% 35.79/23.61 tff(5049,plain,
% 35.79/23.61 (((~![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)))),
% 35.79/23.61 inference(transitivity,[status(thm)],[5048, 5046])).
% 35.79/23.61 tff(5050,plain,
% 35.79/23.61 ((~![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)))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5051,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : ((~node1(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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5050, 5049])).
% 35.79/23.61 tff(5052,plain,
% 35.79/23.61 (m_counter_cell_v_carry_in(c_bit2, s14) | (~node1(c_bit2, s14))),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5051, 3359, 5045])).
% 35.79/23.61 tff(5053,plain,
% 35.79/23.61 (~node1(c_bit2, s14)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5052, 4541])).
% 35.79/23.61 tff(5054,plain,
% 35.79/23.61 (((~![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))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5055,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s14, s15)) | node3(c_bit2, s14, s15))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5056,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s14, s15)) | node3(c_bit2, s14, s15)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5055, 5054])).
% 35.79/23.61 tff(5057,plain,
% 35.79/23.61 (node3(c_bit2, s14, s15)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5056, 81, 553])).
% 35.79/23.61 tff(5058,plain,
% 35.79/23.61 (((~![Y: $i, 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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5059,plain,
% 35.79/23.61 ((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)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5060,plain,
% 35.79/23.61 (((~![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))))),
% 35.79/23.61 inference(monotonicity,[status(thm)],[5059])).
% 35.79/23.61 tff(5061,plain,
% 35.79/23.61 (((~![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)))),
% 35.79/23.61 inference(transitivity,[status(thm)],[5060, 5058])).
% 35.79/23.61 tff(5062,plain,
% 35.79/23.61 ((~![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))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5063,plain,
% 35.79/23.61 ((~![Y: $i, 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))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5062, 5061])).
% 35.79/23.61 tff(5064,plain,
% 35.79/23.61 (m_counter_cell_v_value(c_bit2, s15) | node1(c_bit2, s14)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5063, 199, 5057])).
% 35.79/23.61 tff(5065,plain,
% 35.79/23.61 (m_counter_cell_v_value(c_bit2, s15)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5064, 5053])).
% 35.79/23.61 tff(5066,plain,
% 35.79/23.61 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5067,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15)))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5068,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | (~node2(c_bit2, s15))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5067, 5066])).
% 35.79/23.61 tff(5069,plain,
% 35.79/23.61 ((~m_counter_cell_v_carry_in(c_bit2, s15)) | (~node2(c_bit2, s15))),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5068, 219, 5065])).
% 35.79/23.61 tff(5070,plain,
% 35.79/23.61 (~node2(c_bit2, s15)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5069, 4518])).
% 35.79/23.61 tff(5071,plain,
% 35.79/23.61 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit2, s15, s16))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit2, s15, s16))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5072,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s15, s16)) | node3(c_bit2, s15, s16))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5073,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s15, s16)) | node3(c_bit2, s15, s16)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5072, 5071])).
% 35.79/23.61 tff(5074,plain,
% 35.79/23.61 (node3(c_bit2, s15, s16)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5073, 81, 581])).
% 35.79/23.61 tff(5075,plain,
% 35.79/23.61 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5076,plain,
% 35.79/23.61 ((node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)) | (~m_counter_cell_v_value(c_bit2, s16))) <=> ((~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5077,plain,
% 35.79/23.61 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)) | (~m_counter_cell_v_value(c_bit2, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16))))),
% 35.79/23.61 inference(monotonicity,[status(thm)],[5076])).
% 35.79/23.61 tff(5078,plain,
% 35.79/23.61 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)) | (~m_counter_cell_v_value(c_bit2, s16)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)))),
% 35.79/23.61 inference(transitivity,[status(thm)],[5077, 5075])).
% 35.79/23.61 tff(5079,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s15) | (~node3(c_bit2, s15, s16)) | (~m_counter_cell_v_value(c_bit2, s16)))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5080,plain,
% 35.79/23.61 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15) | (~node3(c_bit2, s15, s16))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5079, 5078])).
% 35.79/23.61 tff(5081,plain,
% 35.79/23.61 ((~m_counter_cell_v_value(c_bit2, s16)) | node2(c_bit2, s15)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5080, 234, 5074])).
% 35.79/23.61 tff(5082,plain,
% 35.79/23.61 (~m_counter_cell_v_value(c_bit2, s16)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5081, 5070])).
% 35.79/23.61 tff(5083,plain,
% 35.79/23.61 (~node4(c_bit0, s16)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[3789, 2875, 593])).
% 35.79/23.61 tff(5084,plain,
% 35.79/23.61 (~m_counter_cell_v_carry_out(c_bit0, s16)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[3793, 2887, 5083])).
% 35.79/23.61 tff(5085,plain,
% 35.79/23.61 (~m_counter_cell_v_carry_in(c_bit1, s16)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[3797, 2901, 5084])).
% 35.79/23.61 tff(5086,plain,
% 35.79/23.61 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s16) | (~node4(c_bit1, s16)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s16) | (~node4(c_bit1, s16)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5087,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s16) | (~node4(c_bit1, s16)))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5088,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s16) | (~node4(c_bit1, s16))),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5087, 5086])).
% 35.79/23.61 tff(5089,plain,
% 35.79/23.61 (~node4(c_bit1, s16)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5088, 3076, 5085])).
% 35.79/23.61 tff(5090,plain,
% 35.79/23.61 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s16)) | node4(c_bit1, s16))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s16)) | node4(c_bit1, s16))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5091,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s16)) | node4(c_bit1, s16))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5092,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s16)) | node4(c_bit1, s16)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5091, 5090])).
% 35.79/23.61 tff(5093,plain,
% 35.79/23.61 (~m_counter_cell_v_carry_out(c_bit1, s16)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5092, 2887, 5089])).
% 35.79/23.61 tff(5094,plain,
% 35.79/23.61 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s16)) | m_counter_cell_v_carry_out(c_bit1, s16))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s16)) | m_counter_cell_v_carry_out(c_bit1, s16))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5095,plain,
% 35.79/23.61 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s16)) | m_counter_cell_v_carry_out(c_bit1, s16))),
% 35.79/23.61 inference(quant_inst,[status(thm)],[])).
% 35.79/23.61 tff(5096,plain,
% 35.79/23.61 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s16)) | m_counter_cell_v_carry_out(c_bit1, s16)),
% 35.79/23.61 inference(modus_ponens,[status(thm)],[5095, 5094])).
% 35.79/23.61 tff(5097,plain,
% 35.79/23.61 (~m_counter_cell_v_carry_in(c_bit2, s16)),
% 35.79/23.61 inference(unit_resolution,[status(thm)],[5096, 3167, 5093])).
% 35.79/23.61 tff(5098,plain,
% 35.79/23.61 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s16) | m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s16) | m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16)))),
% 35.79/23.61 inference(rewrite,[status(thm)],[])).
% 35.79/23.61 tff(5099,plain,
% 35.79/23.61 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s16) | m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5100,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s16) | m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5099, 5098])).
% 35.79/23.62 tff(5101,plain,
% 35.79/23.62 (m_counter_cell_v_value(c_bit2, s16) | (~node2(c_bit2, s16))),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5100, 3291, 5097])).
% 35.79/23.62 tff(5102,plain,
% 35.79/23.62 (~node2(c_bit2, s16)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5101, 5082])).
% 35.79/23.62 tff(5103,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit2, s16, s17))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit2, s16, s17))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5104,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s16, s17)) | node3(c_bit2, s16, s17))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5105,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s16, s17)) | node3(c_bit2, s16, s17)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5104, 5103])).
% 35.79/23.62 tff(5106,plain,
% 35.79/23.62 (node3(c_bit2, s16, s17)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5105, 81, 610])).
% 35.79/23.62 tff(5107,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5108,plain,
% 35.79/23.62 ((node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)) | (~m_counter_cell_v_value(c_bit2, s17))) <=> ((~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5109,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)) | (~m_counter_cell_v_value(c_bit2, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17))))),
% 35.79/23.62 inference(monotonicity,[status(thm)],[5108])).
% 35.79/23.62 tff(5110,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)) | (~m_counter_cell_v_value(c_bit2, s17)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)))),
% 35.79/23.62 inference(transitivity,[status(thm)],[5109, 5107])).
% 35.79/23.62 tff(5111,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s16) | (~node3(c_bit2, s16, s17)) | (~m_counter_cell_v_value(c_bit2, s17)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5112,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16) | (~node3(c_bit2, s16, s17))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5111, 5110])).
% 35.79/23.62 tff(5113,plain,
% 35.79/23.62 ((~m_counter_cell_v_value(c_bit2, s17)) | node2(c_bit2, s16)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5112, 234, 5106])).
% 35.79/23.62 tff(5114,plain,
% 35.79/23.62 (~m_counter_cell_v_value(c_bit2, s17)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5113, 5102])).
% 35.79/23.62 tff(5115,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s17) | m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s17) | m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5116,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s17) | m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5117,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s17) | m_counter_cell_v_value(c_bit2, s17) | (~node2(c_bit2, s17))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5116, 5115])).
% 35.79/23.62 tff(5118,plain,
% 35.79/23.62 (m_counter_cell_v_carry_in(c_bit2, s17) | (~node2(c_bit2, s17))),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5117, 3291, 5114])).
% 35.79/23.62 tff(5119,plain,
% 35.79/23.62 (~node2(c_bit2, s17)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5118, 4507])).
% 35.79/23.62 tff(5120,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit2, s17, s18))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit2, s17, s18))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5121,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s17, s18)) | node3(c_bit2, s17, s18))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5122,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s17, s18)) | node3(c_bit2, s17, s18)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5121, 5120])).
% 35.79/23.62 tff(5123,plain,
% 35.79/23.62 (node3(c_bit2, s17, s18)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5122, 81, 638])).
% 35.79/23.62 tff(5124,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5125,plain,
% 35.79/23.62 ((node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)) | (~m_counter_cell_v_value(c_bit2, s18))) <=> ((~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5126,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)) | (~m_counter_cell_v_value(c_bit2, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18))))),
% 35.79/23.62 inference(monotonicity,[status(thm)],[5125])).
% 35.79/23.62 tff(5127,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)) | (~m_counter_cell_v_value(c_bit2, s18)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)))),
% 35.79/23.62 inference(transitivity,[status(thm)],[5126, 5124])).
% 35.79/23.62 tff(5128,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s17) | (~node3(c_bit2, s17, s18)) | (~m_counter_cell_v_value(c_bit2, s18)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5129,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17) | (~node3(c_bit2, s17, s18))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5128, 5127])).
% 35.79/23.62 tff(5130,plain,
% 35.79/23.62 ((~m_counter_cell_v_value(c_bit2, s18)) | node2(c_bit2, s17)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5129, 234, 5123])).
% 35.79/23.62 tff(5131,plain,
% 35.79/23.62 (~m_counter_cell_v_value(c_bit2, s18)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5130, 5119])).
% 35.79/23.62 tff(5132,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s18) | m_counter_cell_v_value(c_bit2, s18) | (~node2(c_bit2, s18)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s18) | m_counter_cell_v_value(c_bit2, s18) | (~node2(c_bit2, s18)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5133,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s18) | m_counter_cell_v_value(c_bit2, s18) | (~node2(c_bit2, s18)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5134,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s18) | m_counter_cell_v_value(c_bit2, s18) | (~node2(c_bit2, s18))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5133, 5132])).
% 35.79/23.62 tff(5135,plain,
% 35.79/23.62 (~node2(c_bit2, s18)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5134, 3291, 5131, 4476])).
% 35.79/23.62 tff(5136,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit2, s18, s19))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit2, s18, s19))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5137,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s18, s19)) | node3(c_bit2, s18, s19))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5138,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s18, s19)) | node3(c_bit2, s18, s19)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5137, 5136])).
% 35.79/23.62 tff(5139,plain,
% 35.79/23.62 (node3(c_bit2, s18, s19)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5138, 81, 669])).
% 35.79/23.62 tff(5140,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5141,plain,
% 35.79/23.62 ((node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)) | (~m_counter_cell_v_value(c_bit2, s19))) <=> ((~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5142,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)) | (~m_counter_cell_v_value(c_bit2, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19))))),
% 35.79/23.62 inference(monotonicity,[status(thm)],[5141])).
% 35.79/23.62 tff(5143,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)) | (~m_counter_cell_v_value(c_bit2, s19)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)))),
% 35.79/23.62 inference(transitivity,[status(thm)],[5142, 5140])).
% 35.79/23.62 tff(5144,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s18) | (~node3(c_bit2, s18, s19)) | (~m_counter_cell_v_value(c_bit2, s19)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5145,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18) | (~node3(c_bit2, s18, s19))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5144, 5143])).
% 35.79/23.62 tff(5146,plain,
% 35.79/23.62 ((~m_counter_cell_v_value(c_bit2, s19)) | node2(c_bit2, s18)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5145, 234, 5139])).
% 35.79/23.62 tff(5147,plain,
% 35.79/23.62 (~m_counter_cell_v_value(c_bit2, s19)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5146, 5135])).
% 35.79/23.62 tff(5148,assumption,(m_counter_cell_v_value(c_bit1, s18)), introduced(assumption)).
% 35.79/23.62 tff(5149,plain,
% 35.79/23.62 (((~![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, s18)) | (~m_counter_cell_v_value(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s18)) | (~m_counter_cell_v_value(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5150,plain,
% 35.79/23.62 ((~![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, s18)) | (~m_counter_cell_v_value(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit1, s18))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5151,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s18)) | (~m_counter_cell_v_value(c_bit1, s18)) | m_counter_cell_v_carry_out(c_bit1, s18)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5150, 5149])).
% 35.79/23.62 tff(5152,plain,
% 35.79/23.62 ($false),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5151, 3031, 5148, 3182, 4469])).
% 35.79/23.62 tff(5153,plain,(m_counter_cell_v_carry_out(c_bit1, s18) | (~m_counter_cell_v_value(c_bit1, s18)) | (~m_counter_cell_v_carry_in(c_bit1, s18))), inference(lemma,lemma(discharge,[]))).
% 35.79/23.62 tff(5154,plain,
% 35.79/23.62 (~m_counter_cell_v_carry_in(c_bit1, s18)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5153, 4480, 4469])).
% 35.79/23.62 tff(5155,plain,
% 35.79/23.62 (~node1(c_bit1, s18)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[3819, 3359, 4480, 5154])).
% 35.79/23.62 tff(5156,plain,
% 35.79/23.62 (m_counter_cell_v_value(c_bit1, s19)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[3832, 5155])).
% 35.79/23.62 tff(5157,plain,
% 35.79/23.62 (((~![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, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5158,plain,
% 35.79/23.62 ((~![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, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5159,plain,
% 35.79/23.62 ((~![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, s19)) | (~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5158, 5157])).
% 35.79/23.62 tff(5160,plain,
% 35.79/23.62 ((~m_counter_cell_v_value(c_bit1, s19)) | m_counter_cell_v_carry_out(c_bit1, s19)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5159, 3031, 3842])).
% 35.79/23.62 tff(5161,plain,
% 35.79/23.62 (m_counter_cell_v_carry_out(c_bit1, s19)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5160, 5156])).
% 35.79/23.62 tff(5162,plain,
% 35.79/23.62 (((~![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, s19)) | m_counter_cell_v_carry_in(c_bit2, s19))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s19)) | m_counter_cell_v_carry_in(c_bit2, s19))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5163,plain,
% 35.79/23.62 ((~![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, s19)) | m_counter_cell_v_carry_in(c_bit2, s19))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5164,plain,
% 35.79/23.62 ((~![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, s19)) | m_counter_cell_v_carry_in(c_bit2, s19)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5163, 5162])).
% 35.79/23.62 tff(5165,plain,
% 35.79/23.62 (m_counter_cell_v_carry_in(c_bit2, s19)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5164, 4417, 5161])).
% 35.79/23.62 tff(5166,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5167,plain,
% 35.79/23.62 (((~node1(c_bit2, s19)) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5168,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s19)) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19))))),
% 35.79/23.62 inference(monotonicity,[status(thm)],[5167])).
% 35.79/23.62 tff(5169,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s19)) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19)))),
% 35.79/23.62 inference(transitivity,[status(thm)],[5168, 5166])).
% 35.79/23.62 tff(5170,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s19)) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5171,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s19)) | m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5170, 5169])).
% 35.79/23.62 tff(5172,plain,
% 35.79/23.62 (m_counter_cell_v_value(c_bit2, s19) | (~node1(c_bit2, s19))),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5171, 170, 5165])).
% 35.79/23.62 tff(5173,plain,
% 35.79/23.62 (~node1(c_bit2, s19)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5172, 5147])).
% 35.79/23.62 tff(5174,plain,
% 35.79/23.62 (~node2(c_bit1, s19)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[3846, 5156])).
% 35.79/23.62 tff(5175,plain,
% 35.79/23.62 (~m_counter_cell_v_value(c_bit1, s20)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[3858, 5174])).
% 35.79/23.62 tff(5176,plain,
% 35.79/23.62 (~node2(c_bit1, s20)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[3875, 5175])).
% 35.79/23.62 tff(5177,plain,
% 35.79/23.62 (~m_counter_cell_v_value(c_bit1, s21)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[3887, 5176])).
% 35.79/23.62 tff(5178,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s21) | (~node4(c_bit1, s21)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s21) | (~node4(c_bit1, s21)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5179,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s21) | (~node4(c_bit1, s21)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5180,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s21) | (~node4(c_bit1, s21))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5179, 5178])).
% 35.79/23.62 tff(5181,plain,
% 35.79/23.62 (~node4(c_bit1, s21)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5180, 2875, 5177])).
% 35.79/23.62 tff(5182,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s21)) | node4(c_bit1, s21))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s21)) | node4(c_bit1, s21))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5183,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s21)) | node4(c_bit1, s21))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5184,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s21)) | node4(c_bit1, s21)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5183, 5182])).
% 35.79/23.62 tff(5185,plain,
% 35.79/23.62 (~m_counter_cell_v_carry_out(c_bit1, s21)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5184, 2887, 5181])).
% 35.79/23.62 tff(5186,plain,
% 35.79/23.62 (((~![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, s21)) | m_counter_cell_v_carry_out(c_bit1, s21))) <=> ((~![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, s21)) | m_counter_cell_v_carry_out(c_bit1, s21))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5187,plain,
% 35.79/23.62 ((~![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, s21)) | m_counter_cell_v_carry_out(c_bit1, s21))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5188,plain,
% 35.79/23.62 ((~![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, s21)) | m_counter_cell_v_carry_out(c_bit1, s21)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5187, 5186])).
% 35.79/23.62 tff(5189,plain,
% 35.79/23.62 (~m_counter_cell_v_carry_in(c_bit2, s21)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5188, 3167, 5185])).
% 35.79/23.62 tff(5190,assumption,(node1(c_bit2, s21)), introduced(assumption)).
% 35.79/23.62 tff(5191,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5192,plain,
% 35.79/23.62 (((~node1(c_bit2, s21)) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21))) <=> (m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5193,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s21)) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21))))),
% 35.79/23.62 inference(monotonicity,[status(thm)],[5192])).
% 35.79/23.62 tff(5194,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s21)) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21)))),
% 35.79/23.62 inference(transitivity,[status(thm)],[5193, 5191])).
% 35.79/23.62 tff(5195,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s21)) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5196,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21)) | (~node1(c_bit2, s21))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5195, 5194])).
% 35.79/23.62 tff(5197,plain,
% 35.79/23.62 (m_counter_cell_v_carry_in(c_bit2, s21) | (~m_counter_cell_v_value(c_bit2, s21))),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5196, 3359, 5190])).
% 35.79/23.62 tff(5198,plain,
% 35.79/23.62 (~m_counter_cell_v_value(c_bit2, s21)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5197, 5189])).
% 35.79/23.62 tff(5199,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit2, s20, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit2, s20, s21))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5200,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s20, s21)) | node3(c_bit2, s20, s21))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5201,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s20, s21)) | node3(c_bit2, s20, s21)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5200, 5199])).
% 35.79/23.62 tff(5202,plain,
% 35.79/23.62 (node3(c_bit2, s20, s21)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5201, 81, 726])).
% 35.79/23.62 tff(5203,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5204,plain,
% 35.79/23.62 ((node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)) | m_counter_cell_v_value(c_bit2, s21)) <=> (m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5205,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)) | m_counter_cell_v_value(c_bit2, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21))))),
% 35.79/23.62 inference(monotonicity,[status(thm)],[5204])).
% 35.79/23.62 tff(5206,plain,
% 35.79/23.62 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)) | m_counter_cell_v_value(c_bit2, s21))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)))),
% 35.79/23.62 inference(transitivity,[status(thm)],[5205, 5203])).
% 35.79/23.62 tff(5207,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s20) | (~node3(c_bit2, s20, s21)) | m_counter_cell_v_value(c_bit2, s21))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5208,plain,
% 35.79/23.62 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20) | (~node3(c_bit2, s20, s21))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5207, 5206])).
% 35.79/23.62 tff(5209,plain,
% 35.79/23.62 (m_counter_cell_v_value(c_bit2, s21) | node1(c_bit2, s20)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5208, 199, 5202])).
% 35.79/23.62 tff(5210,plain,
% 35.79/23.62 (node1(c_bit2, s20)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5209, 5198])).
% 35.79/23.62 tff(5211,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s20) | (~node4(c_bit1, s20)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s20) | (~node4(c_bit1, s20)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5212,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s20) | (~node4(c_bit1, s20)))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5213,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s20) | (~node4(c_bit1, s20))),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5212, 5211])).
% 35.79/23.62 tff(5214,plain,
% 35.79/23.62 (~node4(c_bit1, s20)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5213, 3076, 3871])).
% 35.79/23.62 tff(5215,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s20)) | node4(c_bit1, s20))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s20)) | node4(c_bit1, s20))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5216,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s20)) | node4(c_bit1, s20))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5217,plain,
% 35.79/23.62 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s20)) | node4(c_bit1, s20)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5216, 5215])).
% 35.79/23.62 tff(5218,plain,
% 35.79/23.62 (~m_counter_cell_v_carry_out(c_bit1, s20)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5217, 2887, 5214])).
% 35.79/23.62 tff(5219,plain,
% 35.79/23.62 (((~![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, s20)) | m_counter_cell_v_carry_out(c_bit1, s20))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s20)) | m_counter_cell_v_carry_out(c_bit1, s20))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.62 tff(5220,plain,
% 35.79/23.62 ((~![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, s20)) | m_counter_cell_v_carry_out(c_bit1, s20))),
% 35.79/23.62 inference(quant_inst,[status(thm)],[])).
% 35.79/23.62 tff(5221,plain,
% 35.79/23.62 ((~![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, s20)) | m_counter_cell_v_carry_out(c_bit1, s20)),
% 35.79/23.62 inference(modus_ponens,[status(thm)],[5220, 5219])).
% 35.79/23.62 tff(5222,plain,
% 35.79/23.62 (~m_counter_cell_v_carry_in(c_bit2, s20)),
% 35.79/23.62 inference(unit_resolution,[status(thm)],[5221, 3167, 5218])).
% 35.79/23.62 tff(5223,plain,
% 35.79/23.62 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20)))),
% 35.79/23.62 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5224,plain,
% 35.79/23.63 (((~node1(c_bit2, s20)) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20))) <=> (m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5225,plain,
% 35.79/23.63 (((~![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, s20)) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20))))),
% 35.79/23.63 inference(monotonicity,[status(thm)],[5224])).
% 35.79/23.63 tff(5226,plain,
% 35.79/23.63 (((~![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, s20)) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20)))),
% 35.79/23.63 inference(transitivity,[status(thm)],[5225, 5223])).
% 35.79/23.63 tff(5227,plain,
% 35.79/23.63 ((~![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, s20)) | m_counter_cell_v_carry_in(c_bit2, s20) | (~m_counter_cell_v_value(c_bit2, s20)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5228,plain,
% 35.79/23.63 ((~![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, s20) | (~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5227, 5226])).
% 35.79/23.63 tff(5229,plain,
% 35.79/23.63 ((~m_counter_cell_v_value(c_bit2, s20)) | (~node1(c_bit2, s20))),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5228, 3359, 5222])).
% 35.79/23.63 tff(5230,plain,
% 35.79/23.63 (~m_counter_cell_v_value(c_bit2, s20)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5229, 5210])).
% 35.79/23.63 tff(5231,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit2, s19, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit2, s19, s20))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5232,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s19, s20)) | node3(c_bit2, s19, s20))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5233,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s19, s20)) | node3(c_bit2, s19, s20)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5232, 5231])).
% 35.79/23.63 tff(5234,plain,
% 35.79/23.63 (node3(c_bit2, s19, s20)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5233, 81, 697])).
% 35.79/23.63 tff(5235,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5236,plain,
% 35.79/23.63 ((node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)) | m_counter_cell_v_value(c_bit2, s20)) <=> (m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5237,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)) | m_counter_cell_v_value(c_bit2, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20))))),
% 35.79/23.63 inference(monotonicity,[status(thm)],[5236])).
% 35.79/23.63 tff(5238,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)) | m_counter_cell_v_value(c_bit2, s20))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)))),
% 35.79/23.63 inference(transitivity,[status(thm)],[5237, 5235])).
% 35.79/23.63 tff(5239,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s19) | (~node3(c_bit2, s19, s20)) | m_counter_cell_v_value(c_bit2, s20))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5240,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19) | (~node3(c_bit2, s19, s20))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5239, 5238])).
% 35.79/23.63 tff(5241,plain,
% 35.79/23.63 (m_counter_cell_v_value(c_bit2, s20) | node1(c_bit2, s19)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5240, 199, 5234])).
% 35.79/23.63 tff(5242,plain,
% 35.79/23.63 ($false),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5241, 5230, 5173])).
% 35.79/23.63 tff(5243,plain,(m_counter_cell_v_carry_in(c_bit1, s14) | (~node1(c_bit2, s21)) | m_counter_cell_v_carry_out(c_bit1, s18)), inference(lemma,lemma(discharge,[]))).
% 35.79/23.63 tff(5244,plain,
% 35.79/23.63 ((~node1(c_bit2, s21)) | m_counter_cell_v_carry_out(c_bit1, s18)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5243, 3207])).
% 35.79/23.63 tff(5245,plain,
% 35.79/23.63 (~node1(c_bit2, s21)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5244, 4468])).
% 35.79/23.63 tff(5246,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit2, s21, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit2, s21, s22))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5247,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s21, s22)) | node3(c_bit2, s21, s22))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5248,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s21, s22)) | node3(c_bit2, s21, s22)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5247, 5246])).
% 35.79/23.63 tff(5249,plain,
% 35.79/23.63 (node3(c_bit2, s21, s22)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5248, 81, 754])).
% 35.79/23.63 tff(5250,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5251,plain,
% 35.79/23.63 ((node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)) | m_counter_cell_v_value(c_bit2, s22)) <=> (m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5252,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)) | m_counter_cell_v_value(c_bit2, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22))))),
% 35.79/23.63 inference(monotonicity,[status(thm)],[5251])).
% 35.79/23.63 tff(5253,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)) | m_counter_cell_v_value(c_bit2, s22))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)))),
% 35.79/23.63 inference(transitivity,[status(thm)],[5252, 5250])).
% 35.79/23.63 tff(5254,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s21) | (~node3(c_bit2, s21, s22)) | m_counter_cell_v_value(c_bit2, s22))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5255,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21) | (~node3(c_bit2, s21, s22))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5254, 5253])).
% 35.79/23.63 tff(5256,plain,
% 35.79/23.63 (m_counter_cell_v_value(c_bit2, s22) | node1(c_bit2, s21)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5255, 199, 5249])).
% 35.79/23.63 tff(5257,plain,
% 35.79/23.63 (m_counter_cell_v_value(c_bit2, s22)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5256, 5245])).
% 35.79/23.63 tff(5258,assumption,(node4(c_bit1, s22)), introduced(assumption)).
% 35.79/23.63 tff(5259,plain,
% 35.79/23.63 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s22) | (~node4(c_bit1, s22)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~node4(c_bit1, s22)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5260,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s22) | (~node4(c_bit1, s22)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5261,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s22) | (~node4(c_bit1, s22))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5260, 5259])).
% 35.79/23.63 tff(5262,plain,
% 35.79/23.63 ($false),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5261, 3076, 3939, 5258])).
% 35.79/23.63 tff(5263,plain,(~node4(c_bit1, s22)), inference(lemma,lemma(discharge,[]))).
% 35.79/23.63 tff(5264,plain,
% 35.79/23.63 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5265,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5266,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s22)) | node4(c_bit1, s22)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5265, 5264])).
% 35.79/23.63 tff(5267,plain,
% 35.79/23.63 (~m_counter_cell_v_carry_out(c_bit1, s22)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5266, 2887, 5263])).
% 35.79/23.63 tff(5268,plain,
% 35.79/23.63 (((~![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, s22)) | m_counter_cell_v_carry_out(c_bit1, s22))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s22)) | m_counter_cell_v_carry_out(c_bit1, s22))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5269,plain,
% 35.79/23.63 ((~![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, s22)) | m_counter_cell_v_carry_out(c_bit1, s22))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5270,plain,
% 35.79/23.63 ((~![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, s22)) | m_counter_cell_v_carry_out(c_bit1, s22)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5269, 5268])).
% 35.79/23.63 tff(5271,plain,
% 35.79/23.63 (~m_counter_cell_v_carry_in(c_bit2, s22)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5270, 3167, 5267])).
% 35.79/23.63 tff(5272,plain,
% 35.79/23.63 (((~![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, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5273,plain,
% 35.79/23.63 (((~node1(c_bit2, s22)) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22))) <=> (m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5274,plain,
% 35.79/23.63 (((~![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, s22)) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22))))),
% 35.79/23.63 inference(monotonicity,[status(thm)],[5273])).
% 35.79/23.63 tff(5275,plain,
% 35.79/23.63 (((~![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, s22)) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22)))),
% 35.79/23.63 inference(transitivity,[status(thm)],[5274, 5272])).
% 35.79/23.63 tff(5276,plain,
% 35.79/23.63 ((~![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, s22)) | m_counter_cell_v_carry_in(c_bit2, s22) | (~m_counter_cell_v_value(c_bit2, s22)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5277,plain,
% 35.79/23.63 ((~![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, s22) | (~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5276, 5275])).
% 35.79/23.63 tff(5278,plain,
% 35.79/23.63 ((~m_counter_cell_v_value(c_bit2, s22)) | (~node1(c_bit2, s22))),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5277, 3359, 5271])).
% 35.79/23.63 tff(5279,plain,
% 35.79/23.63 (~node1(c_bit2, s22)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5278, 5257])).
% 35.79/23.63 tff(5280,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit2, s22, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit2, s22, s23))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5281,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s22, s23)) | node3(c_bit2, s22, s23))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5282,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s22, s23)) | node3(c_bit2, s22, s23)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5281, 5280])).
% 35.79/23.63 tff(5283,plain,
% 35.79/23.63 (node3(c_bit2, s22, s23)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5282, 81, 785])).
% 35.79/23.63 tff(5284,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5285,plain,
% 35.79/23.63 ((node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)) | m_counter_cell_v_value(c_bit2, s23)) <=> (m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5286,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)) | m_counter_cell_v_value(c_bit2, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23))))),
% 35.79/23.63 inference(monotonicity,[status(thm)],[5285])).
% 35.79/23.63 tff(5287,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)) | m_counter_cell_v_value(c_bit2, s23))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)))),
% 35.79/23.63 inference(transitivity,[status(thm)],[5286, 5284])).
% 35.79/23.63 tff(5288,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s22) | (~node3(c_bit2, s22, s23)) | m_counter_cell_v_value(c_bit2, s23))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5289,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22) | (~node3(c_bit2, s22, s23))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5288, 5287])).
% 35.79/23.63 tff(5290,plain,
% 35.79/23.63 (m_counter_cell_v_value(c_bit2, s23) | node1(c_bit2, s22)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5289, 199, 5283])).
% 35.79/23.63 tff(5291,plain,
% 35.79/23.63 (m_counter_cell_v_value(c_bit2, s23)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5290, 5279])).
% 35.79/23.63 tff(5292,plain,
% 35.79/23.63 (((~![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_bit1, s27)) | node2(c_bit1, s26) | (~node3(c_bit1, s26, 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_bit1, s27)) | node2(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5293,plain,
% 35.79/23.63 ((node2(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | (~m_counter_cell_v_value(c_bit1, s27))) <=> ((~m_counter_cell_v_value(c_bit1, s27)) | node2(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5294,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s27)) | node2(c_bit1, s26) | (~node3(c_bit1, s26, s27))))),
% 35.79/23.63 inference(monotonicity,[status(thm)],[5293])).
% 35.79/23.63 tff(5295,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s27)) | node2(c_bit1, s26) | (~node3(c_bit1, s26, s27)))),
% 35.79/23.63 inference(transitivity,[status(thm)],[5294, 5292])).
% 35.79/23.63 tff(5296,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s26) | (~node3(c_bit1, s26, s27)) | (~m_counter_cell_v_value(c_bit1, s27)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5297,plain,
% 35.79/23.63 ((~![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_bit1, s27)) | node2(c_bit1, s26) | (~node3(c_bit1, s26, s27))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5296, 5295])).
% 35.79/23.63 tff(5298,plain,
% 35.79/23.63 ((~m_counter_cell_v_value(c_bit1, s27)) | node2(c_bit1, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5297, 234, 4107])).
% 35.79/23.63 tff(5299,plain,
% 35.79/23.63 (node2(c_bit1, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5298, 4115])).
% 35.79/23.63 tff(5300,assumption,(~m_counter_cell_v_carry_in(c_bit1, s24)), introduced(assumption)).
% 35.79/23.63 tff(5301,assumption,(node2(c_bit1, s26)), introduced(assumption)).
% 35.79/23.63 tff(5302,assumption,(node2(c_bit2, s26)), introduced(assumption)).
% 35.79/23.63 tff(5303,assumption,(m_counter_cell_v_value(c_bit2, s23)), introduced(assumption)).
% 35.79/23.63 tff(5304,plain,
% 35.79/23.63 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s24) | (~node4(c_bit1, s24)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s24) | (~node4(c_bit1, s24)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5305,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s24) | (~node4(c_bit1, s24)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5306,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s24) | (~node4(c_bit1, s24))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5305, 5304])).
% 35.79/23.63 tff(5307,plain,
% 35.79/23.63 (~node4(c_bit1, s24)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5306, 3076, 5300])).
% 35.79/23.63 tff(5308,plain,
% 35.79/23.63 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s24)) | node4(c_bit1, s24))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s24)) | node4(c_bit1, s24))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5309,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s24)) | node4(c_bit1, s24))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5310,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s24)) | node4(c_bit1, s24)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5309, 5308])).
% 35.79/23.63 tff(5311,plain,
% 35.79/23.63 (~m_counter_cell_v_carry_out(c_bit1, s24)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5310, 2887, 5307])).
% 35.79/23.63 tff(5312,plain,
% 35.79/23.63 (((~![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, s24)) | m_counter_cell_v_carry_out(c_bit1, s24))) <=> ((~![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, s24)) | m_counter_cell_v_carry_out(c_bit1, s24))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5313,plain,
% 35.79/23.63 ((~![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, s24)) | m_counter_cell_v_carry_out(c_bit1, s24))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5314,plain,
% 35.79/23.63 ((~![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, s24)) | m_counter_cell_v_carry_out(c_bit1, s24)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5313, 5312])).
% 35.79/23.63 tff(5315,plain,
% 35.79/23.63 (~m_counter_cell_v_carry_in(c_bit2, s24)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5314, 3167, 5311])).
% 35.79/23.63 tff(5316,assumption,(~m_counter_cell_v_carry_in(c_bit1, s26)), introduced(assumption)).
% 35.79/23.63 tff(5317,plain,
% 35.79/23.63 (((~![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_bit1, s26) | m_counter_cell_v_value(c_bit1, s26) | (~node2(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : (m_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, s26) | m_counter_cell_v_value(c_bit1, s26) | (~node2(c_bit1, s26)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5318,plain,
% 35.79/23.63 ((~![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_bit1, s26) | m_counter_cell_v_value(c_bit1, s26) | (~node2(c_bit1, s26)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5319,plain,
% 35.79/23.63 ((~![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_bit1, s26) | m_counter_cell_v_value(c_bit1, s26) | (~node2(c_bit1, s26))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5318, 5317])).
% 35.79/23.63 tff(5320,plain,
% 35.79/23.63 (m_counter_cell_v_carry_in(c_bit1, s26) | m_counter_cell_v_value(c_bit1, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5319, 3291, 5301])).
% 35.79/23.63 tff(5321,plain,
% 35.79/23.63 (m_counter_cell_v_value(c_bit1, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5320, 5316])).
% 35.79/23.63 tff(5322,plain,
% 35.79/23.63 (((~![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_bit1, s26)) | node2(c_bit1, s25) | (~node3(c_bit1, 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_bit1, s26)) | node2(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5323,plain,
% 35.79/23.63 ((node2(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | (~m_counter_cell_v_value(c_bit1, s26))) <=> ((~m_counter_cell_v_value(c_bit1, s26)) | node2(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5324,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s26)) | node2(c_bit1, s25) | (~node3(c_bit1, s25, s26))))),
% 35.79/23.63 inference(monotonicity,[status(thm)],[5323])).
% 35.79/23.63 tff(5325,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s26)) | node2(c_bit1, s25) | (~node3(c_bit1, s25, s26)))),
% 35.79/23.63 inference(transitivity,[status(thm)],[5324, 5322])).
% 35.79/23.63 tff(5326,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s25) | (~node3(c_bit1, s25, s26)) | (~m_counter_cell_v_value(c_bit1, s26)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5327,plain,
% 35.79/23.63 ((~![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_bit1, s26)) | node2(c_bit1, s25) | (~node3(c_bit1, s25, s26))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5326, 5325])).
% 35.79/23.63 tff(5328,plain,
% 35.79/23.63 ((~m_counter_cell_v_value(c_bit1, s26)) | node2(c_bit1, s25)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5327, 234, 4053])).
% 35.79/23.63 tff(5329,plain,
% 35.79/23.63 (node2(c_bit1, s25)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5328, 5321])).
% 35.79/23.63 tff(5330,plain,
% 35.79/23.63 (m_counter_cell_v_carry_out(c_bit0, s25)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[4095, 856])).
% 35.79/23.63 tff(5331,plain,
% 35.79/23.63 (m_counter_cell_v_carry_in(c_bit1, s25)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[4099, 3046, 5330])).
% 35.79/23.63 tff(5332,plain,
% 35.79/23.63 (((~![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_bit1, s25)) | (~m_counter_cell_v_value(c_bit1, s25)) | (~node2(c_bit1, 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_bit1, s25)) | (~m_counter_cell_v_value(c_bit1, s25)) | (~node2(c_bit1, s25)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5333,plain,
% 35.79/23.63 ((~![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_bit1, s25)) | (~m_counter_cell_v_value(c_bit1, s25)) | (~node2(c_bit1, s25)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5334,plain,
% 35.79/23.63 ((~![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_bit1, s25)) | (~m_counter_cell_v_value(c_bit1, s25)) | (~node2(c_bit1, s25))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5333, 5332])).
% 35.79/23.63 tff(5335,plain,
% 35.79/23.63 ((~m_counter_cell_v_value(c_bit1, s25)) | (~node2(c_bit1, s25))),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5334, 219, 5331])).
% 35.79/23.63 tff(5336,plain,
% 35.79/23.63 (~m_counter_cell_v_value(c_bit1, s25)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5335, 5329])).
% 35.79/23.63 tff(5337,plain,
% 35.79/23.63 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s25) | (~node4(c_bit1, s25)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s25) | (~node4(c_bit1, s25)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5338,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s25) | (~node4(c_bit1, s25)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5339,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s25) | (~node4(c_bit1, s25))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5338, 5337])).
% 35.79/23.63 tff(5340,plain,
% 35.79/23.63 (~node4(c_bit1, s25)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5339, 2875, 5336])).
% 35.79/23.63 tff(5341,plain,
% 35.79/23.63 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s25)) | node4(c_bit1, s25))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s25)) | node4(c_bit1, s25))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5342,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s25)) | node4(c_bit1, s25))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5343,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s25)) | node4(c_bit1, s25)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5342, 5341])).
% 35.79/23.63 tff(5344,plain,
% 35.79/23.63 (~m_counter_cell_v_carry_out(c_bit1, s25)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5343, 2887, 5340])).
% 35.79/23.63 tff(5345,plain,
% 35.79/23.63 (((~![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, s25)) | m_counter_cell_v_carry_out(c_bit1, s25))) <=> ((~![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, s25)) | m_counter_cell_v_carry_out(c_bit1, s25))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5346,plain,
% 35.79/23.63 ((~![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, s25)) | m_counter_cell_v_carry_out(c_bit1, s25))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5347,plain,
% 35.79/23.63 ((~![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, s25)) | m_counter_cell_v_carry_out(c_bit1, s25)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5346, 5345])).
% 35.79/23.63 tff(5348,plain,
% 35.79/23.63 (~m_counter_cell_v_carry_in(c_bit2, s25)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5347, 3167, 5344])).
% 35.79/23.63 tff(5349,plain,
% 35.79/23.63 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s26) | (~node4(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~node4(c_bit1, s26)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5350,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s26) | (~node4(c_bit1, s26)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5351,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s26) | (~node4(c_bit1, s26))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 35.79/23.63 tff(5352,plain,
% 35.79/23.63 (~node4(c_bit1, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5351, 3076, 5316])).
% 35.79/23.63 tff(5353,plain,
% 35.79/23.63 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s26)) | node4(c_bit1, s26))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s26)) | node4(c_bit1, s26))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5354,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s26)) | node4(c_bit1, s26))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5355,plain,
% 35.79/23.63 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s26)) | node4(c_bit1, s26)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5354, 5353])).
% 35.79/23.63 tff(5356,plain,
% 35.79/23.63 (~m_counter_cell_v_carry_out(c_bit1, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5355, 2887, 5352])).
% 35.79/23.63 tff(5357,plain,
% 35.79/23.63 (((~![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, s26)) | m_counter_cell_v_carry_out(c_bit1, s26))) <=> ((~![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, s26)) | m_counter_cell_v_carry_out(c_bit1, s26))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5358,plain,
% 35.79/23.63 ((~![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, s26)) | m_counter_cell_v_carry_out(c_bit1, s26))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5359,plain,
% 35.79/23.63 ((~![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, s26)) | m_counter_cell_v_carry_out(c_bit1, s26)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5358, 5357])).
% 35.79/23.63 tff(5360,plain,
% 35.79/23.63 (~m_counter_cell_v_carry_in(c_bit2, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5359, 3167, 5356])).
% 35.79/23.63 tff(5361,plain,
% 35.79/23.63 (((~![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, s26) | m_counter_cell_v_value(c_bit2, s26) | (~node2(c_bit2, s26)))) <=> ((~![I0: $i, X: $i] : (m_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, s26) | m_counter_cell_v_value(c_bit2, s26) | (~node2(c_bit2, s26)))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5362,plain,
% 35.79/23.63 ((~![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, s26) | m_counter_cell_v_value(c_bit2, s26) | (~node2(c_bit2, s26)))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5363,plain,
% 35.79/23.63 ((~![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, s26) | m_counter_cell_v_value(c_bit2, s26) | (~node2(c_bit2, s26))),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5362, 5361])).
% 35.79/23.63 tff(5364,plain,
% 35.79/23.63 (m_counter_cell_v_carry_in(c_bit2, s26) | m_counter_cell_v_value(c_bit2, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5363, 3291, 5302])).
% 35.79/23.63 tff(5365,plain,
% 35.79/23.63 (m_counter_cell_v_value(c_bit2, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5364, 5360])).
% 35.79/23.63 tff(5366,plain,
% 35.79/23.63 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit2, s25, s26))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit2, s25, s26))),
% 35.79/23.63 inference(rewrite,[status(thm)],[])).
% 35.79/23.63 tff(5367,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s25, s26)) | node3(c_bit2, s25, s26))),
% 35.79/23.63 inference(quant_inst,[status(thm)],[])).
% 35.79/23.63 tff(5368,plain,
% 35.79/23.63 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s25, s26)) | node3(c_bit2, s25, s26)),
% 35.79/23.63 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 35.79/23.63 tff(5369,plain,
% 35.79/23.63 (node3(c_bit2, s25, s26)),
% 35.79/23.63 inference(unit_resolution,[status(thm)],[5368, 81, 870])).
% 35.79/23.63 tff(5370,plain,
% 35.79/23.63 (((~![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, s26)) | node2(c_bit2, s25) | (~node3(c_bit2, 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_bit2, s26)) | node2(c_bit2, s25) | (~node3(c_bit2, s25, s26)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5371,plain,
% 35.79/23.64 ((node2(c_bit2, s25) | (~node3(c_bit2, s25, s26)) | (~m_counter_cell_v_value(c_bit2, s26))) <=> ((~m_counter_cell_v_value(c_bit2, s26)) | node2(c_bit2, s25) | (~node3(c_bit2, s25, s26)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5372,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s25) | (~node3(c_bit2, s25, s26)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s26)) | node2(c_bit2, s25) | (~node3(c_bit2, s25, s26))))),
% 35.79/23.64 inference(monotonicity,[status(thm)],[5371])).
% 35.79/23.64 tff(5373,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s25) | (~node3(c_bit2, s25, s26)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s26)) | node2(c_bit2, s25) | (~node3(c_bit2, s25, s26)))),
% 35.79/23.64 inference(transitivity,[status(thm)],[5372, 5370])).
% 35.79/23.64 tff(5374,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s25) | (~node3(c_bit2, s25, s26)) | (~m_counter_cell_v_value(c_bit2, s26)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5375,plain,
% 35.79/23.64 ((~![Y: $i, 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, s26)) | node2(c_bit2, s25) | (~node3(c_bit2, s25, s26))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5374, 5373])).
% 35.79/23.64 tff(5376,plain,
% 35.79/23.64 ((~m_counter_cell_v_value(c_bit2, s26)) | node2(c_bit2, s25)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5375, 234, 5369])).
% 35.79/23.64 tff(5377,plain,
% 35.79/23.64 (node2(c_bit2, s25)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5376, 5365])).
% 35.79/23.64 tff(5378,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : (m_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, s25) | m_counter_cell_v_value(c_bit2, s25) | (~node2(c_bit2, 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_bit2, s25) | m_counter_cell_v_value(c_bit2, s25) | (~node2(c_bit2, s25)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5379,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : (m_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, s25) | m_counter_cell_v_value(c_bit2, s25) | (~node2(c_bit2, s25)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5380,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : (m_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, s25) | m_counter_cell_v_value(c_bit2, s25) | (~node2(c_bit2, s25))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5379, 5378])).
% 35.79/23.64 tff(5381,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit2, s25)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5380, 3291, 5377, 5348])).
% 35.79/23.64 tff(5382,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit2, s24, s25))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit2, s24, s25))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5383,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s24, s25)) | node3(c_bit2, s24, s25))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5384,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s24, s25)) | node3(c_bit2, s24, s25)),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 35.79/23.64 tff(5385,plain,
% 35.79/23.64 (node3(c_bit2, s24, s25)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5384, 81, 844])).
% 35.79/23.64 tff(5386,plain,
% 35.79/23.64 (((~![Y: $i, 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, s25)) | node2(c_bit2, s24) | (~node3(c_bit2, 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_bit2, s25)) | node2(c_bit2, s24) | (~node3(c_bit2, s24, s25)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5387,plain,
% 35.79/23.64 ((node2(c_bit2, s24) | (~node3(c_bit2, s24, s25)) | (~m_counter_cell_v_value(c_bit2, s25))) <=> ((~m_counter_cell_v_value(c_bit2, s25)) | node2(c_bit2, s24) | (~node3(c_bit2, s24, s25)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5388,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s24) | (~node3(c_bit2, s24, s25)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s25)) | node2(c_bit2, s24) | (~node3(c_bit2, s24, s25))))),
% 35.79/23.64 inference(monotonicity,[status(thm)],[5387])).
% 35.79/23.64 tff(5389,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s24) | (~node3(c_bit2, s24, s25)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s25)) | node2(c_bit2, s24) | (~node3(c_bit2, s24, s25)))),
% 35.79/23.64 inference(transitivity,[status(thm)],[5388, 5386])).
% 35.79/23.64 tff(5390,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s24) | (~node3(c_bit2, s24, s25)) | (~m_counter_cell_v_value(c_bit2, s25)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5391,plain,
% 35.79/23.64 ((~![Y: $i, 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, s25)) | node2(c_bit2, s24) | (~node3(c_bit2, s24, s25))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5390, 5389])).
% 35.79/23.64 tff(5392,plain,
% 35.79/23.64 ((~m_counter_cell_v_value(c_bit2, s25)) | node2(c_bit2, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5391, 234, 5385])).
% 35.79/23.64 tff(5393,plain,
% 35.79/23.64 (node2(c_bit2, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5392, 5381])).
% 35.79/23.64 tff(5394,plain,
% 35.79/23.64 (((~![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_bit1, s25) | node1(c_bit1, s24) | (~node3(c_bit1, 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_bit1, s25) | node1(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5395,plain,
% 35.79/23.64 ((node1(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | m_counter_cell_v_value(c_bit1, s25)) <=> (m_counter_cell_v_value(c_bit1, s25) | node1(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5396,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | m_counter_cell_v_value(c_bit1, 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_bit1, s25) | node1(c_bit1, s24) | (~node3(c_bit1, s24, s25))))),
% 35.79/23.64 inference(monotonicity,[status(thm)],[5395])).
% 35.79/23.64 tff(5397,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | m_counter_cell_v_value(c_bit1, 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_bit1, s25) | node1(c_bit1, s24) | (~node3(c_bit1, s24, s25)))),
% 35.79/23.64 inference(transitivity,[status(thm)],[5396, 5394])).
% 35.79/23.64 tff(5398,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s24) | (~node3(c_bit1, s24, s25)) | m_counter_cell_v_value(c_bit1, s25))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5399,plain,
% 35.79/23.64 ((~![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_bit1, s25) | node1(c_bit1, s24) | (~node3(c_bit1, s24, s25))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5398, 5397])).
% 35.79/23.64 tff(5400,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit1, s25) | node1(c_bit1, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5399, 199, 4014])).
% 35.79/23.64 tff(5401,plain,
% 35.79/23.64 (node1(c_bit1, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5400, 5336])).
% 35.79/23.64 tff(5402,plain,
% 35.79/23.64 (((~![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_bit1, s24) | (~m_counter_cell_v_value(c_bit1, s24)) | (~node1(c_bit1, 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_bit1, s24) | (~m_counter_cell_v_value(c_bit1, s24)) | (~node1(c_bit1, s24)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5403,plain,
% 35.79/23.64 (((~node1(c_bit1, s24)) | m_counter_cell_v_carry_in(c_bit1, s24) | (~m_counter_cell_v_value(c_bit1, s24))) <=> (m_counter_cell_v_carry_in(c_bit1, s24) | (~m_counter_cell_v_value(c_bit1, s24)) | (~node1(c_bit1, s24)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5404,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s24)) | m_counter_cell_v_carry_in(c_bit1, s24) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s24) | (~m_counter_cell_v_value(c_bit1, s24)) | (~node1(c_bit1, s24))))),
% 35.79/23.64 inference(monotonicity,[status(thm)],[5403])).
% 35.79/23.64 tff(5405,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s24)) | m_counter_cell_v_carry_in(c_bit1, s24) | (~m_counter_cell_v_value(c_bit1, 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_bit1, s24) | (~m_counter_cell_v_value(c_bit1, s24)) | (~node1(c_bit1, s24)))),
% 35.79/23.64 inference(transitivity,[status(thm)],[5404, 5402])).
% 35.79/23.64 tff(5406,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s24)) | m_counter_cell_v_carry_in(c_bit1, s24) | (~m_counter_cell_v_value(c_bit1, s24)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5407,plain,
% 35.79/23.64 ((~![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_bit1, s24) | (~m_counter_cell_v_value(c_bit1, s24)) | (~node1(c_bit1, s24))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5406, 5405])).
% 35.79/23.64 tff(5408,plain,
% 35.79/23.64 (~m_counter_cell_v_value(c_bit1, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5407, 3359, 5401, 5300])).
% 35.79/23.64 tff(5409,plain,
% 35.79/23.64 (((~![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_bit1, s24) | node1(c_bit1, s23) | (~node3(c_bit1, s23, s24)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s24) | node1(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5410,plain,
% 35.79/23.64 ((node1(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | m_counter_cell_v_value(c_bit1, s24)) <=> (m_counter_cell_v_value(c_bit1, s24) | node1(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5411,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | m_counter_cell_v_value(c_bit1, s24))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s24) | node1(c_bit1, s23) | (~node3(c_bit1, s23, s24))))),
% 35.79/23.64 inference(monotonicity,[status(thm)],[5410])).
% 35.79/23.64 tff(5412,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | m_counter_cell_v_value(c_bit1, s24))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s24) | node1(c_bit1, s23) | (~node3(c_bit1, s23, s24)))),
% 35.79/23.64 inference(transitivity,[status(thm)],[5411, 5409])).
% 35.79/23.64 tff(5413,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s23) | (~node3(c_bit1, s23, s24)) | m_counter_cell_v_value(c_bit1, s24))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5414,plain,
% 35.79/23.64 ((~![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_bit1, s24) | node1(c_bit1, s23) | (~node3(c_bit1, s23, s24))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5413, 5412])).
% 35.79/23.64 tff(5415,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit1, s24) | node1(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5414, 199, 3979])).
% 35.79/23.64 tff(5416,plain,
% 35.79/23.64 (node1(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5415, 5408])).
% 35.79/23.64 tff(5417,plain,
% 35.79/23.64 (((~![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_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23) | (~node1(c_bit1, s23)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23) | (~node1(c_bit1, s23)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5418,plain,
% 35.79/23.64 (((~node1(c_bit1, s23)) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23) | (~node1(c_bit1, s23)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5419,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s23)) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23) | (~node1(c_bit1, s23))))),
% 35.79/23.64 inference(monotonicity,[status(thm)],[5418])).
% 35.79/23.64 tff(5420,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s23)) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23) | (~node1(c_bit1, s23)))),
% 35.79/23.64 inference(transitivity,[status(thm)],[5419, 5417])).
% 35.79/23.64 tff(5421,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s23)) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5422,plain,
% 35.79/23.64 ((~![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_bit1, s23)) | m_counter_cell_v_value(c_bit1, s23) | (~node1(c_bit1, s23))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5421, 5420])).
% 35.79/23.64 tff(5423,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit1, s23) | (~node1(c_bit1, s23))),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5422, 170, 3970])).
% 35.79/23.64 tff(5424,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5423, 5416])).
% 35.79/23.64 tff(5425,plain,
% 35.79/23.64 (((~![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_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5426,plain,
% 35.79/23.64 ((~![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_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5427,plain,
% 35.79/23.64 ((~![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_bit1, s23)) | (~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23)),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5426, 5425])).
% 35.79/23.64 tff(5428,plain,
% 35.79/23.64 ((~m_counter_cell_v_value(c_bit1, s23)) | m_counter_cell_v_carry_out(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5427, 3031, 3970])).
% 35.79/23.64 tff(5429,plain,
% 35.79/23.64 (m_counter_cell_v_carry_out(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5428, 5424])).
% 35.79/23.64 tff(5430,plain,
% 35.79/23.64 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s23)) | m_counter_cell_v_carry_in(c_bit2, s23))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s23)) | m_counter_cell_v_carry_in(c_bit2, s23))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5431,plain,
% 35.79/23.64 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s23)) | m_counter_cell_v_carry_in(c_bit2, s23))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5432,plain,
% 35.79/23.64 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s23)) | m_counter_cell_v_carry_in(c_bit2, s23)),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5431, 5430])).
% 35.79/23.64 tff(5433,plain,
% 35.79/23.64 (m_counter_cell_v_carry_in(c_bit2, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5432, 4417, 5429])).
% 35.79/23.64 tff(5434,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : ((~m_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, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node2(c_bit2, 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_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node2(c_bit2, s23)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5435,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~m_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, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node2(c_bit2, s23)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5436,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~m_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, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node2(c_bit2, s23))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5435, 5434])).
% 35.79/23.64 tff(5437,plain,
% 35.79/23.64 ((~m_counter_cell_v_carry_in(c_bit2, s23)) | (~node2(c_bit2, s23))),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5436, 219, 5303])).
% 35.79/23.64 tff(5438,plain,
% 35.79/23.64 (~node2(c_bit2, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5437, 5433])).
% 35.79/23.64 tff(5439,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit2, s23, s24))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit2, s23, s24))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5440,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s23, s24)) | node3(c_bit2, s23, s24))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5441,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s23, s24)) | node3(c_bit2, s23, s24)),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5440, 5439])).
% 35.79/23.64 tff(5442,plain,
% 35.79/23.64 (node3(c_bit2, s23, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5441, 81, 813])).
% 35.79/23.64 tff(5443,plain,
% 35.79/23.64 (((~![Y: $i, 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, s24)) | node2(c_bit2, s23) | (~node3(c_bit2, 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_bit2, s24)) | node2(c_bit2, s23) | (~node3(c_bit2, s23, s24)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5444,plain,
% 35.79/23.64 ((node2(c_bit2, s23) | (~node3(c_bit2, s23, s24)) | (~m_counter_cell_v_value(c_bit2, s24))) <=> ((~m_counter_cell_v_value(c_bit2, s24)) | node2(c_bit2, s23) | (~node3(c_bit2, s23, s24)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5445,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s23) | (~node3(c_bit2, s23, s24)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s24)) | node2(c_bit2, s23) | (~node3(c_bit2, s23, s24))))),
% 35.79/23.64 inference(monotonicity,[status(thm)],[5444])).
% 35.79/23.64 tff(5446,plain,
% 35.79/23.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s23) | (~node3(c_bit2, s23, s24)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s24)) | node2(c_bit2, s23) | (~node3(c_bit2, s23, s24)))),
% 35.79/23.64 inference(transitivity,[status(thm)],[5445, 5443])).
% 35.79/23.64 tff(5447,plain,
% 35.79/23.64 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s23) | (~node3(c_bit2, s23, s24)) | (~m_counter_cell_v_value(c_bit2, s24)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5448,plain,
% 35.79/23.64 ((~![Y: $i, 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, s24)) | node2(c_bit2, s23) | (~node3(c_bit2, s23, s24))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5447, 5446])).
% 35.79/23.64 tff(5449,plain,
% 35.79/23.64 ((~m_counter_cell_v_value(c_bit2, s24)) | node2(c_bit2, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5448, 234, 5442])).
% 35.79/23.64 tff(5450,plain,
% 35.79/23.64 (~m_counter_cell_v_value(c_bit2, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5449, 5438])).
% 35.79/23.64 tff(5451,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : (m_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, s24) | m_counter_cell_v_value(c_bit2, s24) | (~node2(c_bit2, 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_bit2, s24) | m_counter_cell_v_value(c_bit2, s24) | (~node2(c_bit2, s24)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5452,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : (m_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, s24) | m_counter_cell_v_value(c_bit2, s24) | (~node2(c_bit2, s24)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5453,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s24) | m_counter_cell_v_value(c_bit2, s24) | (~node2(c_bit2, s24))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5452, 5451])).
% 35.79/23.64 tff(5454,plain,
% 35.79/23.64 (m_counter_cell_v_carry_in(c_bit2, s24) | (~node2(c_bit2, s24))),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5453, 3291, 5450])).
% 35.79/23.64 tff(5455,plain,
% 35.79/23.64 ($false),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5454, 5393, 5315])).
% 35.79/23.64 tff(5456,plain,(m_counter_cell_v_carry_in(c_bit1, s26) | (~node2(c_bit2, s26)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_in(c_bit1, s24) | (~node2(c_bit1, s26))), inference(lemma,lemma(discharge,[]))).
% 35.79/23.64 tff(5457,plain,
% 35.79/23.64 (m_counter_cell_v_carry_in(c_bit1, s26)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5456, 5300, 5303, 5302, 5301])).
% 35.79/23.64 tff(5458,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : ((~m_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, s26)) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node2(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s26)) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node2(c_bit1, s26)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5459,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~m_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, s26)) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node2(c_bit1, s26)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5460,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~m_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, s26)) | (~m_counter_cell_v_value(c_bit1, s26)) | (~node2(c_bit1, s26))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5459, 5458])).
% 35.79/23.64 tff(5461,plain,
% 35.79/23.64 ((~m_counter_cell_v_carry_in(c_bit1, s26)) | (~m_counter_cell_v_value(c_bit1, s26))),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5460, 219, 5301])).
% 35.79/23.64 tff(5462,plain,
% 35.79/23.64 (~m_counter_cell_v_value(c_bit1, s26)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5461, 5457])).
% 35.79/23.64 tff(5463,plain,
% 35.79/23.64 (node1(c_bit1, s25)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[4060, 5462])).
% 35.79/23.64 tff(5464,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit1, s25) | (~node1(c_bit1, s25))),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[4068, 170, 5331])).
% 35.79/23.64 tff(5465,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit1, s25)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5464, 5463])).
% 35.79/23.64 tff(5466,plain,
% 35.79/23.64 (node2(c_bit1, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[4021, 5465])).
% 35.79/23.64 tff(5467,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit1, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[4008, 3291, 5466, 5300])).
% 35.79/23.64 tff(5468,plain,
% 35.79/23.64 (node2(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[3986, 5467])).
% 35.79/23.64 tff(5469,plain,
% 35.79/23.64 (~m_counter_cell_v_value(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[3974, 5468])).
% 35.79/23.64 tff(5470,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s23) | (~node4(c_bit1, s23)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s23) | (~node4(c_bit1, s23)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5471,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s23) | (~node4(c_bit1, s23)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5472,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s23) | (~node4(c_bit1, s23))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5471, 5470])).
% 35.79/23.64 tff(5473,plain,
% 35.79/23.64 (~node4(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5472, 2875, 5469])).
% 35.79/23.64 tff(5474,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s23)) | node4(c_bit1, s23))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s23)) | node4(c_bit1, s23))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5475,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s23)) | node4(c_bit1, s23))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5476,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s23)) | node4(c_bit1, s23)),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5475, 5474])).
% 35.79/23.64 tff(5477,plain,
% 35.79/23.64 (~m_counter_cell_v_carry_out(c_bit1, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5476, 2887, 5473])).
% 35.79/23.64 tff(5478,plain,
% 35.79/23.64 (((~![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, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))) <=> ((~![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, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5479,plain,
% 35.79/23.64 ((~![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, s23)) | m_counter_cell_v_carry_out(c_bit1, s23))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5480,plain,
% 35.79/23.64 ((~![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, s23)) | m_counter_cell_v_carry_out(c_bit1, s23)),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5479, 5478])).
% 35.79/23.64 tff(5481,plain,
% 35.79/23.64 (~m_counter_cell_v_carry_in(c_bit2, s23)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5480, 3167, 5477])).
% 35.79/23.64 tff(5482,assumption,(node4(c_bit1, s24)), introduced(assumption)).
% 35.79/23.64 tff(5483,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s24) | (~node4(c_bit1, s24)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s24) | (~node4(c_bit1, s24)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5484,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s24) | (~node4(c_bit1, s24)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5485,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s24) | (~node4(c_bit1, s24))),
% 35.79/23.64 inference(modus_ponens,[status(thm)],[5484, 5483])).
% 35.79/23.64 tff(5486,plain,
% 35.79/23.64 (m_counter_cell_v_value(c_bit1, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5485, 2875, 5482])).
% 35.79/23.64 tff(5487,plain,
% 35.79/23.64 (m_counter_cell_v_carry_in(c_bit1, s24)),
% 35.79/23.64 inference(unit_resolution,[status(thm)],[5306, 3076, 5482])).
% 35.79/23.64 tff(5488,assumption,(node2(c_bit1, s24)), introduced(assumption)).
% 35.79/23.64 tff(5489,plain,
% 35.79/23.64 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.79/23.64 inference(rewrite,[status(thm)],[])).
% 35.79/23.64 tff(5490,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.79/23.64 inference(quant_inst,[status(thm)],[])).
% 35.79/23.64 tff(5491,plain,
% 35.79/23.64 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s24)) | (~m_counter_cell_v_value(c_bit1, s24)) | (~node2(c_bit1, s24))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5490, 5489])).
% 35.79/23.65 tff(5492,plain,
% 35.79/23.65 ((~m_counter_cell_v_carry_in(c_bit1, s24)) | (~m_counter_cell_v_value(c_bit1, s24))),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5491, 219, 5488])).
% 35.79/23.65 tff(5493,plain,
% 35.79/23.65 ($false),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5492, 5487, 5486])).
% 35.79/23.65 tff(5494,plain,((~node4(c_bit1, s24)) | (~node2(c_bit1, s24))), inference(lemma,lemma(discharge,[]))).
% 35.79/23.65 tff(5495,plain,
% 35.79/23.65 (~node4(c_bit1, s24)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5494, 5466])).
% 35.79/23.65 tff(5496,plain,
% 35.79/23.65 (~m_counter_cell_v_carry_out(c_bit1, s24)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5310, 2887, 5495])).
% 35.79/23.65 tff(5497,plain,
% 35.79/23.65 (~m_counter_cell_v_carry_in(c_bit2, s24)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5314, 3167, 5496])).
% 35.79/23.65 tff(5498,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s26) | (~node4(c_bit1, s26)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s26) | (~node4(c_bit1, s26)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5499,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s26) | (~node4(c_bit1, s26)))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5500,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s26) | (~node4(c_bit1, s26))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5499, 5498])).
% 35.79/23.65 tff(5501,plain,
% 35.79/23.65 (~node4(c_bit1, s26)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5500, 2875, 5462])).
% 35.79/23.65 tff(5502,plain,
% 35.79/23.65 (~m_counter_cell_v_carry_out(c_bit1, s26)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5355, 2887, 5501])).
% 35.79/23.65 tff(5503,plain,
% 35.79/23.65 (~m_counter_cell_v_carry_in(c_bit2, s26)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5359, 3167, 5502])).
% 35.79/23.65 tff(5504,plain,
% 35.79/23.65 (m_counter_cell_v_value(c_bit2, s26)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5364, 5503])).
% 35.79/23.65 tff(5505,plain,
% 35.79/23.65 (node2(c_bit2, s25)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5376, 5504])).
% 35.79/23.65 tff(5506,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s25)) | (~m_counter_cell_v_value(c_bit1, s25)) | m_counter_cell_v_carry_out(c_bit1, 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_bit1, s25)) | (~m_counter_cell_v_value(c_bit1, s25)) | m_counter_cell_v_carry_out(c_bit1, s25))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5507,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s25)) | (~m_counter_cell_v_value(c_bit1, s25)) | m_counter_cell_v_carry_out(c_bit1, s25))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5508,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s25)) | (~m_counter_cell_v_value(c_bit1, s25)) | m_counter_cell_v_carry_out(c_bit1, s25)),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5507, 5506])).
% 35.79/23.65 tff(5509,plain,
% 35.79/23.65 ((~m_counter_cell_v_value(c_bit1, s25)) | m_counter_cell_v_carry_out(c_bit1, s25)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5508, 3031, 5331])).
% 35.79/23.65 tff(5510,plain,
% 35.79/23.65 (m_counter_cell_v_carry_out(c_bit1, s25)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5509, 5465])).
% 35.79/23.65 tff(5511,plain,
% 35.79/23.65 (((~![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, s25)) | m_counter_cell_v_carry_in(c_bit2, s25))) <=> ((~![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, s25)) | m_counter_cell_v_carry_in(c_bit2, s25))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5512,plain,
% 35.79/23.65 ((~![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, s25)) | m_counter_cell_v_carry_in(c_bit2, s25))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5513,plain,
% 35.79/23.65 ((~![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, s25)) | m_counter_cell_v_carry_in(c_bit2, s25)),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5512, 5511])).
% 35.79/23.65 tff(5514,plain,
% 35.79/23.65 (m_counter_cell_v_carry_in(c_bit2, s25)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5513, 4417, 5510])).
% 35.79/23.65 tff(5515,plain,
% 35.79/23.65 (((~![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, s25)) | (~m_counter_cell_v_value(c_bit2, s25)) | (~node2(c_bit2, 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_bit2, s25)) | (~m_counter_cell_v_value(c_bit2, s25)) | (~node2(c_bit2, s25)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5516,plain,
% 35.79/23.65 ((~![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, s25)) | (~m_counter_cell_v_value(c_bit2, s25)) | (~node2(c_bit2, s25)))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5517,plain,
% 35.79/23.65 ((~![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, s25)) | (~m_counter_cell_v_value(c_bit2, s25)) | (~node2(c_bit2, s25))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5516, 5515])).
% 35.79/23.65 tff(5518,plain,
% 35.79/23.65 ((~m_counter_cell_v_value(c_bit2, s25)) | (~node2(c_bit2, s25))),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5517, 219, 5514])).
% 35.79/23.65 tff(5519,plain,
% 35.79/23.65 (~m_counter_cell_v_value(c_bit2, s25)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5518, 5505])).
% 35.79/23.65 tff(5520,plain,
% 35.79/23.65 (((~![Y: $i, 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, s25) | node1(c_bit2, s24) | (~node3(c_bit2, 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_bit2, s25) | node1(c_bit2, s24) | (~node3(c_bit2, s24, s25)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5521,plain,
% 35.79/23.65 ((node1(c_bit2, s24) | (~node3(c_bit2, s24, s25)) | m_counter_cell_v_value(c_bit2, s25)) <=> (m_counter_cell_v_value(c_bit2, s25) | node1(c_bit2, s24) | (~node3(c_bit2, s24, s25)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5522,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s24) | (~node3(c_bit2, s24, s25)) | m_counter_cell_v_value(c_bit2, 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_bit2, s25) | node1(c_bit2, s24) | (~node3(c_bit2, s24, s25))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5521])).
% 35.79/23.65 tff(5523,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s24) | (~node3(c_bit2, s24, s25)) | m_counter_cell_v_value(c_bit2, 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_bit2, s25) | node1(c_bit2, s24) | (~node3(c_bit2, s24, s25)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5522, 5520])).
% 35.79/23.65 tff(5524,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s24) | (~node3(c_bit2, s24, s25)) | m_counter_cell_v_value(c_bit2, s25))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5525,plain,
% 35.79/23.65 ((~![Y: $i, 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, s25) | node1(c_bit2, s24) | (~node3(c_bit2, s24, s25))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5524, 5523])).
% 35.79/23.65 tff(5526,plain,
% 35.79/23.65 (m_counter_cell_v_value(c_bit2, s25) | node1(c_bit2, s24)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5525, 199, 5385])).
% 35.79/23.65 tff(5527,plain,
% 35.79/23.65 (node1(c_bit2, s24)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5526, 5519])).
% 35.79/23.65 tff(5528,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : ((~node1(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, s24) | (~m_counter_cell_v_value(c_bit2, s24)) | (~node1(c_bit2, 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_bit2, s24) | (~m_counter_cell_v_value(c_bit2, s24)) | (~node1(c_bit2, s24)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5529,plain,
% 35.79/23.65 (((~node1(c_bit2, s24)) | m_counter_cell_v_carry_in(c_bit2, s24) | (~m_counter_cell_v_value(c_bit2, s24))) <=> (m_counter_cell_v_carry_in(c_bit2, s24) | (~m_counter_cell_v_value(c_bit2, s24)) | (~node1(c_bit2, s24)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5530,plain,
% 35.79/23.65 (((~![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, s24)) | m_counter_cell_v_carry_in(c_bit2, s24) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s24) | (~m_counter_cell_v_value(c_bit2, s24)) | (~node1(c_bit2, s24))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5529])).
% 35.79/23.65 tff(5531,plain,
% 35.79/23.65 (((~![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, s24)) | m_counter_cell_v_carry_in(c_bit2, s24) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s24) | (~m_counter_cell_v_value(c_bit2, s24)) | (~node1(c_bit2, s24)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5530, 5528])).
% 35.79/23.65 tff(5532,plain,
% 35.79/23.65 ((~![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, s24)) | m_counter_cell_v_carry_in(c_bit2, s24) | (~m_counter_cell_v_value(c_bit2, s24)))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5533,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~node1(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, s24) | (~m_counter_cell_v_value(c_bit2, s24)) | (~node1(c_bit2, s24))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5532, 5531])).
% 35.79/23.65 tff(5534,plain,
% 35.79/23.65 (~m_counter_cell_v_value(c_bit2, s24)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5533, 3359, 5527, 5497])).
% 35.79/23.65 tff(5535,plain,
% 35.79/23.65 (((~![Y: $i, 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, s24) | node1(c_bit2, s23) | (~node3(c_bit2, s23, s24)))) <=> ((~![Y: $i, 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, s24) | node1(c_bit2, s23) | (~node3(c_bit2, s23, s24)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5536,plain,
% 35.79/23.65 ((node1(c_bit2, s23) | (~node3(c_bit2, s23, s24)) | m_counter_cell_v_value(c_bit2, s24)) <=> (m_counter_cell_v_value(c_bit2, s24) | node1(c_bit2, s23) | (~node3(c_bit2, s23, s24)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5537,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s23) | (~node3(c_bit2, s23, s24)) | m_counter_cell_v_value(c_bit2, s24))) <=> ((~![Y: $i, 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, s24) | node1(c_bit2, s23) | (~node3(c_bit2, s23, s24))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5536])).
% 35.79/23.65 tff(5538,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s23) | (~node3(c_bit2, s23, s24)) | m_counter_cell_v_value(c_bit2, s24))) <=> ((~![Y: $i, 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, s24) | node1(c_bit2, s23) | (~node3(c_bit2, s23, s24)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5537, 5535])).
% 35.79/23.65 tff(5539,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s23) | (~node3(c_bit2, s23, s24)) | m_counter_cell_v_value(c_bit2, s24))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5540,plain,
% 35.79/23.65 ((~![Y: $i, 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, s24) | node1(c_bit2, s23) | (~node3(c_bit2, s23, s24))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5539, 5538])).
% 35.79/23.65 tff(5541,plain,
% 35.79/23.65 (m_counter_cell_v_value(c_bit2, s24) | node1(c_bit2, s23)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5540, 199, 5442])).
% 35.79/23.65 tff(5542,plain,
% 35.79/23.65 (node1(c_bit2, s23)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5541, 5534])).
% 35.79/23.65 tff(5543,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : ((~node1(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, s23) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node1(c_bit2, s23)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s23) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node1(c_bit2, s23)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5544,plain,
% 35.79/23.65 (((~node1(c_bit2, s23)) | m_counter_cell_v_carry_in(c_bit2, s23) | (~m_counter_cell_v_value(c_bit2, s23))) <=> (m_counter_cell_v_carry_in(c_bit2, s23) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node1(c_bit2, s23)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5545,plain,
% 35.79/23.65 (((~![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, s23)) | m_counter_cell_v_carry_in(c_bit2, s23) | (~m_counter_cell_v_value(c_bit2, s23)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s23) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node1(c_bit2, s23))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5544])).
% 35.79/23.65 tff(5546,plain,
% 35.79/23.65 (((~![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, s23)) | m_counter_cell_v_carry_in(c_bit2, s23) | (~m_counter_cell_v_value(c_bit2, s23)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s23) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node1(c_bit2, s23)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5545, 5543])).
% 35.79/23.65 tff(5547,plain,
% 35.79/23.65 ((~![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, s23)) | m_counter_cell_v_carry_in(c_bit2, s23) | (~m_counter_cell_v_value(c_bit2, s23)))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5548,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s23) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node1(c_bit2, s23))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5547, 5546])).
% 35.79/23.65 tff(5549,plain,
% 35.79/23.65 (m_counter_cell_v_carry_in(c_bit2, s23) | (~node1(c_bit2, s23))),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5548, 3359, 5303])).
% 35.79/23.65 tff(5550,plain,
% 35.79/23.65 ($false),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5549, 5542, 5481])).
% 35.79/23.65 tff(5551,plain,(m_counter_cell_v_carry_in(c_bit1, s24) | (~m_counter_cell_v_value(c_bit2, s23)) | (~node2(c_bit2, s26)) | (~node2(c_bit1, s26))), inference(lemma,lemma(discharge,[]))).
% 35.79/23.65 tff(5552,plain,
% 35.79/23.65 ((~m_counter_cell_v_value(c_bit2, s23)) | (~node2(c_bit2, s26)) | (~node2(c_bit1, s26))),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5551, 4005])).
% 35.79/23.65 tff(5553,plain,
% 35.79/23.65 (~node2(c_bit2, s26)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5552, 5299, 5291])).
% 35.79/23.65 tff(5554,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit2, s26, s27))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit2, s26, s27))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5555,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s26, s27)) | node3(c_bit2, s26, s27))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5556,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s26, s27)) | node3(c_bit2, s26, s27)),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5555, 5554])).
% 35.79/23.65 tff(5557,plain,
% 35.79/23.65 (node3(c_bit2, s26, s27)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5556, 81, 901])).
% 35.79/23.65 tff(5558,plain,
% 35.79/23.65 (((~![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, s27)) | node2(c_bit2, s26) | (~node3(c_bit2, s26, 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_bit2, s27)) | node2(c_bit2, s26) | (~node3(c_bit2, s26, s27)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5559,plain,
% 35.79/23.65 ((node2(c_bit2, s26) | (~node3(c_bit2, s26, s27)) | (~m_counter_cell_v_value(c_bit2, s27))) <=> ((~m_counter_cell_v_value(c_bit2, s27)) | node2(c_bit2, s26) | (~node3(c_bit2, s26, s27)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5560,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s26) | (~node3(c_bit2, s26, s27)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s27)) | node2(c_bit2, s26) | (~node3(c_bit2, s26, s27))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5559])).
% 35.79/23.65 tff(5561,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s26) | (~node3(c_bit2, s26, s27)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s27)) | node2(c_bit2, s26) | (~node3(c_bit2, s26, s27)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5560, 5558])).
% 35.79/23.65 tff(5562,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s26) | (~node3(c_bit2, s26, s27)) | (~m_counter_cell_v_value(c_bit2, s27)))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5563,plain,
% 35.79/23.65 ((~![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, s27)) | node2(c_bit2, s26) | (~node3(c_bit2, s26, s27))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5562, 5561])).
% 35.79/23.65 tff(5564,plain,
% 35.79/23.65 ((~m_counter_cell_v_value(c_bit2, s27)) | node2(c_bit2, s26)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5563, 234, 5557])).
% 35.79/23.65 tff(5565,plain,
% 35.79/23.65 (~m_counter_cell_v_value(c_bit2, s27)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5564, 5553])).
% 35.79/23.65 tff(5566,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : ((~node1(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, s27)) | m_counter_cell_v_value(c_bit2, s27) | (~node1(c_bit2, s27)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s27)) | m_counter_cell_v_value(c_bit2, s27) | (~node1(c_bit2, s27)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5567,plain,
% 35.79/23.65 (((~node1(c_bit2, s27)) | (~m_counter_cell_v_carry_in(c_bit2, s27)) | m_counter_cell_v_value(c_bit2, s27)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s27)) | m_counter_cell_v_value(c_bit2, s27) | (~node1(c_bit2, s27)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5568,plain,
% 35.79/23.65 (((~![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, s27)) | (~m_counter_cell_v_carry_in(c_bit2, s27)) | m_counter_cell_v_value(c_bit2, s27))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s27)) | m_counter_cell_v_value(c_bit2, s27) | (~node1(c_bit2, s27))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5567])).
% 35.79/23.65 tff(5569,plain,
% 35.79/23.65 (((~![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, s27)) | (~m_counter_cell_v_carry_in(c_bit2, s27)) | m_counter_cell_v_value(c_bit2, s27))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s27)) | m_counter_cell_v_value(c_bit2, s27) | (~node1(c_bit2, s27)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5568, 5566])).
% 35.79/23.65 tff(5570,plain,
% 35.79/23.65 ((~![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, s27)) | (~m_counter_cell_v_carry_in(c_bit2, s27)) | m_counter_cell_v_value(c_bit2, s27))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5571,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~node1(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, s27)) | m_counter_cell_v_value(c_bit2, s27) | (~node1(c_bit2, s27))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5570, 5569])).
% 35.79/23.65 tff(5572,plain,
% 35.79/23.65 (~node1(c_bit2, s27)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5571, 170, 5565, 4452])).
% 35.79/23.65 tff(5573,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit2, s27, s28))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit2, s27, s28))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5574,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s27, s28)) | node3(c_bit2, s27, s28))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5575,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s27, s28)) | node3(c_bit2, s27, s28)),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5574, 5573])).
% 35.79/23.65 tff(5576,plain,
% 35.79/23.65 (node3(c_bit2, s27, s28)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5575, 81, 929])).
% 35.79/23.65 tff(5577,plain,
% 35.79/23.65 (((~![Y: $i, 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, s28) | node1(c_bit2, s27) | (~node3(c_bit2, s27, s28)))) <=> ((~![Y: $i, 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, s28) | node1(c_bit2, s27) | (~node3(c_bit2, s27, s28)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5578,plain,
% 35.79/23.65 ((node1(c_bit2, s27) | (~node3(c_bit2, s27, s28)) | m_counter_cell_v_value(c_bit2, s28)) <=> (m_counter_cell_v_value(c_bit2, s28) | node1(c_bit2, s27) | (~node3(c_bit2, s27, s28)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5579,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s27) | (~node3(c_bit2, s27, s28)) | m_counter_cell_v_value(c_bit2, s28))) <=> ((~![Y: $i, 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, s28) | node1(c_bit2, s27) | (~node3(c_bit2, s27, s28))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5578])).
% 35.79/23.65 tff(5580,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s27) | (~node3(c_bit2, s27, s28)) | m_counter_cell_v_value(c_bit2, s28))) <=> ((~![Y: $i, 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, s28) | node1(c_bit2, s27) | (~node3(c_bit2, s27, s28)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5579, 5577])).
% 35.79/23.65 tff(5581,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s27) | (~node3(c_bit2, s27, s28)) | m_counter_cell_v_value(c_bit2, s28))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5582,plain,
% 35.79/23.65 ((~![Y: $i, 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, s28) | node1(c_bit2, s27) | (~node3(c_bit2, s27, s28))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5581, 5580])).
% 35.79/23.65 tff(5583,plain,
% 35.79/23.65 (m_counter_cell_v_value(c_bit2, s28) | node1(c_bit2, s27)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5582, 199, 5576])).
% 35.79/23.65 tff(5584,plain,
% 35.79/23.65 (m_counter_cell_v_value(c_bit2, s28)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5583, 5572])).
% 35.79/23.65 tff(5585,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s28) | (~node4(c_bit1, s28)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s28) | (~node4(c_bit1, s28)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5586,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s28) | (~node4(c_bit1, s28)))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5587,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s28) | (~node4(c_bit1, s28))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5586, 5585])).
% 35.79/23.65 tff(5588,plain,
% 35.79/23.65 (~node4(c_bit1, s28)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5587, 3076, 4156])).
% 35.79/23.65 tff(5589,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s28)) | node4(c_bit1, s28))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s28)) | node4(c_bit1, s28))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5590,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s28)) | node4(c_bit1, s28))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5591,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s28)) | node4(c_bit1, s28)),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5590, 5589])).
% 35.79/23.65 tff(5592,plain,
% 35.79/23.65 (~m_counter_cell_v_carry_out(c_bit1, s28)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5591, 2887, 5588])).
% 35.79/23.65 tff(5593,plain,
% 35.79/23.65 (((~![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, s28)) | m_counter_cell_v_carry_out(c_bit1, s28))) <=> ((~![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, s28)) | m_counter_cell_v_carry_out(c_bit1, s28))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5594,plain,
% 35.79/23.65 ((~![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, s28)) | m_counter_cell_v_carry_out(c_bit1, s28))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5595,plain,
% 35.79/23.65 ((~![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, s28)) | m_counter_cell_v_carry_out(c_bit1, s28)),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5594, 5593])).
% 35.79/23.65 tff(5596,plain,
% 35.79/23.65 (~m_counter_cell_v_carry_in(c_bit2, s28)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5595, 3167, 5592])).
% 35.79/23.65 tff(5597,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : ((~node1(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, s28) | (~m_counter_cell_v_value(c_bit2, s28)) | (~node1(c_bit2, 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_bit2, s28) | (~m_counter_cell_v_value(c_bit2, s28)) | (~node1(c_bit2, s28)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5598,plain,
% 35.79/23.65 (((~node1(c_bit2, s28)) | m_counter_cell_v_carry_in(c_bit2, s28) | (~m_counter_cell_v_value(c_bit2, s28))) <=> (m_counter_cell_v_carry_in(c_bit2, s28) | (~m_counter_cell_v_value(c_bit2, s28)) | (~node1(c_bit2, s28)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5599,plain,
% 35.79/23.65 (((~![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, s28)) | m_counter_cell_v_carry_in(c_bit2, s28) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s28) | (~m_counter_cell_v_value(c_bit2, s28)) | (~node1(c_bit2, s28))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5598])).
% 35.79/23.65 tff(5600,plain,
% 35.79/23.65 (((~![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, s28)) | m_counter_cell_v_carry_in(c_bit2, s28) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s28) | (~m_counter_cell_v_value(c_bit2, s28)) | (~node1(c_bit2, s28)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5599, 5597])).
% 35.79/23.65 tff(5601,plain,
% 35.79/23.65 ((~![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, s28)) | m_counter_cell_v_carry_in(c_bit2, s28) | (~m_counter_cell_v_value(c_bit2, s28)))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5602,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~node1(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, s28) | (~m_counter_cell_v_value(c_bit2, s28)) | (~node1(c_bit2, s28))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5601, 5600])).
% 35.79/23.65 tff(5603,plain,
% 35.79/23.65 ((~m_counter_cell_v_value(c_bit2, s28)) | (~node1(c_bit2, s28))),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5602, 3359, 5596])).
% 35.79/23.65 tff(5604,plain,
% 35.79/23.65 (~node1(c_bit2, s28)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5603, 5584])).
% 35.79/23.65 tff(5605,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit2, s28, s29))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit2, s28, s29))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5606,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s28, s29)) | node3(c_bit2, s28, s29))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5607,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s28, s29)) | node3(c_bit2, s28, s29)),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5606, 5605])).
% 35.79/23.65 tff(5608,plain,
% 35.79/23.65 (node3(c_bit2, s28, s29)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5607, 81, 958])).
% 35.79/23.65 tff(5609,plain,
% 35.79/23.65 (((~![Y: $i, 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, s29) | node1(c_bit2, s28) | (~node3(c_bit2, 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_bit2, s29) | node1(c_bit2, s28) | (~node3(c_bit2, s28, s29)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5610,plain,
% 35.79/23.65 ((node1(c_bit2, s28) | (~node3(c_bit2, s28, s29)) | m_counter_cell_v_value(c_bit2, s29)) <=> (m_counter_cell_v_value(c_bit2, s29) | node1(c_bit2, s28) | (~node3(c_bit2, s28, s29)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5611,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s28) | (~node3(c_bit2, s28, s29)) | m_counter_cell_v_value(c_bit2, 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_bit2, s29) | node1(c_bit2, s28) | (~node3(c_bit2, s28, s29))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5610])).
% 35.79/23.65 tff(5612,plain,
% 35.79/23.65 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s28) | (~node3(c_bit2, s28, s29)) | m_counter_cell_v_value(c_bit2, 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_bit2, s29) | node1(c_bit2, s28) | (~node3(c_bit2, s28, s29)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5611, 5609])).
% 35.79/23.65 tff(5613,plain,
% 35.79/23.65 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s28) | (~node3(c_bit2, s28, s29)) | m_counter_cell_v_value(c_bit2, s29))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5614,plain,
% 35.79/23.65 ((~![Y: $i, 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, s29) | node1(c_bit2, s28) | (~node3(c_bit2, s28, s29))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5613, 5612])).
% 35.79/23.65 tff(5615,plain,
% 35.79/23.65 (m_counter_cell_v_value(c_bit2, s29) | node1(c_bit2, s28)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5614, 199, 5608])).
% 35.79/23.65 tff(5616,plain,
% 35.79/23.65 (m_counter_cell_v_value(c_bit2, s29)),
% 35.79/23.65 inference(unit_resolution,[status(thm)],[5615, 5604])).
% 35.79/23.65 tff(5617,plain,
% 35.79/23.65 (((~![I0: $i, X: $i] : ((~node1(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, s29) | (~m_counter_cell_v_value(c_bit2, s29)) | (~node1(c_bit2, 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_bit2, s29) | (~m_counter_cell_v_value(c_bit2, s29)) | (~node1(c_bit2, s29)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5618,plain,
% 35.79/23.65 (((~node1(c_bit2, s29)) | m_counter_cell_v_carry_in(c_bit2, s29) | (~m_counter_cell_v_value(c_bit2, s29))) <=> (m_counter_cell_v_carry_in(c_bit2, s29) | (~m_counter_cell_v_value(c_bit2, s29)) | (~node1(c_bit2, s29)))),
% 35.79/23.65 inference(rewrite,[status(thm)],[])).
% 35.79/23.65 tff(5619,plain,
% 35.79/23.65 (((~![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, s29)) | m_counter_cell_v_carry_in(c_bit2, s29) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s29) | (~m_counter_cell_v_value(c_bit2, s29)) | (~node1(c_bit2, s29))))),
% 35.79/23.65 inference(monotonicity,[status(thm)],[5618])).
% 35.79/23.65 tff(5620,plain,
% 35.79/23.65 (((~![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, s29)) | m_counter_cell_v_carry_in(c_bit2, s29) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s29) | (~m_counter_cell_v_value(c_bit2, s29)) | (~node1(c_bit2, s29)))),
% 35.79/23.65 inference(transitivity,[status(thm)],[5619, 5617])).
% 35.79/23.65 tff(5621,plain,
% 35.79/23.65 ((~![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, s29)) | m_counter_cell_v_carry_in(c_bit2, s29) | (~m_counter_cell_v_value(c_bit2, s29)))),
% 35.79/23.65 inference(quant_inst,[status(thm)],[])).
% 35.79/23.65 tff(5622,plain,
% 35.79/23.65 ((~![I0: $i, X: $i] : ((~node1(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, s29) | (~m_counter_cell_v_value(c_bit2, s29)) | (~node1(c_bit2, s29))),
% 35.79/23.65 inference(modus_ponens,[status(thm)],[5621, 5620])).
% 35.79/23.65 tff(5623,plain,
% 35.79/23.65 (m_counter_cell_v_carry_in(c_bit2, s29) | (~node1(c_bit2, s29))),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5622, 3359, 5616])).
% 35.79/23.66 tff(5624,plain,
% 35.79/23.66 (~node1(c_bit2, s29)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5623, 4435])).
% 35.79/23.66 tff(5625,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit2, s29, s30))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit2, s29, s30))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5626,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s29, s30)) | node3(c_bit2, s29, s30))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5627,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s29, s30)) | node3(c_bit2, s29, s30)),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5626, 5625])).
% 35.79/23.66 tff(5628,plain,
% 35.79/23.66 (node3(c_bit2, s29, s30)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5627, 81, 986])).
% 35.79/23.66 tff(5629,plain,
% 35.79/23.66 (((~![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, s30) | node1(c_bit2, s29) | (~node3(c_bit2, 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_bit2, s30) | node1(c_bit2, s29) | (~node3(c_bit2, s29, s30)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5630,plain,
% 35.79/23.66 ((node1(c_bit2, s29) | (~node3(c_bit2, s29, s30)) | m_counter_cell_v_value(c_bit2, s30)) <=> (m_counter_cell_v_value(c_bit2, s30) | node1(c_bit2, s29) | (~node3(c_bit2, s29, s30)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5631,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s29) | (~node3(c_bit2, s29, s30)) | m_counter_cell_v_value(c_bit2, 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_bit2, s30) | node1(c_bit2, s29) | (~node3(c_bit2, s29, s30))))),
% 35.79/23.66 inference(monotonicity,[status(thm)],[5630])).
% 35.79/23.66 tff(5632,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s29) | (~node3(c_bit2, s29, s30)) | m_counter_cell_v_value(c_bit2, 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_bit2, s30) | node1(c_bit2, s29) | (~node3(c_bit2, s29, s30)))),
% 35.79/23.66 inference(transitivity,[status(thm)],[5631, 5629])).
% 35.79/23.66 tff(5633,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s29) | (~node3(c_bit2, s29, s30)) | m_counter_cell_v_value(c_bit2, s30))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5634,plain,
% 35.79/23.66 ((~![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, s30) | node1(c_bit2, s29) | (~node3(c_bit2, s29, s30))),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5633, 5632])).
% 35.79/23.66 tff(5635,plain,
% 35.79/23.66 (m_counter_cell_v_value(c_bit2, s30) | node1(c_bit2, s29)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5634, 199, 5628])).
% 35.79/23.66 tff(5636,plain,
% 35.79/23.66 (m_counter_cell_v_value(c_bit2, s30)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5635, 5624])).
% 35.79/23.66 tff(5637,plain,
% 35.79/23.66 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s30) | (~node4(c_bit1, s30)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~node4(c_bit1, s30)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5638,plain,
% 35.79/23.66 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s30) | (~node4(c_bit1, s30)))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5639,plain,
% 35.79/23.66 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s30) | (~node4(c_bit1, s30))),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5638, 5637])).
% 35.79/23.66 tff(5640,plain,
% 35.79/23.66 (~node4(c_bit1, s30)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5639, 3076, 4223])).
% 35.79/23.66 tff(5641,plain,
% 35.79/23.66 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s30)) | node4(c_bit1, s30))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s30)) | node4(c_bit1, s30))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5642,plain,
% 35.79/23.66 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s30)) | node4(c_bit1, s30))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5643,plain,
% 35.79/23.66 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s30)) | node4(c_bit1, s30)),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5642, 5641])).
% 35.79/23.66 tff(5644,plain,
% 35.79/23.66 (~m_counter_cell_v_carry_out(c_bit1, s30)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5643, 2887, 5640])).
% 35.79/23.66 tff(5645,plain,
% 35.79/23.66 (((~![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, s30)) | m_counter_cell_v_carry_out(c_bit1, s30))) <=> ((~![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, s30)) | m_counter_cell_v_carry_out(c_bit1, s30))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5646,plain,
% 35.79/23.66 ((~![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, s30)) | m_counter_cell_v_carry_out(c_bit1, s30))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5647,plain,
% 35.79/23.66 ((~![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, s30)) | m_counter_cell_v_carry_out(c_bit1, s30)),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5646, 5645])).
% 35.79/23.66 tff(5648,plain,
% 35.79/23.66 (~m_counter_cell_v_carry_in(c_bit2, s30)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5647, 3167, 5644])).
% 35.79/23.66 tff(5649,plain,
% 35.79/23.66 (((~![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, s30) | (~m_counter_cell_v_value(c_bit2, s30)) | (~node1(c_bit2, 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_bit2, s30) | (~m_counter_cell_v_value(c_bit2, s30)) | (~node1(c_bit2, s30)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5650,plain,
% 35.79/23.66 (((~node1(c_bit2, s30)) | m_counter_cell_v_carry_in(c_bit2, s30) | (~m_counter_cell_v_value(c_bit2, s30))) <=> (m_counter_cell_v_carry_in(c_bit2, s30) | (~m_counter_cell_v_value(c_bit2, s30)) | (~node1(c_bit2, s30)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5651,plain,
% 35.79/23.66 (((~![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, s30)) | m_counter_cell_v_carry_in(c_bit2, s30) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s30) | (~m_counter_cell_v_value(c_bit2, s30)) | (~node1(c_bit2, s30))))),
% 35.79/23.66 inference(monotonicity,[status(thm)],[5650])).
% 35.79/23.66 tff(5652,plain,
% 35.79/23.66 (((~![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, s30)) | m_counter_cell_v_carry_in(c_bit2, s30) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s30) | (~m_counter_cell_v_value(c_bit2, s30)) | (~node1(c_bit2, s30)))),
% 35.79/23.66 inference(transitivity,[status(thm)],[5651, 5649])).
% 35.79/23.66 tff(5653,plain,
% 35.79/23.66 ((~![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, s30)) | m_counter_cell_v_carry_in(c_bit2, s30) | (~m_counter_cell_v_value(c_bit2, s30)))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5654,plain,
% 35.79/23.66 ((~![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, s30) | (~m_counter_cell_v_value(c_bit2, s30)) | (~node1(c_bit2, s30))),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5653, 5652])).
% 35.79/23.66 tff(5655,plain,
% 35.79/23.66 ((~m_counter_cell_v_value(c_bit2, s30)) | (~node1(c_bit2, s30))),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5654, 3359, 5648])).
% 35.79/23.66 tff(5656,plain,
% 35.79/23.66 (~node1(c_bit2, s30)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5655, 5636])).
% 35.79/23.66 tff(5657,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit2, s30, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit2, s30, s31))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5658,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s30, s31)) | node3(c_bit2, s30, s31))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5659,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s30, s31)) | node3(c_bit2, s30, s31)),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5658, 5657])).
% 35.79/23.66 tff(5660,plain,
% 35.79/23.66 (node3(c_bit2, s30, s31)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5659, 81, 1017])).
% 35.79/23.66 tff(5661,plain,
% 35.79/23.66 (((~![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, s31) | node1(c_bit2, s30) | (~node3(c_bit2, 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_bit2, s31) | node1(c_bit2, s30) | (~node3(c_bit2, s30, s31)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5662,plain,
% 35.79/23.66 ((node1(c_bit2, s30) | (~node3(c_bit2, s30, s31)) | m_counter_cell_v_value(c_bit2, s31)) <=> (m_counter_cell_v_value(c_bit2, s31) | node1(c_bit2, s30) | (~node3(c_bit2, s30, s31)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5663,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s30) | (~node3(c_bit2, s30, s31)) | m_counter_cell_v_value(c_bit2, 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_bit2, s31) | node1(c_bit2, s30) | (~node3(c_bit2, s30, s31))))),
% 35.79/23.66 inference(monotonicity,[status(thm)],[5662])).
% 35.79/23.66 tff(5664,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s30) | (~node3(c_bit2, s30, s31)) | m_counter_cell_v_value(c_bit2, 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_bit2, s31) | node1(c_bit2, s30) | (~node3(c_bit2, s30, s31)))),
% 35.79/23.66 inference(transitivity,[status(thm)],[5663, 5661])).
% 35.79/23.66 tff(5665,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s30) | (~node3(c_bit2, s30, s31)) | m_counter_cell_v_value(c_bit2, s31))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5666,plain,
% 35.79/23.66 ((~![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, s31) | node1(c_bit2, s30) | (~node3(c_bit2, s30, s31))),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5665, 5664])).
% 35.79/23.66 tff(5667,plain,
% 35.79/23.66 (m_counter_cell_v_value(c_bit2, s31) | node1(c_bit2, s30)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5666, 199, 5660])).
% 35.79/23.66 tff(5668,plain,
% 35.79/23.66 (m_counter_cell_v_value(c_bit2, s31)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5667, 5656])).
% 35.79/23.66 tff(5669,assumption,(~m_counter_cell_v_carry_out(c_bit1, s31)), introduced(assumption)).
% 35.79/23.66 tff(5670,assumption,(m_counter_cell_v_carry_in(c_bit1, s31)), introduced(assumption)).
% 35.79/23.66 tff(5671,plain,
% 35.79/23.66 (((~![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, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | m_counter_cell_v_carry_out(c_bit1, 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_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | m_counter_cell_v_carry_out(c_bit1, s31))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5672,plain,
% 35.79/23.66 ((~![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, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | m_counter_cell_v_carry_out(c_bit1, s31))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5673,plain,
% 35.79/23.66 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31)) | m_counter_cell_v_carry_out(c_bit1, s31)),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5672, 5671])).
% 35.79/23.66 tff(5674,plain,
% 35.79/23.66 ($false),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5673, 3031, 5670, 4257, 5669])).
% 35.79/23.66 tff(5675,plain,(m_counter_cell_v_carry_out(c_bit1, s31) | (~m_counter_cell_v_carry_in(c_bit1, s31)) | (~m_counter_cell_v_value(c_bit1, s31))), inference(lemma,lemma(discharge,[]))).
% 35.79/23.66 tff(5676,plain,
% 35.79/23.66 (m_counter_cell_v_carry_out(c_bit1, s31) | (~m_counter_cell_v_value(c_bit1, s31))),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5675, 4256])).
% 35.79/23.66 tff(5677,plain,
% 35.79/23.66 (m_counter_cell_v_carry_out(c_bit1, s31)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5676, 4243])).
% 35.79/23.66 tff(5678,assumption,(~m_counter_cell_v_carry_in(c_bit2, s31)), introduced(assumption)).
% 35.79/23.66 tff(5679,assumption,(m_counter_cell_v_carry_out(c_bit1, s31)), introduced(assumption)).
% 35.79/23.66 tff(5680,plain,
% 35.79/23.66 (((~![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, s31)) | m_counter_cell_v_carry_in(c_bit2, s31))) <=> ((~![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, s31)) | m_counter_cell_v_carry_in(c_bit2, s31))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5681,plain,
% 35.79/23.66 ((~![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, s31)) | m_counter_cell_v_carry_in(c_bit2, s31))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5682,plain,
% 35.79/23.66 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s31)) | m_counter_cell_v_carry_in(c_bit2, s31)),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5681, 5680])).
% 35.79/23.66 tff(5683,plain,
% 35.79/23.66 ($false),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5682, 4417, 5679, 5678])).
% 35.79/23.66 tff(5684,plain,(m_counter_cell_v_carry_in(c_bit2, s31) | (~m_counter_cell_v_carry_out(c_bit1, s31))), inference(lemma,lemma(discharge,[]))).
% 35.79/23.66 tff(5685,plain,
% 35.79/23.66 (m_counter_cell_v_carry_in(c_bit2, s31)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5684, 5677])).
% 35.79/23.66 tff(5686,plain,
% 35.79/23.66 (((~![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, s31)) | (~m_counter_cell_v_value(c_bit2, s31)) | (~node2(c_bit2, 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_bit2, s31)) | (~m_counter_cell_v_value(c_bit2, s31)) | (~node2(c_bit2, s31)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5687,plain,
% 35.79/23.66 ((~![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, s31)) | (~m_counter_cell_v_value(c_bit2, s31)) | (~node2(c_bit2, s31)))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5688,plain,
% 35.79/23.66 ((~![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, s31)) | (~m_counter_cell_v_value(c_bit2, s31)) | (~node2(c_bit2, s31))),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5687, 5686])).
% 35.79/23.66 tff(5689,plain,
% 35.79/23.66 (~node2(c_bit2, s31)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5688, 219, 5685, 5668])).
% 35.79/23.66 tff(5690,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit2, s31, s32))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit2, s31, s32))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5691,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s31, s32)) | node3(c_bit2, s31, s32))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5692,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s31, s32)) | node3(c_bit2, s31, s32)),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5691, 5690])).
% 35.79/23.66 tff(5693,plain,
% 35.79/23.66 (node3(c_bit2, s31, s32)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5692, 81, 1045])).
% 35.79/23.66 tff(5694,plain,
% 35.79/23.66 (((~![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, s32)) | node2(c_bit2, s31) | (~node3(c_bit2, 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_bit2, s32)) | node2(c_bit2, s31) | (~node3(c_bit2, s31, s32)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5695,plain,
% 35.79/23.66 ((node2(c_bit2, s31) | (~node3(c_bit2, s31, s32)) | (~m_counter_cell_v_value(c_bit2, s32))) <=> ((~m_counter_cell_v_value(c_bit2, s32)) | node2(c_bit2, s31) | (~node3(c_bit2, s31, s32)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.79/23.66 tff(5696,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s31) | (~node3(c_bit2, s31, s32)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s32)) | node2(c_bit2, s31) | (~node3(c_bit2, s31, s32))))),
% 35.79/23.66 inference(monotonicity,[status(thm)],[5695])).
% 35.79/23.66 tff(5697,plain,
% 35.79/23.66 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s31) | (~node3(c_bit2, s31, s32)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s32)) | node2(c_bit2, s31) | (~node3(c_bit2, s31, s32)))),
% 35.79/23.66 inference(transitivity,[status(thm)],[5696, 5694])).
% 35.79/23.66 tff(5698,plain,
% 35.79/23.66 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s31) | (~node3(c_bit2, s31, s32)) | (~m_counter_cell_v_value(c_bit2, s32)))),
% 35.79/23.66 inference(quant_inst,[status(thm)],[])).
% 35.79/23.66 tff(5699,plain,
% 35.79/23.66 ((~![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, s32)) | node2(c_bit2, s31) | (~node3(c_bit2, s31, s32))),
% 35.79/23.66 inference(modus_ponens,[status(thm)],[5698, 5697])).
% 35.79/23.66 tff(5700,plain,
% 35.79/23.66 ((~m_counter_cell_v_value(c_bit2, s32)) | node2(c_bit2, s31)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5699, 234, 5693])).
% 35.79/23.66 tff(5701,plain,
% 35.79/23.66 (~m_counter_cell_v_value(c_bit2, s32)),
% 35.79/23.66 inference(unit_resolution,[status(thm)],[5700, 5689])).
% 35.79/23.66 tff(5702,assumption,(node4(c_bit1, s32)), introduced(assumption)).
% 35.79/23.66 tff(5703,plain,
% 35.79/23.66 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s32) | (~node4(c_bit1, s32)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s32) | (~node4(c_bit1, s32)))),
% 35.79/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5704,plain,
% 35.86/23.66 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s32) | (~node4(c_bit1, s32)))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5705,plain,
% 35.86/23.66 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s32) | (~node4(c_bit1, s32))),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5704, 5703])).
% 35.86/23.66 tff(5706,plain,
% 35.86/23.66 ($false),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5705, 3076, 4294, 5702])).
% 35.86/23.66 tff(5707,plain,(~node4(c_bit1, s32)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.66 tff(5708,plain,
% 35.86/23.66 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s32)) | node4(c_bit1, s32))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s32)) | node4(c_bit1, s32))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5709,plain,
% 35.86/23.66 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s32)) | node4(c_bit1, s32))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5710,plain,
% 35.86/23.66 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s32)) | node4(c_bit1, s32)),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5709, 5708])).
% 35.86/23.66 tff(5711,plain,
% 35.86/23.66 (~m_counter_cell_v_carry_out(c_bit1, s32)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5710, 2887, 5707])).
% 35.86/23.66 tff(5712,plain,
% 35.86/23.66 (((~![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, s32)) | m_counter_cell_v_carry_out(c_bit1, s32))) <=> ((~![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, s32)) | m_counter_cell_v_carry_out(c_bit1, s32))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5713,plain,
% 35.86/23.66 ((~![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, s32)) | m_counter_cell_v_carry_out(c_bit1, s32))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5714,plain,
% 35.86/23.66 ((~![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, s32)) | m_counter_cell_v_carry_out(c_bit1, s32)),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5713, 5712])).
% 35.86/23.66 tff(5715,plain,
% 35.86/23.66 (~m_counter_cell_v_carry_in(c_bit2, s32)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5714, 3167, 5711])).
% 35.86/23.66 tff(5716,plain,
% 35.86/23.66 (((~![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, s32) | m_counter_cell_v_value(c_bit2, s32) | (~node2(c_bit2, 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_bit2, s32) | m_counter_cell_v_value(c_bit2, s32) | (~node2(c_bit2, s32)))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5717,plain,
% 35.86/23.66 ((~![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, s32) | m_counter_cell_v_value(c_bit2, s32) | (~node2(c_bit2, s32)))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5718,plain,
% 35.86/23.66 ((~![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, s32) | m_counter_cell_v_value(c_bit2, s32) | (~node2(c_bit2, s32))),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5717, 5716])).
% 35.86/23.66 tff(5719,plain,
% 35.86/23.66 (m_counter_cell_v_value(c_bit2, s32) | (~node2(c_bit2, s32))),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5718, 3291, 5715])).
% 35.86/23.66 tff(5720,plain,
% 35.86/23.66 (~node2(c_bit2, s32)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5719, 5701])).
% 35.86/23.66 tff(5721,plain,
% 35.86/23.66 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit2, s32, s33))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit2, s32, s33))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5722,plain,
% 35.86/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s32, s33)) | node3(c_bit2, s32, s33))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5723,plain,
% 35.86/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s32, s33)) | node3(c_bit2, s32, s33)),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5722, 5721])).
% 35.86/23.66 tff(5724,plain,
% 35.86/23.66 (node3(c_bit2, s32, s33)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5723, 81, 1076])).
% 35.86/23.66 tff(5725,plain,
% 35.86/23.66 (((~![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, s33)) | node2(c_bit2, s32) | (~node3(c_bit2, 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_bit2, s33)) | node2(c_bit2, s32) | (~node3(c_bit2, s32, s33)))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5726,plain,
% 35.86/23.66 ((node2(c_bit2, s32) | (~node3(c_bit2, s32, s33)) | (~m_counter_cell_v_value(c_bit2, s33))) <=> ((~m_counter_cell_v_value(c_bit2, s33)) | node2(c_bit2, s32) | (~node3(c_bit2, s32, s33)))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5727,plain,
% 35.86/23.66 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s32) | (~node3(c_bit2, s32, s33)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s33)) | node2(c_bit2, s32) | (~node3(c_bit2, s32, s33))))),
% 35.86/23.66 inference(monotonicity,[status(thm)],[5726])).
% 35.86/23.66 tff(5728,plain,
% 35.86/23.66 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s32) | (~node3(c_bit2, s32, s33)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s33)) | node2(c_bit2, s32) | (~node3(c_bit2, s32, s33)))),
% 35.86/23.66 inference(transitivity,[status(thm)],[5727, 5725])).
% 35.86/23.66 tff(5729,plain,
% 35.86/23.66 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s32) | (~node3(c_bit2, s32, s33)) | (~m_counter_cell_v_value(c_bit2, s33)))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5730,plain,
% 35.86/23.66 ((~![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, s33)) | node2(c_bit2, s32) | (~node3(c_bit2, s32, s33))),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5729, 5728])).
% 35.86/23.66 tff(5731,plain,
% 35.86/23.66 ((~m_counter_cell_v_value(c_bit2, s33)) | node2(c_bit2, s32)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5730, 234, 5724])).
% 35.86/23.66 tff(5732,plain,
% 35.86/23.66 (~m_counter_cell_v_value(c_bit2, s33)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5731, 5720])).
% 35.86/23.66 tff(5733,plain,
% 35.86/23.66 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s33) | (~node4(c_bit1, s33)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s33) | (~node4(c_bit1, s33)))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5734,plain,
% 35.86/23.66 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s33) | (~node4(c_bit1, s33)))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5735,plain,
% 35.86/23.66 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s33) | (~node4(c_bit1, s33))),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5734, 5733])).
% 35.86/23.66 tff(5736,plain,
% 35.86/23.66 (~node4(c_bit1, s33)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5735, 2875, 4314])).
% 35.86/23.66 tff(5737,assumption,(~node4(c_bit1, s33)), introduced(assumption)).
% 35.86/23.66 tff(5738,assumption,(m_counter_cell_v_carry_out(c_bit1, s33)), introduced(assumption)).
% 35.86/23.66 tff(5739,plain,
% 35.86/23.66 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s33)) | node4(c_bit1, s33))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s33)) | node4(c_bit1, s33))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5740,plain,
% 35.86/23.66 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s33)) | node4(c_bit1, s33))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5741,plain,
% 35.86/23.66 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s33)) | node4(c_bit1, s33)),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5740, 5739])).
% 35.86/23.66 tff(5742,plain,
% 35.86/23.66 ($false),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5741, 2887, 5738, 5737])).
% 35.86/23.66 tff(5743,plain,(node4(c_bit1, s33) | (~m_counter_cell_v_carry_out(c_bit1, s33))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.66 tff(5744,plain,
% 35.86/23.66 (~m_counter_cell_v_carry_out(c_bit1, s33)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5743, 5736])).
% 35.86/23.66 tff(5745,plain,
% 35.86/23.66 (((~![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, s33)) | m_counter_cell_v_carry_out(c_bit1, s33))) <=> ((~![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, s33)) | m_counter_cell_v_carry_out(c_bit1, s33))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5746,plain,
% 35.86/23.66 ((~![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, s33)) | m_counter_cell_v_carry_out(c_bit1, s33))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5747,plain,
% 35.86/23.66 ((~![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, s33)) | m_counter_cell_v_carry_out(c_bit1, s33)),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5746, 5745])).
% 35.86/23.66 tff(5748,plain,
% 35.86/23.66 (~m_counter_cell_v_carry_in(c_bit2, s33)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5747, 3167, 5744])).
% 35.86/23.66 tff(5749,plain,
% 35.86/23.66 (((~![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, s33) | m_counter_cell_v_value(c_bit2, s33) | (~node2(c_bit2, 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_bit2, s33) | m_counter_cell_v_value(c_bit2, s33) | (~node2(c_bit2, s33)))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5750,plain,
% 35.86/23.66 ((~![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, s33) | m_counter_cell_v_value(c_bit2, s33) | (~node2(c_bit2, s33)))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5751,plain,
% 35.86/23.66 ((~![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, s33) | m_counter_cell_v_value(c_bit2, s33) | (~node2(c_bit2, s33))),
% 35.86/23.66 inference(modus_ponens,[status(thm)],[5750, 5749])).
% 35.86/23.66 tff(5752,plain,
% 35.86/23.66 (m_counter_cell_v_value(c_bit2, s33) | (~node2(c_bit2, s33))),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5751, 3291, 5748])).
% 35.86/23.66 tff(5753,plain,
% 35.86/23.66 (~node2(c_bit2, s33)),
% 35.86/23.66 inference(unit_resolution,[status(thm)],[5752, 5732])).
% 35.86/23.66 tff(5754,plain,
% 35.86/23.66 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit2, s33, s34))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit2, s33, s34))),
% 35.86/23.66 inference(rewrite,[status(thm)],[])).
% 35.86/23.66 tff(5755,plain,
% 35.86/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s33, s34)) | node3(c_bit2, s33, s34))),
% 35.86/23.66 inference(quant_inst,[status(thm)],[])).
% 35.86/23.66 tff(5756,plain,
% 35.86/23.66 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s33, s34)) | node3(c_bit2, s33, s34)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5755, 5754])).
% 35.86/23.67 tff(5757,plain,
% 35.86/23.67 (node3(c_bit2, s33, s34)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5756, 81, 1104])).
% 35.86/23.67 tff(5758,plain,
% 35.86/23.67 (((~![Y: $i, 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, s34)) | node2(c_bit2, s33) | (~node3(c_bit2, 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_bit2, s34)) | node2(c_bit2, s33) | (~node3(c_bit2, s33, s34)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5759,plain,
% 35.86/23.67 ((node2(c_bit2, s33) | (~node3(c_bit2, s33, s34)) | (~m_counter_cell_v_value(c_bit2, s34))) <=> ((~m_counter_cell_v_value(c_bit2, s34)) | node2(c_bit2, s33) | (~node3(c_bit2, s33, s34)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5760,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s33) | (~node3(c_bit2, s33, s34)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s34)) | node2(c_bit2, s33) | (~node3(c_bit2, s33, s34))))),
% 35.86/23.67 inference(monotonicity,[status(thm)],[5759])).
% 35.86/23.67 tff(5761,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s33) | (~node3(c_bit2, s33, s34)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s34)) | node2(c_bit2, s33) | (~node3(c_bit2, s33, s34)))),
% 35.86/23.67 inference(transitivity,[status(thm)],[5760, 5758])).
% 35.86/23.67 tff(5762,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s33) | (~node3(c_bit2, s33, s34)) | (~m_counter_cell_v_value(c_bit2, s34)))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5763,plain,
% 35.86/23.67 ((~![Y: $i, 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, s34)) | node2(c_bit2, s33) | (~node3(c_bit2, s33, s34))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5762, 5761])).
% 35.86/23.67 tff(5764,plain,
% 35.86/23.67 ((~m_counter_cell_v_value(c_bit2, s34)) | node2(c_bit2, s33)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5763, 234, 5757])).
% 35.86/23.67 tff(5765,plain,
% 35.86/23.67 (~m_counter_cell_v_value(c_bit2, s34)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5764, 5753])).
% 35.86/23.67 tff(5766,plain,
% 35.86/23.67 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s34) | (~node4(c_bit1, s34)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~node4(c_bit1, s34)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5767,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s34) | (~node4(c_bit1, s34)))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5768,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s34) | (~node4(c_bit1, s34))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5767, 5766])).
% 35.86/23.67 tff(5769,plain,
% 35.86/23.67 (~node4(c_bit1, s34)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5768, 3076, 4366])).
% 35.86/23.67 tff(5770,plain,
% 35.86/23.67 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s34)) | node4(c_bit1, s34))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s34)) | node4(c_bit1, s34))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5771,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s34)) | node4(c_bit1, s34))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5772,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s34)) | node4(c_bit1, s34)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5771, 5770])).
% 35.86/23.67 tff(5773,plain,
% 35.86/23.67 (~m_counter_cell_v_carry_out(c_bit1, s34)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5772, 2887, 5769])).
% 35.86/23.67 tff(5774,plain,
% 35.86/23.67 (((~![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, s34)) | m_counter_cell_v_carry_out(c_bit1, s34))) <=> ((~![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, s34)) | m_counter_cell_v_carry_out(c_bit1, s34))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5775,plain,
% 35.86/23.67 ((~![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, s34)) | m_counter_cell_v_carry_out(c_bit1, s34))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5776,plain,
% 35.86/23.67 ((~![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, s34)) | m_counter_cell_v_carry_out(c_bit1, s34)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5775, 5774])).
% 35.86/23.67 tff(5777,plain,
% 35.86/23.67 (~m_counter_cell_v_carry_in(c_bit2, s34)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5776, 3167, 5773])).
% 35.86/23.67 tff(5778,plain,
% 35.86/23.67 (((~![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_bit2, s34) | m_counter_cell_v_value(c_bit2, s34) | (~node2(c_bit2, s34)))) <=> ((~![I0: $i, X: $i] : (m_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, s34) | m_counter_cell_v_value(c_bit2, s34) | (~node2(c_bit2, s34)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5779,plain,
% 35.86/23.67 ((~![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_bit2, s34) | m_counter_cell_v_value(c_bit2, s34) | (~node2(c_bit2, s34)))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5780,plain,
% 35.86/23.67 ((~![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_bit2, s34) | m_counter_cell_v_value(c_bit2, s34) | (~node2(c_bit2, s34))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5779, 5778])).
% 35.86/23.67 tff(5781,plain,
% 35.86/23.67 (m_counter_cell_v_value(c_bit2, s34) | (~node2(c_bit2, s34))),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5780, 3291, 5777])).
% 35.86/23.67 tff(5782,plain,
% 35.86/23.67 (~node2(c_bit2, s34)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5781, 5765])).
% 35.86/23.67 tff(5783,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit2, s34, s35))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit2, s34, s35))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5784,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s34, s35)) | node3(c_bit2, s34, s35))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5785,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s34, s35)) | node3(c_bit2, s34, s35)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5784, 5783])).
% 35.86/23.67 tff(5786,plain,
% 35.86/23.67 (node3(c_bit2, s34, s35)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5785, 81, 1135])).
% 35.86/23.67 tff(5787,plain,
% 35.86/23.67 (((~![Y: $i, 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, s35)) | node2(c_bit2, s34) | (~node3(c_bit2, s34, s35)))) <=> ((~![Y: $i, 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, s35)) | node2(c_bit2, s34) | (~node3(c_bit2, s34, s35)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5788,plain,
% 35.86/23.67 ((node2(c_bit2, s34) | (~node3(c_bit2, s34, s35)) | (~m_counter_cell_v_value(c_bit2, s35))) <=> ((~m_counter_cell_v_value(c_bit2, s35)) | node2(c_bit2, s34) | (~node3(c_bit2, s34, s35)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5789,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s34) | (~node3(c_bit2, s34, s35)) | (~m_counter_cell_v_value(c_bit2, s35)))) <=> ((~![Y: $i, 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, s35)) | node2(c_bit2, s34) | (~node3(c_bit2, s34, s35))))),
% 35.86/23.67 inference(monotonicity,[status(thm)],[5788])).
% 35.86/23.67 tff(5790,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s34) | (~node3(c_bit2, s34, s35)) | (~m_counter_cell_v_value(c_bit2, s35)))) <=> ((~![Y: $i, 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, s35)) | node2(c_bit2, s34) | (~node3(c_bit2, s34, s35)))),
% 35.86/23.67 inference(transitivity,[status(thm)],[5789, 5787])).
% 35.86/23.67 tff(5791,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s34) | (~node3(c_bit2, s34, s35)) | (~m_counter_cell_v_value(c_bit2, s35)))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5792,plain,
% 35.86/23.67 ((~![Y: $i, 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, s35)) | node2(c_bit2, s34) | (~node3(c_bit2, s34, s35))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5791, 5790])).
% 35.86/23.67 tff(5793,plain,
% 35.86/23.67 ((~m_counter_cell_v_value(c_bit2, s35)) | node2(c_bit2, s34)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5792, 234, 5786])).
% 35.86/23.67 tff(5794,plain,
% 35.86/23.67 (~m_counter_cell_v_value(c_bit2, s35)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5793, 5782])).
% 35.86/23.67 tff(5795,plain,
% 35.86/23.67 (((~![I0: $i, X: $i] : ((~node1(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, s35)) | m_counter_cell_v_value(c_bit2, s35) | (~node1(c_bit2, s35)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s35)) | m_counter_cell_v_value(c_bit2, s35) | (~node1(c_bit2, s35)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5796,plain,
% 35.86/23.67 (((~node1(c_bit2, s35)) | (~m_counter_cell_v_carry_in(c_bit2, s35)) | m_counter_cell_v_value(c_bit2, s35)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s35)) | m_counter_cell_v_value(c_bit2, s35) | (~node1(c_bit2, s35)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5797,plain,
% 35.86/23.67 (((~![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, s35)) | (~m_counter_cell_v_carry_in(c_bit2, s35)) | m_counter_cell_v_value(c_bit2, s35))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s35)) | m_counter_cell_v_value(c_bit2, s35) | (~node1(c_bit2, s35))))),
% 35.86/23.67 inference(monotonicity,[status(thm)],[5796])).
% 35.86/23.67 tff(5798,plain,
% 35.86/23.67 (((~![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, s35)) | (~m_counter_cell_v_carry_in(c_bit2, s35)) | m_counter_cell_v_value(c_bit2, s35))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s35)) | m_counter_cell_v_value(c_bit2, s35) | (~node1(c_bit2, s35)))),
% 35.86/23.67 inference(transitivity,[status(thm)],[5797, 5795])).
% 35.86/23.67 tff(5799,plain,
% 35.86/23.67 ((~![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, s35)) | (~m_counter_cell_v_carry_in(c_bit2, s35)) | m_counter_cell_v_value(c_bit2, s35))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5800,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : ((~node1(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, s35)) | m_counter_cell_v_value(c_bit2, s35) | (~node1(c_bit2, s35))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5799, 5798])).
% 35.86/23.67 tff(5801,plain,
% 35.86/23.67 (~node1(c_bit2, s35)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5800, 170, 5794, 4423])).
% 35.86/23.67 tff(5802,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit2, s35, s36))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit2, s35, s36))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5803,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit2, s35, s36))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5804,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit2, s35, s36)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5803, 5802])).
% 35.86/23.67 tff(5805,plain,
% 35.86/23.67 (node3(c_bit2, s35, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5804, 81, 1163])).
% 35.86/23.67 tff(5806,plain,
% 35.86/23.67 (((~![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, s36) | node1(c_bit2, s35) | (~node3(c_bit2, s35, s36)))) <=> ((~![Y: $i, 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, s36) | node1(c_bit2, s35) | (~node3(c_bit2, s35, s36)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5807,plain,
% 35.86/23.67 ((node1(c_bit2, s35) | (~node3(c_bit2, s35, s36)) | m_counter_cell_v_value(c_bit2, s36)) <=> (m_counter_cell_v_value(c_bit2, s36) | node1(c_bit2, s35) | (~node3(c_bit2, s35, s36)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5808,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s35) | (~node3(c_bit2, s35, s36)) | m_counter_cell_v_value(c_bit2, s36))) <=> ((~![Y: $i, 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, s36) | node1(c_bit2, s35) | (~node3(c_bit2, s35, s36))))),
% 35.86/23.67 inference(monotonicity,[status(thm)],[5807])).
% 35.86/23.67 tff(5809,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s35) | (~node3(c_bit2, s35, s36)) | m_counter_cell_v_value(c_bit2, s36))) <=> ((~![Y: $i, 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, s36) | node1(c_bit2, s35) | (~node3(c_bit2, s35, s36)))),
% 35.86/23.67 inference(transitivity,[status(thm)],[5808, 5806])).
% 35.86/23.67 tff(5810,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s35) | (~node3(c_bit2, s35, s36)) | m_counter_cell_v_value(c_bit2, s36))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5811,plain,
% 35.86/23.67 ((~![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, s36) | node1(c_bit2, s35) | (~node3(c_bit2, s35, s36))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5810, 5809])).
% 35.86/23.67 tff(5812,plain,
% 35.86/23.67 (m_counter_cell_v_value(c_bit2, s36) | node1(c_bit2, s35)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5811, 199, 5805])).
% 35.86/23.67 tff(5813,plain,
% 35.86/23.67 (m_counter_cell_v_value(c_bit2, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5812, 5801])).
% 35.86/23.67 tff(5814,plain,
% 35.86/23.67 (((~![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)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5815,plain,
% 35.86/23.67 ((~![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)))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5816,plain,
% 35.86/23.67 ((~![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))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5815, 5814])).
% 35.86/23.67 tff(5817,plain,
% 35.86/23.67 (~node4(c_bit0, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5816, 2875, 1175])).
% 35.86/23.67 tff(5818,assumption,(m_counter_cell_v_carry_out(c_bit0, s36)), introduced(assumption)).
% 35.86/23.67 tff(5819,plain,
% 35.86/23.67 (((~![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))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5820,plain,
% 35.86/23.67 ((~![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))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5821,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s36)) | node4(c_bit0, s36)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5820, 5819])).
% 35.86/23.67 tff(5822,plain,
% 35.86/23.67 ($false),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5821, 2887, 5818, 5817])).
% 35.86/23.67 tff(5823,plain,(~m_counter_cell_v_carry_out(c_bit0, s36)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.67 tff(5824,assumption,(m_counter_cell_v_carry_in(c_bit1, s36)), introduced(assumption)).
% 35.86/23.67 tff(5825,assumption,(~m_counter_cell_v_carry_out(c_bit0, s36)), introduced(assumption)).
% 35.86/23.67 tff(5826,plain,
% 35.86/23.67 (((~![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))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5827,plain,
% 35.86/23.67 ((~![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))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5828,plain,
% 35.86/23.67 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s36)) | m_counter_cell_v_carry_out(c_bit0, s36)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5827, 5826])).
% 35.86/23.67 tff(5829,plain,
% 35.86/23.67 ($false),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5828, 2901, 5825, 5824])).
% 35.86/23.67 tff(5830,plain,(m_counter_cell_v_carry_out(c_bit0, s36) | (~m_counter_cell_v_carry_in(c_bit1, s36))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.67 tff(5831,plain,
% 35.86/23.67 (~m_counter_cell_v_carry_in(c_bit1, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5830, 5823])).
% 35.86/23.67 tff(5832,assumption,(node4(c_bit1, s36)), introduced(assumption)).
% 35.86/23.67 tff(5833,assumption,(~m_counter_cell_v_carry_in(c_bit1, s36)), introduced(assumption)).
% 35.86/23.67 tff(5834,plain,
% 35.86/23.67 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s36) | (~node4(c_bit1, s36)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s36) | (~node4(c_bit1, s36)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5835,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s36) | (~node4(c_bit1, s36)))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5836,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s36) | (~node4(c_bit1, s36))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5835, 5834])).
% 35.86/23.67 tff(5837,plain,
% 35.86/23.67 ($false),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5836, 3076, 5833, 5832])).
% 35.86/23.67 tff(5838,plain,((~node4(c_bit1, s36)) | m_counter_cell_v_carry_in(c_bit1, s36)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.67 tff(5839,plain,
% 35.86/23.67 (~node4(c_bit1, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5838, 5831])).
% 35.86/23.67 tff(5840,assumption,(~node4(c_bit1, s36)), introduced(assumption)).
% 35.86/23.67 tff(5841,assumption,(m_counter_cell_v_carry_out(c_bit1, s36)), introduced(assumption)).
% 35.86/23.67 tff(5842,plain,
% 35.86/23.67 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s36)) | node4(c_bit1, s36))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s36)) | node4(c_bit1, s36))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5843,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s36)) | node4(c_bit1, s36))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5844,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s36)) | node4(c_bit1, s36)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5843, 5842])).
% 35.86/23.67 tff(5845,plain,
% 35.86/23.67 ($false),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5844, 2887, 5841, 5840])).
% 35.86/23.67 tff(5846,plain,((~m_counter_cell_v_carry_out(c_bit1, s36)) | node4(c_bit1, s36)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.67 tff(5847,plain,
% 35.86/23.67 (~m_counter_cell_v_carry_out(c_bit1, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5846, 5839])).
% 35.86/23.67 tff(5848,assumption,(m_counter_cell_v_carry_in(c_bit2, s36)), introduced(assumption)).
% 35.86/23.67 tff(5849,assumption,(~m_counter_cell_v_carry_out(c_bit1, s36)), introduced(assumption)).
% 35.86/23.67 tff(5850,plain,
% 35.86/23.67 (((~![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, s36)) | m_counter_cell_v_carry_out(c_bit1, s36))) <=> ((~![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, s36)) | m_counter_cell_v_carry_out(c_bit1, s36))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5851,plain,
% 35.86/23.67 ((~![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, s36)) | m_counter_cell_v_carry_out(c_bit1, s36))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5852,plain,
% 35.86/23.67 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s36)) | m_counter_cell_v_carry_out(c_bit1, s36)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5851, 5850])).
% 35.86/23.67 tff(5853,plain,
% 35.86/23.67 ($false),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5852, 3167, 5849, 5848])).
% 35.86/23.67 tff(5854,plain,((~m_counter_cell_v_carry_in(c_bit2, s36)) | m_counter_cell_v_carry_out(c_bit1, s36)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.67 tff(5855,plain,
% 35.86/23.67 (~m_counter_cell_v_carry_in(c_bit2, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5854, 5847])).
% 35.86/23.67 tff(5856,plain,
% 35.86/23.67 (((~![I0: $i, X: $i] : ((~node1(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, s36) | (~m_counter_cell_v_value(c_bit2, s36)) | (~node1(c_bit2, 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_bit2, s36) | (~m_counter_cell_v_value(c_bit2, s36)) | (~node1(c_bit2, s36)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5857,plain,
% 35.86/23.67 (((~node1(c_bit2, s36)) | m_counter_cell_v_carry_in(c_bit2, s36) | (~m_counter_cell_v_value(c_bit2, s36))) <=> (m_counter_cell_v_carry_in(c_bit2, s36) | (~m_counter_cell_v_value(c_bit2, s36)) | (~node1(c_bit2, s36)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5858,plain,
% 35.86/23.67 (((~![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, s36)) | m_counter_cell_v_carry_in(c_bit2, s36) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s36) | (~m_counter_cell_v_value(c_bit2, s36)) | (~node1(c_bit2, s36))))),
% 35.86/23.67 inference(monotonicity,[status(thm)],[5857])).
% 35.86/23.67 tff(5859,plain,
% 35.86/23.67 (((~![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, s36)) | m_counter_cell_v_carry_in(c_bit2, s36) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s36) | (~m_counter_cell_v_value(c_bit2, s36)) | (~node1(c_bit2, s36)))),
% 35.86/23.67 inference(transitivity,[status(thm)],[5858, 5856])).
% 35.86/23.67 tff(5860,plain,
% 35.86/23.67 ((~![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, s36)) | m_counter_cell_v_carry_in(c_bit2, s36) | (~m_counter_cell_v_value(c_bit2, s36)))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5861,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : ((~node1(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, s36) | (~m_counter_cell_v_value(c_bit2, s36)) | (~node1(c_bit2, s36))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5860, 5859])).
% 35.86/23.67 tff(5862,plain,
% 35.86/23.67 (~node1(c_bit2, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5861, 3359, 5855, 5813])).
% 35.86/23.67 tff(5863,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit2, s36, s37))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit2, s36, s37))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5864,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit2, s36, s37))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5865,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit2, s36, s37)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5864, 5863])).
% 35.86/23.67 tff(5866,plain,
% 35.86/23.67 (node3(c_bit2, s36, s37)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5865, 81, 1194])).
% 35.86/23.67 tff(5867,plain,
% 35.86/23.67 (((~![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, s37) | node1(c_bit2, s36) | (~node3(c_bit2, 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_bit2, s37) | node1(c_bit2, s36) | (~node3(c_bit2, s36, s37)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5868,plain,
% 35.86/23.67 ((node1(c_bit2, s36) | (~node3(c_bit2, s36, s37)) | m_counter_cell_v_value(c_bit2, s37)) <=> (m_counter_cell_v_value(c_bit2, s37) | node1(c_bit2, s36) | (~node3(c_bit2, s36, s37)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5869,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s36) | (~node3(c_bit2, s36, s37)) | m_counter_cell_v_value(c_bit2, 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_bit2, s37) | node1(c_bit2, s36) | (~node3(c_bit2, s36, s37))))),
% 35.86/23.67 inference(monotonicity,[status(thm)],[5868])).
% 35.86/23.67 tff(5870,plain,
% 35.86/23.67 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s36) | (~node3(c_bit2, s36, s37)) | m_counter_cell_v_value(c_bit2, 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_bit2, s37) | node1(c_bit2, s36) | (~node3(c_bit2, s36, s37)))),
% 35.86/23.67 inference(transitivity,[status(thm)],[5869, 5867])).
% 35.86/23.67 tff(5871,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s36) | (~node3(c_bit2, s36, s37)) | m_counter_cell_v_value(c_bit2, s37))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5872,plain,
% 35.86/23.67 ((~![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, s37) | node1(c_bit2, s36) | (~node3(c_bit2, s36, s37))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5871, 5870])).
% 35.86/23.67 tff(5873,plain,
% 35.86/23.67 (m_counter_cell_v_value(c_bit2, s37) | node1(c_bit2, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5872, 199, 5866])).
% 35.86/23.67 tff(5874,plain,
% 35.86/23.67 (m_counter_cell_v_value(c_bit2, s37)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5873, 5862])).
% 35.86/23.67 tff(5875,assumption,(node2(c_bit1, s35)), introduced(assumption)).
% 35.86/23.67 tff(5876,plain,
% 35.86/23.67 (((~![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_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)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5877,plain,
% 35.86/23.67 ((~![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_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35)))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5878,plain,
% 35.86/23.67 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35)) | (~node2(c_bit1, s35))),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5877, 5876])).
% 35.86/23.67 tff(5879,plain,
% 35.86/23.67 ($false),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5878, 219, 4398, 4395, 5875])).
% 35.86/23.67 tff(5880,plain,((~node2(c_bit1, s35)) | (~m_counter_cell_v_value(c_bit1, s35))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.67 tff(5881,plain,
% 35.86/23.67 (~node2(c_bit1, s35)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5880, 4386])).
% 35.86/23.67 tff(5882,plain,
% 35.86/23.67 (((~![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))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5883,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s35, s36)) | node3(c_bit1, s35, s36))),
% 35.86/23.67 inference(quant_inst,[status(thm)],[])).
% 35.86/23.67 tff(5884,plain,
% 35.86/23.67 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s35, s36)) | node3(c_bit1, s35, s36)),
% 35.86/23.67 inference(modus_ponens,[status(thm)],[5883, 5882])).
% 35.86/23.67 tff(5885,plain,
% 35.86/23.67 (node3(c_bit1, s35, s36)),
% 35.86/23.67 inference(unit_resolution,[status(thm)],[5884, 81, 1163])).
% 35.86/23.67 tff(5886,plain,
% 35.86/23.67 (((~![Y: $i, I0: $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)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5887,plain,
% 35.86/23.67 ((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)))),
% 35.86/23.67 inference(rewrite,[status(thm)],[])).
% 35.86/23.67 tff(5888,plain,
% 35.86/23.67 (((~![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))))),
% 35.86/23.67 inference(monotonicity,[status(thm)],[5887])).
% 35.86/23.67 tff(5889,plain,
% 35.86/23.67 (((~![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)))),
% 35.86/23.68 inference(transitivity,[status(thm)],[5888, 5886])).
% 35.86/23.68 tff(5890,plain,
% 35.86/23.68 ((~![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)))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5891,plain,
% 35.86/23.68 ((~![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_bit1, s36)) | node2(c_bit1, s35) | (~node3(c_bit1, s35, s36))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5890, 5889])).
% 35.86/23.68 tff(5892,plain,
% 35.86/23.68 ((~m_counter_cell_v_value(c_bit1, s36)) | node2(c_bit1, s35)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5891, 234, 5885])).
% 35.86/23.68 tff(5893,plain,
% 35.86/23.68 (~m_counter_cell_v_value(c_bit1, s36)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5892, 5881])).
% 35.86/23.68 tff(5894,assumption,(~m_counter_cell_v_value(c_bit1, s36)), introduced(assumption)).
% 35.86/23.68 tff(5895,assumption,(node2(c_bit1, s36)), introduced(assumption)).
% 35.86/23.68 tff(5896,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5897,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5898,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s36) | m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5897, 5896])).
% 35.86/23.68 tff(5899,plain,
% 35.86/23.68 ($false),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5898, 3291, 5895, 5894, 5831])).
% 35.86/23.68 tff(5900,plain,(m_counter_cell_v_value(c_bit1, s36) | (~node2(c_bit1, s36))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.68 tff(5901,plain,
% 35.86/23.68 (~node2(c_bit1, s36)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5900, 5893])).
% 35.86/23.68 tff(5902,plain,
% 35.86/23.68 (((~![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))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5903,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s36, s37)) | node3(c_bit1, s36, s37))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5904,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s36, s37)) | node3(c_bit1, s36, s37)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5903, 5902])).
% 35.86/23.68 tff(5905,plain,
% 35.86/23.68 (node3(c_bit1, s36, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5904, 81, 1194])).
% 35.86/23.68 tff(5906,plain,
% 35.86/23.68 (((~![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_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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5907,plain,
% 35.86/23.68 ((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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5908,plain,
% 35.86/23.68 (((~![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))))),
% 35.86/23.68 inference(monotonicity,[status(thm)],[5907])).
% 35.86/23.68 tff(5909,plain,
% 35.86/23.68 (((~![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)))),
% 35.86/23.68 inference(transitivity,[status(thm)],[5908, 5906])).
% 35.86/23.68 tff(5910,plain,
% 35.86/23.68 ((~![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)))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5911,plain,
% 35.86/23.68 ((~![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_bit1, s37)) | node2(c_bit1, s36) | (~node3(c_bit1, s36, s37))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5910, 5909])).
% 35.86/23.68 tff(5912,plain,
% 35.86/23.68 ((~m_counter_cell_v_value(c_bit1, s37)) | node2(c_bit1, s36)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5911, 234, 5905])).
% 35.86/23.68 tff(5913,plain,
% 35.86/23.68 (~m_counter_cell_v_value(c_bit1, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5912, 5901])).
% 35.86/23.68 tff(5914,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s37) | (~node4(c_bit1, s37)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s37) | (~node4(c_bit1, s37)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5915,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s37) | (~node4(c_bit1, s37)))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5916,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s37) | (~node4(c_bit1, s37))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5915, 5914])).
% 35.86/23.68 tff(5917,plain,
% 35.86/23.68 (~node4(c_bit1, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5916, 2875, 5913])).
% 35.86/23.68 tff(5918,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s37)) | node4(c_bit1, s37))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s37)) | node4(c_bit1, s37))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5919,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s37)) | node4(c_bit1, s37))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5920,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s37)) | node4(c_bit1, s37)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 35.86/23.68 tff(5921,plain,
% 35.86/23.68 (~m_counter_cell_v_carry_out(c_bit1, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5920, 2887, 5917])).
% 35.86/23.68 tff(5922,plain,
% 35.86/23.68 (((~![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, s37)) | m_counter_cell_v_carry_out(c_bit1, s37))) <=> ((~![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, s37)) | m_counter_cell_v_carry_out(c_bit1, s37))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5923,plain,
% 35.86/23.68 ((~![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, s37)) | m_counter_cell_v_carry_out(c_bit1, s37))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5924,plain,
% 35.86/23.68 ((~![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, s37)) | m_counter_cell_v_carry_out(c_bit1, s37)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5923, 5922])).
% 35.86/23.68 tff(5925,plain,
% 35.86/23.68 (~m_counter_cell_v_carry_in(c_bit2, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5924, 3167, 5921])).
% 35.86/23.68 tff(5926,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : ((~node1(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, s37) | (~m_counter_cell_v_value(c_bit2, s37)) | (~node1(c_bit2, 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_bit2, s37) | (~m_counter_cell_v_value(c_bit2, s37)) | (~node1(c_bit2, s37)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5927,plain,
% 35.86/23.68 (((~node1(c_bit2, s37)) | m_counter_cell_v_carry_in(c_bit2, s37) | (~m_counter_cell_v_value(c_bit2, s37))) <=> (m_counter_cell_v_carry_in(c_bit2, s37) | (~m_counter_cell_v_value(c_bit2, s37)) | (~node1(c_bit2, s37)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5928,plain,
% 35.86/23.68 (((~![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, s37)) | m_counter_cell_v_carry_in(c_bit2, s37) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s37) | (~m_counter_cell_v_value(c_bit2, s37)) | (~node1(c_bit2, s37))))),
% 35.86/23.68 inference(monotonicity,[status(thm)],[5927])).
% 35.86/23.68 tff(5929,plain,
% 35.86/23.68 (((~![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, s37)) | m_counter_cell_v_carry_in(c_bit2, s37) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s37) | (~m_counter_cell_v_value(c_bit2, s37)) | (~node1(c_bit2, s37)))),
% 35.86/23.68 inference(transitivity,[status(thm)],[5928, 5926])).
% 35.86/23.68 tff(5930,plain,
% 35.86/23.68 ((~![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, s37)) | m_counter_cell_v_carry_in(c_bit2, s37) | (~m_counter_cell_v_value(c_bit2, s37)))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5931,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~node1(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, s37) | (~m_counter_cell_v_value(c_bit2, s37)) | (~node1(c_bit2, s37))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5930, 5929])).
% 35.86/23.68 tff(5932,plain,
% 35.86/23.68 ((~m_counter_cell_v_value(c_bit2, s37)) | (~node1(c_bit2, s37))),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5931, 3359, 5925])).
% 35.86/23.68 tff(5933,plain,
% 35.86/23.68 (~node1(c_bit2, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5932, 5874])).
% 35.86/23.68 tff(5934,plain,
% 35.86/23.68 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit2, s37, s38))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit2, s37, s38))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5935,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit2, s37, s38))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5936,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit2, s37, s38)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5935, 5934])).
% 35.86/23.68 tff(5937,plain,
% 35.86/23.68 (node3(c_bit2, s37, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5936, 81, 1222])).
% 35.86/23.68 tff(5938,plain,
% 35.86/23.68 (((~![Y: $i, 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, s38) | node1(c_bit2, s37) | (~node3(c_bit2, 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_bit2, s38) | node1(c_bit2, s37) | (~node3(c_bit2, s37, s38)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5939,plain,
% 35.86/23.68 ((node1(c_bit2, s37) | (~node3(c_bit2, s37, s38)) | m_counter_cell_v_value(c_bit2, s38)) <=> (m_counter_cell_v_value(c_bit2, s38) | node1(c_bit2, s37) | (~node3(c_bit2, s37, s38)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5940,plain,
% 35.86/23.68 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s37) | (~node3(c_bit2, s37, s38)) | m_counter_cell_v_value(c_bit2, 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_bit2, s38) | node1(c_bit2, s37) | (~node3(c_bit2, s37, s38))))),
% 35.86/23.68 inference(monotonicity,[status(thm)],[5939])).
% 35.86/23.68 tff(5941,plain,
% 35.86/23.68 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s37) | (~node3(c_bit2, s37, s38)) | m_counter_cell_v_value(c_bit2, 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_bit2, s38) | node1(c_bit2, s37) | (~node3(c_bit2, s37, s38)))),
% 35.86/23.68 inference(transitivity,[status(thm)],[5940, 5938])).
% 35.86/23.68 tff(5942,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s37) | (~node3(c_bit2, s37, s38)) | m_counter_cell_v_value(c_bit2, s38))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5943,plain,
% 35.86/23.68 ((~![Y: $i, 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, s38) | node1(c_bit2, s37) | (~node3(c_bit2, s37, s38))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5942, 5941])).
% 35.86/23.68 tff(5944,plain,
% 35.86/23.68 (m_counter_cell_v_value(c_bit2, s38) | node1(c_bit2, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5943, 199, 5937])).
% 35.86/23.68 tff(5945,plain,
% 35.86/23.68 (m_counter_cell_v_value(c_bit2, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5944, 5933])).
% 35.86/23.68 tff(5946,assumption,(node4(c_bit1, s38)), introduced(assumption)).
% 35.86/23.68 tff(5947,plain,
% 35.86/23.68 (((~![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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5948,plain,
% 35.86/23.68 ((~![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)))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5949,plain,
% 35.86/23.68 ((~![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))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5948, 5947])).
% 35.86/23.68 tff(5950,plain,
% 35.86/23.68 (~node4(c_bit0, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5949, 2875, 1234])).
% 35.86/23.68 tff(5951,assumption,(m_counter_cell_v_carry_out(c_bit0, s38)), introduced(assumption)).
% 35.86/23.68 tff(5952,plain,
% 35.86/23.68 (((~![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))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5953,plain,
% 35.86/23.68 ((~![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))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5954,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s38)) | node4(c_bit0, s38)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5953, 5952])).
% 35.86/23.68 tff(5955,plain,
% 35.86/23.68 ($false),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5954, 2887, 5951, 5950])).
% 35.86/23.68 tff(5956,plain,(~m_counter_cell_v_carry_out(c_bit0, s38)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.68 tff(5957,assumption,(m_counter_cell_v_carry_in(c_bit1, s38)), introduced(assumption)).
% 35.86/23.68 tff(5958,assumption,(~m_counter_cell_v_carry_out(c_bit0, s38)), introduced(assumption)).
% 35.86/23.68 tff(5959,plain,
% 35.86/23.68 (((~![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))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5960,plain,
% 35.86/23.68 ((~![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))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5961,plain,
% 35.86/23.68 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s38)) | m_counter_cell_v_carry_out(c_bit0, s38)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5960, 5959])).
% 35.86/23.68 tff(5962,plain,
% 35.86/23.68 ($false),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5961, 2901, 5958, 5957])).
% 35.86/23.68 tff(5963,plain,(m_counter_cell_v_carry_out(c_bit0, s38) | (~m_counter_cell_v_carry_in(c_bit1, s38))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.68 tff(5964,plain,
% 35.86/23.68 (~m_counter_cell_v_carry_in(c_bit1, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5963, 5956])).
% 35.86/23.68 tff(5965,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s38) | (~node4(c_bit1, s38)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~node4(c_bit1, s38)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5966,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s38) | (~node4(c_bit1, s38)))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5967,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~node4(c_bit1, s38))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5966, 5965])).
% 35.86/23.68 tff(5968,plain,
% 35.86/23.68 ($false),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5967, 3076, 5964, 5946])).
% 35.86/23.68 tff(5969,plain,(~node4(c_bit1, s38)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.68 tff(5970,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s38)) | node4(c_bit1, s38))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s38)) | node4(c_bit1, s38))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5971,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s38)) | node4(c_bit1, s38))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5972,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s38)) | node4(c_bit1, s38)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5971, 5970])).
% 35.86/23.68 tff(5973,plain,
% 35.86/23.68 (~m_counter_cell_v_carry_out(c_bit1, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5972, 2887, 5969])).
% 35.86/23.68 tff(5974,assumption,(m_counter_cell_v_carry_in(c_bit2, s38)), introduced(assumption)).
% 35.86/23.68 tff(5975,assumption,(~m_counter_cell_v_carry_out(c_bit1, s38)), introduced(assumption)).
% 35.86/23.68 tff(5976,plain,
% 35.86/23.68 (((~![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, s38)) | m_counter_cell_v_carry_out(c_bit1, s38))) <=> ((~![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, s38)) | m_counter_cell_v_carry_out(c_bit1, s38))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5977,plain,
% 35.86/23.68 ((~![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, s38)) | m_counter_cell_v_carry_out(c_bit1, s38))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5978,plain,
% 35.86/23.68 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s38)) | m_counter_cell_v_carry_out(c_bit1, s38)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5977, 5976])).
% 35.86/23.68 tff(5979,plain,
% 35.86/23.68 ($false),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5978, 3167, 5975, 5974])).
% 35.86/23.68 tff(5980,plain,((~m_counter_cell_v_carry_in(c_bit2, s38)) | m_counter_cell_v_carry_out(c_bit1, s38)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.68 tff(5981,plain,
% 35.86/23.68 (~m_counter_cell_v_carry_in(c_bit2, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5980, 5973])).
% 35.86/23.68 tff(5982,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : ((~node1(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, s38) | (~m_counter_cell_v_value(c_bit2, s38)) | (~node1(c_bit2, 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_bit2, s38) | (~m_counter_cell_v_value(c_bit2, s38)) | (~node1(c_bit2, s38)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5983,plain,
% 35.86/23.68 (((~node1(c_bit2, s38)) | m_counter_cell_v_carry_in(c_bit2, s38) | (~m_counter_cell_v_value(c_bit2, s38))) <=> (m_counter_cell_v_carry_in(c_bit2, s38) | (~m_counter_cell_v_value(c_bit2, s38)) | (~node1(c_bit2, s38)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5984,plain,
% 35.86/23.68 (((~![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, s38)) | m_counter_cell_v_carry_in(c_bit2, s38) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s38) | (~m_counter_cell_v_value(c_bit2, s38)) | (~node1(c_bit2, s38))))),
% 35.86/23.68 inference(monotonicity,[status(thm)],[5983])).
% 35.86/23.68 tff(5985,plain,
% 35.86/23.68 (((~![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, s38)) | m_counter_cell_v_carry_in(c_bit2, s38) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s38) | (~m_counter_cell_v_value(c_bit2, s38)) | (~node1(c_bit2, s38)))),
% 35.86/23.68 inference(transitivity,[status(thm)],[5984, 5982])).
% 35.86/23.68 tff(5986,plain,
% 35.86/23.68 ((~![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, s38)) | m_counter_cell_v_carry_in(c_bit2, s38) | (~m_counter_cell_v_value(c_bit2, s38)))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5987,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~node1(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, s38) | (~m_counter_cell_v_value(c_bit2, s38)) | (~node1(c_bit2, s38))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5986, 5985])).
% 35.86/23.68 tff(5988,plain,
% 35.86/23.68 ((~m_counter_cell_v_value(c_bit2, s38)) | (~node1(c_bit2, s38))),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5987, 3359, 5981])).
% 35.86/23.68 tff(5989,plain,
% 35.86/23.68 (~node1(c_bit2, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5988, 5945])).
% 35.86/23.68 tff(5990,plain,
% 35.86/23.68 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit2, s38, s39))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit2, s38, s39))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5991,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit2, s38, s39))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5992,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit2, s38, s39)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5991, 5990])).
% 35.86/23.68 tff(5993,plain,
% 35.86/23.68 (node3(c_bit2, s38, s39)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5992, 81, 1253])).
% 35.86/23.68 tff(5994,plain,
% 35.86/23.68 (((~![Y: $i, 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, s39) | node1(c_bit2, s38) | (~node3(c_bit2, 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_bit2, s39) | node1(c_bit2, s38) | (~node3(c_bit2, s38, s39)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5995,plain,
% 35.86/23.68 ((node1(c_bit2, s38) | (~node3(c_bit2, s38, s39)) | m_counter_cell_v_value(c_bit2, s39)) <=> (m_counter_cell_v_value(c_bit2, s39) | node1(c_bit2, s38) | (~node3(c_bit2, s38, s39)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(5996,plain,
% 35.86/23.68 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s38) | (~node3(c_bit2, s38, s39)) | m_counter_cell_v_value(c_bit2, 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_bit2, s39) | node1(c_bit2, s38) | (~node3(c_bit2, s38, s39))))),
% 35.86/23.68 inference(monotonicity,[status(thm)],[5995])).
% 35.86/23.68 tff(5997,plain,
% 35.86/23.68 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s38) | (~node3(c_bit2, s38, s39)) | m_counter_cell_v_value(c_bit2, 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_bit2, s39) | node1(c_bit2, s38) | (~node3(c_bit2, s38, s39)))),
% 35.86/23.68 inference(transitivity,[status(thm)],[5996, 5994])).
% 35.86/23.68 tff(5998,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s38) | (~node3(c_bit2, s38, s39)) | m_counter_cell_v_value(c_bit2, s39))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(5999,plain,
% 35.86/23.68 ((~![Y: $i, 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, s39) | node1(c_bit2, s38) | (~node3(c_bit2, s38, s39))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[5998, 5997])).
% 35.86/23.68 tff(6000,plain,
% 35.86/23.68 (m_counter_cell_v_value(c_bit2, s39) | node1(c_bit2, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[5999, 199, 5993])).
% 35.86/23.68 tff(6001,plain,
% 35.86/23.68 (m_counter_cell_v_value(c_bit2, s39)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6000, 5989])).
% 35.86/23.68 tff(6002,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6003,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(6004,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[6003, 6002])).
% 35.86/23.68 tff(6005,plain,
% 35.86/23.68 ((~m_counter_cell_v_value(c_bit0, s37)) | m_counter_cell_v_carry_out(c_bit0, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6004, 3031, 1210])).
% 35.86/23.68 tff(6006,plain,
% 35.86/23.68 (m_counter_cell_v_carry_out(c_bit0, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6005, 1206])).
% 35.86/23.68 tff(6007,plain,
% 35.86/23.68 (((~![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))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6008,plain,
% 35.86/23.68 ((~![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))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(6009,plain,
% 35.86/23.68 ((~![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)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[6008, 6007])).
% 35.86/23.68 tff(6010,plain,
% 35.86/23.68 (m_counter_cell_v_carry_in(c_bit1, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6009, 3046, 6006])).
% 35.86/23.68 tff(6011,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6012,plain,
% 35.86/23.68 (((~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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6013,plain,
% 35.86/23.68 (((~![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))))),
% 35.86/23.68 inference(monotonicity,[status(thm)],[6012])).
% 35.86/23.68 tff(6014,plain,
% 35.86/23.68 (((~![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)))),
% 35.86/23.68 inference(transitivity,[status(thm)],[6013, 6011])).
% 35.86/23.68 tff(6015,plain,
% 35.86/23.68 ((~![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))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(6016,plain,
% 35.86/23.68 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[6015, 6014])).
% 35.86/23.68 tff(6017,plain,
% 35.86/23.68 (m_counter_cell_v_value(c_bit1, s37) | (~node1(c_bit1, s37))),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6016, 170, 6010])).
% 35.86/23.68 tff(6018,plain,
% 35.86/23.68 (~node1(c_bit1, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6017, 5913])).
% 35.86/23.68 tff(6019,plain,
% 35.86/23.68 (((~![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))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6020,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s37, s38)) | node3(c_bit1, s37, s38))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(6021,plain,
% 35.86/23.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s37, s38)) | node3(c_bit1, s37, s38)),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[6020, 6019])).
% 35.86/23.68 tff(6022,plain,
% 35.86/23.68 (node3(c_bit1, s37, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6021, 81, 1222])).
% 35.86/23.68 tff(6023,plain,
% 35.86/23.68 (((~![Y: $i, I0: $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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6024,plain,
% 35.86/23.68 ((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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6025,plain,
% 35.86/23.68 (((~![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))))),
% 35.86/23.68 inference(monotonicity,[status(thm)],[6024])).
% 35.86/23.68 tff(6026,plain,
% 35.86/23.68 (((~![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)))),
% 35.86/23.68 inference(transitivity,[status(thm)],[6025, 6023])).
% 35.86/23.68 tff(6027,plain,
% 35.86/23.68 ((~![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))),
% 35.86/23.68 inference(quant_inst,[status(thm)],[])).
% 35.86/23.68 tff(6028,plain,
% 35.86/23.68 ((~![Y: $i, I0: $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))),
% 35.86/23.68 inference(modus_ponens,[status(thm)],[6027, 6026])).
% 35.86/23.68 tff(6029,plain,
% 35.86/23.68 (m_counter_cell_v_value(c_bit1, s38) | node1(c_bit1, s37)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6028, 199, 6022])).
% 35.86/23.68 tff(6030,plain,
% 35.86/23.68 (m_counter_cell_v_value(c_bit1, s38)),
% 35.86/23.68 inference(unit_resolution,[status(thm)],[6029, 6018])).
% 35.86/23.68 tff(6031,assumption,(~m_counter_cell_v_carry_in(c_bit1, s38)), introduced(assumption)).
% 35.86/23.68 tff(6032,assumption,(m_counter_cell_v_value(c_bit1, s38)), introduced(assumption)).
% 35.86/23.68 tff(6033,assumption,(node1(c_bit1, s38)), introduced(assumption)).
% 35.86/23.68 tff(6034,plain,
% 35.86/23.68 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6035,plain,
% 35.86/23.68 (((~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)))),
% 35.86/23.68 inference(rewrite,[status(thm)],[])).
% 35.86/23.68 tff(6036,plain,
% 35.86/23.68 (((~![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))))),
% 35.86/23.69 inference(monotonicity,[status(thm)],[6035])).
% 35.86/23.69 tff(6037,plain,
% 35.86/23.69 (((~![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)))),
% 35.86/23.69 inference(transitivity,[status(thm)],[6036, 6034])).
% 35.86/23.69 tff(6038,plain,
% 35.86/23.69 ((~![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)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6039,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s38) | (~m_counter_cell_v_value(c_bit1, s38)) | (~node1(c_bit1, s38))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6038, 6037])).
% 35.86/23.69 tff(6040,plain,
% 35.86/23.69 ($false),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6039, 3359, 6033, 6032, 6031])).
% 35.86/23.69 tff(6041,plain,(m_counter_cell_v_carry_in(c_bit1, s38) | (~node1(c_bit1, s38)) | (~m_counter_cell_v_value(c_bit1, s38))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.69 tff(6042,plain,
% 35.86/23.69 ((~node1(c_bit1, s38)) | (~m_counter_cell_v_value(c_bit1, s38))),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6041, 5964])).
% 35.86/23.69 tff(6043,plain,
% 35.86/23.69 (~node1(c_bit1, s38)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6042, 6030])).
% 35.86/23.69 tff(6044,plain,
% 35.86/23.69 (((~![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))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6045,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s38, s39)) | node3(c_bit1, s38, s39))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6046,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s38, s39)) | node3(c_bit1, s38, s39)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6045, 6044])).
% 35.86/23.69 tff(6047,plain,
% 35.86/23.69 (node3(c_bit1, s38, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6046, 81, 1253])).
% 35.86/23.69 tff(6048,plain,
% 35.86/23.69 (((~![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_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)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6049,plain,
% 35.86/23.69 ((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)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6050,plain,
% 35.86/23.69 (((~![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))))),
% 35.86/23.69 inference(monotonicity,[status(thm)],[6049])).
% 35.86/23.69 tff(6051,plain,
% 35.86/23.69 (((~![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)))),
% 35.86/23.69 inference(transitivity,[status(thm)],[6050, 6048])).
% 35.86/23.69 tff(6052,plain,
% 35.86/23.69 ((~![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))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6053,plain,
% 35.86/23.69 ((~![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_bit1, s39) | node1(c_bit1, s38) | (~node3(c_bit1, s38, s39))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6052, 6051])).
% 35.86/23.69 tff(6054,plain,
% 35.86/23.69 (m_counter_cell_v_value(c_bit1, s39) | node1(c_bit1, s38)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6053, 199, 6047])).
% 35.86/23.69 tff(6055,plain,
% 35.86/23.69 (m_counter_cell_v_value(c_bit1, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6054, 6043])).
% 35.86/23.69 tff(6056,plain,
% 35.86/23.69 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6057,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6058,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6057, 6056])).
% 35.86/23.69 tff(6059,plain,
% 35.86/23.69 ((~m_counter_cell_v_value(c_bit0, s39)) | m_counter_cell_v_carry_out(c_bit0, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6058, 3031, 1269])).
% 35.86/23.69 tff(6060,plain,
% 35.86/23.69 (m_counter_cell_v_carry_out(c_bit0, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6059, 1265])).
% 35.86/23.69 tff(6061,plain,
% 35.86/23.69 (((~![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))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6062,plain,
% 35.86/23.69 ((~![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))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6063,plain,
% 35.86/23.69 ((~![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)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6062, 6061])).
% 35.86/23.69 tff(6064,plain,
% 35.86/23.69 (m_counter_cell_v_carry_in(c_bit1, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6063, 3046, 6060])).
% 35.86/23.69 tff(6065,plain,
% 35.86/23.69 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, 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_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, s39))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6066,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, s39))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6067,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, s39)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6066, 6065])).
% 35.86/23.69 tff(6068,plain,
% 35.86/23.69 ((~m_counter_cell_v_value(c_bit1, s39)) | m_counter_cell_v_carry_out(c_bit1, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6067, 3031, 6064])).
% 35.86/23.69 tff(6069,plain,
% 35.86/23.69 (m_counter_cell_v_carry_out(c_bit1, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6068, 6055])).
% 35.86/23.69 tff(6070,plain,
% 35.86/23.69 (((~![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, s39)) | m_counter_cell_v_carry_in(c_bit2, s39))) <=> ((~![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, s39)) | m_counter_cell_v_carry_in(c_bit2, s39))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6071,plain,
% 35.86/23.69 ((~![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, s39)) | m_counter_cell_v_carry_in(c_bit2, s39))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6072,plain,
% 35.86/23.69 ((~![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, s39)) | m_counter_cell_v_carry_in(c_bit2, s39)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6071, 6070])).
% 35.86/23.69 tff(6073,plain,
% 35.86/23.69 (m_counter_cell_v_carry_in(c_bit2, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6072, 4417, 6069])).
% 35.86/23.69 tff(6074,plain,
% 35.86/23.69 (((~![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, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | (~node2(c_bit2, 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_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | (~node2(c_bit2, s39)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6075,plain,
% 35.86/23.69 ((~![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, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | (~node2(c_bit2, s39)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6076,plain,
% 35.86/23.69 ((~![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, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | (~node2(c_bit2, s39))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6075, 6074])).
% 35.86/23.69 tff(6077,plain,
% 35.86/23.69 ((~m_counter_cell_v_value(c_bit2, s39)) | (~node2(c_bit2, s39))),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6076, 219, 6073])).
% 35.86/23.69 tff(6078,plain,
% 35.86/23.69 (~node2(c_bit2, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6077, 6001])).
% 35.86/23.69 tff(6079,plain,
% 35.86/23.69 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit2, s39, s40))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit2, s39, s40))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6080,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit2, s39, s40))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6081,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit2, s39, s40)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6080, 6079])).
% 35.86/23.69 tff(6082,plain,
% 35.86/23.69 (node3(c_bit2, s39, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6081, 81, 1281])).
% 35.86/23.69 tff(6083,plain,
% 35.86/23.69 (((~![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, s40)) | node2(c_bit2, s39) | (~node3(c_bit2, 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_bit2, s40)) | node2(c_bit2, s39) | (~node3(c_bit2, s39, s40)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6084,plain,
% 35.86/23.69 ((node2(c_bit2, s39) | (~node3(c_bit2, s39, s40)) | (~m_counter_cell_v_value(c_bit2, s40))) <=> ((~m_counter_cell_v_value(c_bit2, s40)) | node2(c_bit2, s39) | (~node3(c_bit2, s39, s40)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6085,plain,
% 35.86/23.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s39) | (~node3(c_bit2, s39, s40)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s40)) | node2(c_bit2, s39) | (~node3(c_bit2, s39, s40))))),
% 35.86/23.69 inference(monotonicity,[status(thm)],[6084])).
% 35.86/23.69 tff(6086,plain,
% 35.86/23.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s39) | (~node3(c_bit2, s39, s40)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s40)) | node2(c_bit2, s39) | (~node3(c_bit2, s39, s40)))),
% 35.86/23.69 inference(transitivity,[status(thm)],[6085, 6083])).
% 35.86/23.69 tff(6087,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s39) | (~node3(c_bit2, s39, s40)) | (~m_counter_cell_v_value(c_bit2, s40)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6088,plain,
% 35.86/23.69 ((~![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, s40)) | node2(c_bit2, s39) | (~node3(c_bit2, s39, s40))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6087, 6086])).
% 35.86/23.69 tff(6089,plain,
% 35.86/23.69 ((~m_counter_cell_v_value(c_bit2, s40)) | node2(c_bit2, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6088, 234, 6082])).
% 35.86/23.69 tff(6090,plain,
% 35.86/23.69 (~m_counter_cell_v_value(c_bit2, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6089, 6078])).
% 35.86/23.69 tff(6091,plain,
% 35.86/23.69 (((~![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)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6092,plain,
% 35.86/23.69 ((~![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)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6093,plain,
% 35.86/23.69 ((~![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))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6092, 6091])).
% 35.86/23.69 tff(6094,plain,
% 35.86/23.69 (~node4(c_bit0, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6093, 2875, 1293])).
% 35.86/23.69 tff(6095,assumption,(m_counter_cell_v_carry_out(c_bit0, s40)), introduced(assumption)).
% 35.86/23.69 tff(6096,plain,
% 35.86/23.69 (((~![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))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6097,plain,
% 35.86/23.69 ((~![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))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6098,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s40)) | node4(c_bit0, s40)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6097, 6096])).
% 35.86/23.69 tff(6099,plain,
% 35.86/23.69 ($false),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6098, 2887, 6095, 6094])).
% 35.86/23.69 tff(6100,plain,(~m_counter_cell_v_carry_out(c_bit0, s40)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.69 tff(6101,plain,
% 35.86/23.69 (((~![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))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6102,plain,
% 35.86/23.69 ((~![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))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6103,plain,
% 35.86/23.69 ((~![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)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6102, 6101])).
% 35.86/23.69 tff(6104,plain,
% 35.86/23.69 (~m_counter_cell_v_carry_in(c_bit1, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6103, 2901, 6100])).
% 35.86/23.69 tff(6105,plain,
% 35.86/23.69 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s40) | (~node4(c_bit1, s40)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s40) | (~node4(c_bit1, s40)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6106,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s40) | (~node4(c_bit1, s40)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6107,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s40) | (~node4(c_bit1, s40))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6106, 6105])).
% 35.86/23.69 tff(6108,plain,
% 35.86/23.69 (~node4(c_bit1, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6107, 3076, 6104])).
% 35.86/23.69 tff(6109,plain,
% 35.86/23.69 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s40)) | node4(c_bit1, s40))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s40)) | node4(c_bit1, s40))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6110,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s40)) | node4(c_bit1, s40))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6111,plain,
% 35.86/23.69 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s40)) | node4(c_bit1, s40)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6110, 6109])).
% 35.86/23.69 tff(6112,plain,
% 35.86/23.69 (~m_counter_cell_v_carry_out(c_bit1, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6111, 2887, 6108])).
% 35.86/23.69 tff(6113,plain,
% 35.86/23.69 (((~![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, s40)) | m_counter_cell_v_carry_out(c_bit1, s40))) <=> ((~![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, s40)) | m_counter_cell_v_carry_out(c_bit1, s40))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6114,plain,
% 35.86/23.69 ((~![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, s40)) | m_counter_cell_v_carry_out(c_bit1, s40))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6115,plain,
% 35.86/23.69 ((~![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, s40)) | m_counter_cell_v_carry_out(c_bit1, s40)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 35.86/23.69 tff(6116,plain,
% 35.86/23.69 (~m_counter_cell_v_carry_in(c_bit2, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6115, 3167, 6112])).
% 35.86/23.69 tff(6117,plain,
% 35.86/23.69 (((~![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, s40) | m_counter_cell_v_value(c_bit2, s40) | (~node2(c_bit2, 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_bit2, s40) | m_counter_cell_v_value(c_bit2, s40) | (~node2(c_bit2, s40)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6118,plain,
% 35.86/23.69 ((~![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, s40) | m_counter_cell_v_value(c_bit2, s40) | (~node2(c_bit2, s40)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6119,plain,
% 35.86/23.69 ((~![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, s40) | m_counter_cell_v_value(c_bit2, s40) | (~node2(c_bit2, s40))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6118, 6117])).
% 35.86/23.69 tff(6120,plain,
% 35.86/23.69 (m_counter_cell_v_value(c_bit2, s40) | (~node2(c_bit2, s40))),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6119, 3291, 6116])).
% 35.86/23.69 tff(6121,plain,
% 35.86/23.69 (~node2(c_bit2, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6120, 6090])).
% 35.86/23.69 tff(6122,plain,
% 35.86/23.69 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit2, s40, s41))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit2, s40, s41))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6123,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit2, s40, s41))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6124,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit2, s40, s41)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6123, 6122])).
% 35.86/23.69 tff(6125,plain,
% 35.86/23.69 (node3(c_bit2, s40, s41)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6124, 81, 1312])).
% 35.86/23.69 tff(6126,plain,
% 35.86/23.69 (((~![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, s41)) | node2(c_bit2, s40) | (~node3(c_bit2, 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_bit2, s41)) | node2(c_bit2, s40) | (~node3(c_bit2, s40, s41)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6127,plain,
% 35.86/23.69 ((node2(c_bit2, s40) | (~node3(c_bit2, s40, s41)) | (~m_counter_cell_v_value(c_bit2, s41))) <=> ((~m_counter_cell_v_value(c_bit2, s41)) | node2(c_bit2, s40) | (~node3(c_bit2, s40, s41)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6128,plain,
% 35.86/23.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s40) | (~node3(c_bit2, s40, s41)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s41)) | node2(c_bit2, s40) | (~node3(c_bit2, s40, s41))))),
% 35.86/23.69 inference(monotonicity,[status(thm)],[6127])).
% 35.86/23.69 tff(6129,plain,
% 35.86/23.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s40) | (~node3(c_bit2, s40, s41)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s41)) | node2(c_bit2, s40) | (~node3(c_bit2, s40, s41)))),
% 35.86/23.69 inference(transitivity,[status(thm)],[6128, 6126])).
% 35.86/23.69 tff(6130,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s40) | (~node3(c_bit2, s40, s41)) | (~m_counter_cell_v_value(c_bit2, s41)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6131,plain,
% 35.86/23.69 ((~![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, s41)) | node2(c_bit2, s40) | (~node3(c_bit2, s40, s41))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6130, 6129])).
% 35.86/23.69 tff(6132,plain,
% 35.86/23.69 ((~m_counter_cell_v_value(c_bit2, s41)) | node2(c_bit2, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6131, 234, 6125])).
% 35.86/23.69 tff(6133,plain,
% 35.86/23.69 (~m_counter_cell_v_value(c_bit2, s41)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6132, 6121])).
% 35.86/23.69 tff(6134,plain,
% 35.86/23.69 (((~![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_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)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6135,plain,
% 35.86/23.69 ((~![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_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6136,plain,
% 35.86/23.69 ((~![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_bit1, s39)) | (~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6135, 6134])).
% 35.86/23.69 tff(6137,plain,
% 35.86/23.69 ((~m_counter_cell_v_value(c_bit1, s39)) | (~node2(c_bit1, s39))),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6136, 219, 6064])).
% 35.86/23.69 tff(6138,plain,
% 35.86/23.69 (~node2(c_bit1, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6137, 6055])).
% 35.86/23.69 tff(6139,plain,
% 35.86/23.69 (((~![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))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6140,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s39, s40)) | node3(c_bit1, s39, s40))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6141,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s39, s40)) | node3(c_bit1, s39, s40)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6140, 6139])).
% 35.86/23.69 tff(6142,plain,
% 35.86/23.69 (node3(c_bit1, s39, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6141, 81, 1281])).
% 35.86/23.69 tff(6143,plain,
% 35.86/23.69 (((~![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_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)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6144,plain,
% 35.86/23.69 ((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)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6145,plain,
% 35.86/23.69 (((~![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))))),
% 35.86/23.69 inference(monotonicity,[status(thm)],[6144])).
% 35.86/23.69 tff(6146,plain,
% 35.86/23.69 (((~![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)))),
% 35.86/23.69 inference(transitivity,[status(thm)],[6145, 6143])).
% 35.86/23.69 tff(6147,plain,
% 35.86/23.69 ((~![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)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6148,plain,
% 35.86/23.69 ((~![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_bit1, s40)) | node2(c_bit1, s39) | (~node3(c_bit1, s39, s40))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6147, 6146])).
% 35.86/23.69 tff(6149,plain,
% 35.86/23.69 ((~m_counter_cell_v_value(c_bit1, s40)) | node2(c_bit1, s39)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6148, 234, 6142])).
% 35.86/23.69 tff(6150,plain,
% 35.86/23.69 (~m_counter_cell_v_value(c_bit1, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6149, 6138])).
% 35.86/23.69 tff(6151,plain,
% 35.86/23.69 (((~![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_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)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6152,plain,
% 35.86/23.69 ((~![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_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40)))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6153,plain,
% 35.86/23.69 ((~![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_bit1, s40) | m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40))),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6152, 6151])).
% 35.86/23.69 tff(6154,plain,
% 35.86/23.69 (m_counter_cell_v_value(c_bit1, s40) | (~node2(c_bit1, s40))),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6153, 3291, 6104])).
% 35.86/23.69 tff(6155,plain,
% 35.86/23.69 (~node2(c_bit1, s40)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6154, 6150])).
% 35.86/23.69 tff(6156,plain,
% 35.86/23.69 (((~![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))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6157,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s40, s41)) | node3(c_bit1, s40, s41))),
% 35.86/23.69 inference(quant_inst,[status(thm)],[])).
% 35.86/23.69 tff(6158,plain,
% 35.86/23.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s40, s41)) | node3(c_bit1, s40, s41)),
% 35.86/23.69 inference(modus_ponens,[status(thm)],[6157, 6156])).
% 35.86/23.69 tff(6159,plain,
% 35.86/23.69 (node3(c_bit1, s40, s41)),
% 35.86/23.69 inference(unit_resolution,[status(thm)],[6158, 81, 1312])).
% 35.86/23.69 tff(6160,plain,
% 35.86/23.69 (((~![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_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)))),
% 35.86/23.69 inference(rewrite,[status(thm)],[])).
% 35.86/23.69 tff(6161,plain,
% 35.86/23.69 ((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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6162,plain,
% 35.86/23.70 (((~![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))))),
% 35.86/23.70 inference(monotonicity,[status(thm)],[6161])).
% 35.86/23.70 tff(6163,plain,
% 35.86/23.70 (((~![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)))),
% 35.86/23.70 inference(transitivity,[status(thm)],[6162, 6160])).
% 35.86/23.70 tff(6164,plain,
% 35.86/23.70 ((~![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)))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6165,plain,
% 35.86/23.70 ((~![Y: $i, I0: $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))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6164, 6163])).
% 35.86/23.70 tff(6166,plain,
% 35.86/23.70 ((~m_counter_cell_v_value(c_bit1, s41)) | node2(c_bit1, s40)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6165, 234, 6159])).
% 35.86/23.70 tff(6167,plain,
% 35.86/23.70 (~m_counter_cell_v_value(c_bit1, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6166, 6155])).
% 35.86/23.70 tff(6168,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s41) | (~node4(c_bit1, s41)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s41) | (~node4(c_bit1, s41)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6169,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s41) | (~node4(c_bit1, s41)))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6170,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s41) | (~node4(c_bit1, s41))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6169, 6168])).
% 35.86/23.70 tff(6171,plain,
% 35.86/23.70 (~node4(c_bit1, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6170, 2875, 6167])).
% 35.86/23.70 tff(6172,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s41)) | node4(c_bit1, s41))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s41)) | node4(c_bit1, s41))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6173,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s41)) | node4(c_bit1, s41))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6174,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s41)) | node4(c_bit1, s41)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6173, 6172])).
% 35.86/23.70 tff(6175,plain,
% 35.86/23.70 (~m_counter_cell_v_carry_out(c_bit1, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6174, 2887, 6171])).
% 35.86/23.70 tff(6176,plain,
% 35.86/23.70 (((~![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, s41)) | m_counter_cell_v_carry_out(c_bit1, s41))) <=> ((~![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, s41)) | m_counter_cell_v_carry_out(c_bit1, s41))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6177,plain,
% 35.86/23.70 ((~![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, s41)) | m_counter_cell_v_carry_out(c_bit1, s41))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6178,plain,
% 35.86/23.70 ((~![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, s41)) | m_counter_cell_v_carry_out(c_bit1, s41)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6177, 6176])).
% 35.86/23.70 tff(6179,plain,
% 35.86/23.70 (~m_counter_cell_v_carry_in(c_bit2, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6178, 3167, 6175])).
% 35.86/23.70 tff(6180,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : (m_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, s41) | m_counter_cell_v_value(c_bit2, s41) | (~node2(c_bit2, 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_bit2, s41) | m_counter_cell_v_value(c_bit2, s41) | (~node2(c_bit2, s41)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6181,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : (m_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, s41) | m_counter_cell_v_value(c_bit2, s41) | (~node2(c_bit2, s41)))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6182,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : (m_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, s41) | m_counter_cell_v_value(c_bit2, s41) | (~node2(c_bit2, s41))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6181, 6180])).
% 35.86/23.70 tff(6183,plain,
% 35.86/23.70 (m_counter_cell_v_value(c_bit2, s41) | (~node2(c_bit2, s41))),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6182, 3291, 6179])).
% 35.86/23.70 tff(6184,plain,
% 35.86/23.70 (~node2(c_bit2, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6183, 6133])).
% 35.86/23.70 tff(6185,plain,
% 35.86/23.70 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit2, s41, s42))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit2, s41, s42))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6186,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit2, s41, s42))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6187,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit2, s41, s42)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6186, 6185])).
% 35.86/23.70 tff(6188,plain,
% 35.86/23.70 (node3(c_bit2, s41, s42)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6187, 81, 1340])).
% 35.86/23.70 tff(6189,plain,
% 35.86/23.70 (((~![Y: $i, 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, s42)) | node2(c_bit2, s41) | (~node3(c_bit2, s41, s42)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s42)) | node2(c_bit2, s41) | (~node3(c_bit2, s41, s42)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6190,plain,
% 35.86/23.70 ((node2(c_bit2, s41) | (~node3(c_bit2, s41, s42)) | (~m_counter_cell_v_value(c_bit2, s42))) <=> ((~m_counter_cell_v_value(c_bit2, s42)) | node2(c_bit2, s41) | (~node3(c_bit2, s41, s42)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6191,plain,
% 35.86/23.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s41) | (~node3(c_bit2, s41, s42)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s42)) | node2(c_bit2, s41) | (~node3(c_bit2, s41, s42))))),
% 35.86/23.70 inference(monotonicity,[status(thm)],[6190])).
% 35.86/23.70 tff(6192,plain,
% 35.86/23.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s41) | (~node3(c_bit2, s41, s42)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s42)) | node2(c_bit2, s41) | (~node3(c_bit2, s41, s42)))),
% 35.86/23.70 inference(transitivity,[status(thm)],[6191, 6189])).
% 35.86/23.70 tff(6193,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s41) | (~node3(c_bit2, s41, s42)) | (~m_counter_cell_v_value(c_bit2, s42)))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6194,plain,
% 35.86/23.70 ((~![Y: $i, 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, s42)) | node2(c_bit2, s41) | (~node3(c_bit2, s41, s42))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6193, 6192])).
% 35.86/23.70 tff(6195,plain,
% 35.86/23.70 ((~m_counter_cell_v_value(c_bit2, s42)) | node2(c_bit2, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6194, 234, 6188])).
% 35.86/23.70 tff(6196,plain,
% 35.86/23.70 (~m_counter_cell_v_value(c_bit2, s42)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6195, 6184])).
% 35.86/23.70 tff(6197,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : (m_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, s42) | m_counter_cell_v_value(c_bit2, s42) | (~node2(c_bit2, s42)))) <=> ((~![I0: $i, X: $i] : (m_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, s42) | m_counter_cell_v_value(c_bit2, s42) | (~node2(c_bit2, s42)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6198,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : (m_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, s42) | m_counter_cell_v_value(c_bit2, s42) | (~node2(c_bit2, s42)))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6199,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : (m_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, s42) | m_counter_cell_v_value(c_bit2, s42) | (~node2(c_bit2, s42))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6198, 6197])).
% 35.86/23.70 tff(6200,plain,
% 35.86/23.70 (m_counter_cell_v_carry_in(c_bit2, s42) | (~node2(c_bit2, s42))),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6199, 3291, 6196])).
% 35.86/23.70 tff(6201,plain,
% 35.86/23.70 (~node2(c_bit2, s42)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6200, 3171])).
% 35.86/23.70 tff(6202,plain,
% 35.86/23.70 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit2, s42, s43))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit2, s42, s43))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6203,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit2, s42, s43))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6204,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit2, s42, s43)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6203, 6202])).
% 35.86/23.70 tff(6205,plain,
% 35.86/23.70 (node3(c_bit2, s42, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6204, 81, 1371])).
% 35.86/23.70 tff(6206,plain,
% 35.86/23.70 (((~![Y: $i, 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, s43)) | node2(c_bit2, s42) | (~node3(c_bit2, s42, 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_bit2, s43)) | node2(c_bit2, s42) | (~node3(c_bit2, s42, s43)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6207,plain,
% 35.86/23.70 ((node2(c_bit2, s42) | (~node3(c_bit2, s42, s43)) | (~m_counter_cell_v_value(c_bit2, s43))) <=> ((~m_counter_cell_v_value(c_bit2, s43)) | node2(c_bit2, s42) | (~node3(c_bit2, s42, s43)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6208,plain,
% 35.86/23.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s42) | (~node3(c_bit2, s42, s43)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s43)) | node2(c_bit2, s42) | (~node3(c_bit2, s42, s43))))),
% 35.86/23.70 inference(monotonicity,[status(thm)],[6207])).
% 35.86/23.70 tff(6209,plain,
% 35.86/23.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s42) | (~node3(c_bit2, s42, s43)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s43)) | node2(c_bit2, s42) | (~node3(c_bit2, s42, s43)))),
% 35.86/23.70 inference(transitivity,[status(thm)],[6208, 6206])).
% 35.86/23.70 tff(6210,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s42) | (~node3(c_bit2, s42, s43)) | (~m_counter_cell_v_value(c_bit2, s43)))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6211,plain,
% 35.86/23.70 ((~![Y: $i, 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, s43)) | node2(c_bit2, s42) | (~node3(c_bit2, s42, s43))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6210, 6209])).
% 35.86/23.70 tff(6212,plain,
% 35.86/23.70 ((~m_counter_cell_v_value(c_bit2, s43)) | node2(c_bit2, s42)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6211, 234, 6205])).
% 35.86/23.70 tff(6213,plain,
% 35.86/23.70 (~m_counter_cell_v_value(c_bit2, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6212, 6201])).
% 35.86/23.70 tff(6214,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6215,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6216,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6215, 6214])).
% 35.86/23.70 tff(6217,plain,
% 35.86/23.70 ((~m_counter_cell_v_value(c_bit0, s41)) | m_counter_cell_v_carry_out(c_bit0, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6216, 3031, 1328])).
% 35.86/23.70 tff(6218,plain,
% 35.86/23.70 (m_counter_cell_v_carry_out(c_bit0, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6217, 1324])).
% 35.86/23.70 tff(6219,plain,
% 35.86/23.70 (((~![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))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6220,plain,
% 35.86/23.70 ((~![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))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6221,plain,
% 35.86/23.70 ((~![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)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6220, 6219])).
% 35.86/23.70 tff(6222,plain,
% 35.86/23.70 (m_counter_cell_v_carry_in(c_bit1, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6221, 3046, 6218])).
% 35.86/23.70 tff(6223,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6224,plain,
% 35.86/23.70 (((~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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6225,plain,
% 35.86/23.70 (((~![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))))),
% 35.86/23.70 inference(monotonicity,[status(thm)],[6224])).
% 35.86/23.70 tff(6226,plain,
% 35.86/23.70 (((~![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)))),
% 35.86/23.70 inference(transitivity,[status(thm)],[6225, 6223])).
% 35.86/23.70 tff(6227,plain,
% 35.86/23.70 ((~![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))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6228,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6227, 6226])).
% 35.86/23.70 tff(6229,plain,
% 35.86/23.70 (m_counter_cell_v_value(c_bit1, s41) | (~node1(c_bit1, s41))),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6228, 170, 6222])).
% 35.86/23.70 tff(6230,plain,
% 35.86/23.70 (~node1(c_bit1, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6229, 6167])).
% 35.86/23.70 tff(6231,plain,
% 35.86/23.70 (((~![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))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6232,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s41, s42)) | node3(c_bit1, s41, s42))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6233,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s41, s42)) | node3(c_bit1, s41, s42)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6232, 6231])).
% 35.86/23.70 tff(6234,plain,
% 35.86/23.70 (node3(c_bit1, s41, s42)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6233, 81, 1340])).
% 35.86/23.70 tff(6235,plain,
% 35.86/23.70 (((~![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_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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6236,plain,
% 35.86/23.70 ((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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6237,plain,
% 35.86/23.70 (((~![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))))),
% 35.86/23.70 inference(monotonicity,[status(thm)],[6236])).
% 35.86/23.70 tff(6238,plain,
% 35.86/23.70 (((~![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)))),
% 35.86/23.70 inference(transitivity,[status(thm)],[6237, 6235])).
% 35.86/23.70 tff(6239,plain,
% 35.86/23.70 ((~![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))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6240,plain,
% 35.86/23.70 ((~![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_bit1, s42) | node1(c_bit1, s41) | (~node3(c_bit1, s41, s42))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6239, 6238])).
% 35.86/23.70 tff(6241,plain,
% 35.86/23.70 (m_counter_cell_v_value(c_bit1, s42) | node1(c_bit1, s41)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6240, 199, 6234])).
% 35.86/23.70 tff(6242,plain,
% 35.86/23.70 (m_counter_cell_v_value(c_bit1, s42)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6241, 6230])).
% 35.86/23.70 tff(6243,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6244,plain,
% 35.86/23.70 (((~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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6245,plain,
% 35.86/23.70 (((~![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))))),
% 35.86/23.70 inference(monotonicity,[status(thm)],[6244])).
% 35.86/23.70 tff(6246,plain,
% 35.86/23.70 (((~![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)))),
% 35.86/23.70 inference(transitivity,[status(thm)],[6245, 6243])).
% 35.86/23.70 tff(6247,plain,
% 35.86/23.70 ((~![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)))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6248,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6247, 6246])).
% 35.86/23.70 tff(6249,plain,
% 35.86/23.70 (m_counter_cell_v_carry_in(c_bit1, s42) | (~node1(c_bit1, s42))),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6248, 3359, 6242])).
% 35.86/23.70 tff(6250,plain,
% 35.86/23.70 (~node1(c_bit1, s42)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6249, 3146])).
% 35.86/23.70 tff(6251,plain,
% 35.86/23.70 (((~![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))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6252,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s42, s43)) | node3(c_bit1, s42, s43))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6253,plain,
% 35.86/23.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s42, s43)) | node3(c_bit1, s42, s43)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6252, 6251])).
% 35.86/23.70 tff(6254,plain,
% 35.86/23.70 (node3(c_bit1, s42, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6253, 81, 1371])).
% 35.86/23.70 tff(6255,plain,
% 35.86/23.70 (((~![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_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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6256,plain,
% 35.86/23.70 ((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)))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6257,plain,
% 35.86/23.70 (((~![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))))),
% 35.86/23.70 inference(monotonicity,[status(thm)],[6256])).
% 35.86/23.70 tff(6258,plain,
% 35.86/23.70 (((~![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)))),
% 35.86/23.70 inference(transitivity,[status(thm)],[6257, 6255])).
% 35.86/23.70 tff(6259,plain,
% 35.86/23.70 ((~![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))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6260,plain,
% 35.86/23.70 ((~![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_bit1, s43) | node1(c_bit1, s42) | (~node3(c_bit1, s42, s43))),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6259, 6258])).
% 35.86/23.70 tff(6261,plain,
% 35.86/23.70 (m_counter_cell_v_value(c_bit1, s43) | node1(c_bit1, s42)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6260, 199, 6254])).
% 35.86/23.70 tff(6262,plain,
% 35.86/23.70 (m_counter_cell_v_value(c_bit1, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6261, 6250])).
% 35.86/23.70 tff(6263,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6264,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6265,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6264, 6263])).
% 35.86/23.70 tff(6266,plain,
% 35.86/23.70 ((~m_counter_cell_v_value(c_bit0, s43)) | m_counter_cell_v_carry_out(c_bit0, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6265, 3031, 1387])).
% 35.86/23.70 tff(6267,plain,
% 35.86/23.70 (m_counter_cell_v_carry_out(c_bit0, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6266, 1383])).
% 35.86/23.70 tff(6268,plain,
% 35.86/23.70 (((~![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))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6269,plain,
% 35.86/23.70 ((~![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))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6270,plain,
% 35.86/23.70 ((~![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)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6269, 6268])).
% 35.86/23.70 tff(6271,plain,
% 35.86/23.70 (m_counter_cell_v_carry_in(c_bit1, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6270, 3046, 6267])).
% 35.86/23.70 tff(6272,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, 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_bit1, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6273,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6274,plain,
% 35.86/23.70 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s43)) | (~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6273, 6272])).
% 35.86/23.70 tff(6275,plain,
% 35.86/23.70 ((~m_counter_cell_v_value(c_bit1, s43)) | m_counter_cell_v_carry_out(c_bit1, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6274, 3031, 6271])).
% 35.86/23.70 tff(6276,plain,
% 35.86/23.70 (m_counter_cell_v_carry_out(c_bit1, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6275, 6262])).
% 35.86/23.70 tff(6277,plain,
% 35.86/23.70 (((~![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, s43)) | m_counter_cell_v_carry_in(c_bit2, s43))) <=> ((~![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, s43)) | m_counter_cell_v_carry_in(c_bit2, s43))),
% 35.86/23.70 inference(rewrite,[status(thm)],[])).
% 35.86/23.70 tff(6278,plain,
% 35.86/23.70 ((~![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, s43)) | m_counter_cell_v_carry_in(c_bit2, s43))),
% 35.86/23.70 inference(quant_inst,[status(thm)],[])).
% 35.86/23.70 tff(6279,plain,
% 35.86/23.70 ((~![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, s43)) | m_counter_cell_v_carry_in(c_bit2, s43)),
% 35.86/23.70 inference(modus_ponens,[status(thm)],[6278, 6277])).
% 35.86/23.70 tff(6280,plain,
% 35.86/23.70 (m_counter_cell_v_carry_in(c_bit2, s43)),
% 35.86/23.70 inference(unit_resolution,[status(thm)],[6279, 4417, 6276])).
% 35.86/23.70 tff(6281,plain,
% 35.86/23.70 (((~![I0: $i, X: $i] : ((~node1(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, s43)) | m_counter_cell_v_value(c_bit2, s43) | (~node1(c_bit2, s43)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s43)) | m_counter_cell_v_value(c_bit2, s43) | (~node1(c_bit2, s43)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6282,plain,
% 35.86/23.71 (((~node1(c_bit2, s43)) | (~m_counter_cell_v_carry_in(c_bit2, s43)) | m_counter_cell_v_value(c_bit2, s43)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s43)) | m_counter_cell_v_value(c_bit2, s43) | (~node1(c_bit2, s43)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6283,plain,
% 35.86/23.71 (((~![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, s43)) | (~m_counter_cell_v_carry_in(c_bit2, s43)) | m_counter_cell_v_value(c_bit2, s43))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s43)) | m_counter_cell_v_value(c_bit2, s43) | (~node1(c_bit2, s43))))),
% 35.86/23.71 inference(monotonicity,[status(thm)],[6282])).
% 35.86/23.71 tff(6284,plain,
% 35.86/23.71 (((~![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, s43)) | (~m_counter_cell_v_carry_in(c_bit2, s43)) | m_counter_cell_v_value(c_bit2, s43))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s43)) | m_counter_cell_v_value(c_bit2, s43) | (~node1(c_bit2, s43)))),
% 35.86/23.71 inference(transitivity,[status(thm)],[6283, 6281])).
% 35.86/23.71 tff(6285,plain,
% 35.86/23.71 ((~![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, s43)) | (~m_counter_cell_v_carry_in(c_bit2, s43)) | m_counter_cell_v_value(c_bit2, s43))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6286,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~node1(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, s43)) | m_counter_cell_v_value(c_bit2, s43) | (~node1(c_bit2, s43))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6285, 6284])).
% 35.86/23.71 tff(6287,plain,
% 35.86/23.71 (m_counter_cell_v_value(c_bit2, s43) | (~node1(c_bit2, s43))),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6286, 170, 6280])).
% 35.86/23.71 tff(6288,plain,
% 35.86/23.71 (~node1(c_bit2, s43)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6287, 6213])).
% 35.86/23.71 tff(6289,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit2, s43, s44))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit2, s43, s44))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6290,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit2, s43, s44))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6291,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit2, s43, s44)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6290, 6289])).
% 35.86/23.71 tff(6292,plain,
% 35.86/23.71 (node3(c_bit2, s43, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6291, 81, 1399])).
% 35.86/23.71 tff(6293,plain,
% 35.86/23.71 (((~![Y: $i, 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, s44) | node1(c_bit2, s43) | (~node3(c_bit2, s43, s44)))) <=> ((~![Y: $i, 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, s44) | node1(c_bit2, s43) | (~node3(c_bit2, s43, s44)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6294,plain,
% 35.86/23.71 ((node1(c_bit2, s43) | (~node3(c_bit2, s43, s44)) | m_counter_cell_v_value(c_bit2, s44)) <=> (m_counter_cell_v_value(c_bit2, s44) | node1(c_bit2, s43) | (~node3(c_bit2, s43, s44)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6295,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s43) | (~node3(c_bit2, s43, s44)) | m_counter_cell_v_value(c_bit2, s44))) <=> ((~![Y: $i, 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, s44) | node1(c_bit2, s43) | (~node3(c_bit2, s43, s44))))),
% 35.86/23.71 inference(monotonicity,[status(thm)],[6294])).
% 35.86/23.71 tff(6296,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s43) | (~node3(c_bit2, s43, s44)) | m_counter_cell_v_value(c_bit2, s44))) <=> ((~![Y: $i, 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, s44) | node1(c_bit2, s43) | (~node3(c_bit2, s43, s44)))),
% 35.86/23.71 inference(transitivity,[status(thm)],[6295, 6293])).
% 35.86/23.71 tff(6297,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s43) | (~node3(c_bit2, s43, s44)) | m_counter_cell_v_value(c_bit2, s44))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6298,plain,
% 35.86/23.71 ((~![Y: $i, 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, s44) | node1(c_bit2, s43) | (~node3(c_bit2, s43, s44))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6297, 6296])).
% 35.86/23.71 tff(6299,plain,
% 35.86/23.71 (m_counter_cell_v_value(c_bit2, s44) | node1(c_bit2, s43)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6298, 199, 6292])).
% 35.86/23.71 tff(6300,plain,
% 35.86/23.71 (m_counter_cell_v_value(c_bit2, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6299, 6288])).
% 35.86/23.71 tff(6301,plain,
% 35.86/23.71 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6302,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6303,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~m_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))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6302, 6301])).
% 35.86/23.71 tff(6304,plain,
% 35.86/23.71 ((~m_counter_cell_v_value(c_bit1, s43)) | (~node2(c_bit1, s43))),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6303, 219, 6271])).
% 35.86/23.71 tff(6305,plain,
% 35.86/23.71 (~node2(c_bit1, s43)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6304, 6262])).
% 35.86/23.71 tff(6306,plain,
% 35.86/23.71 (((~![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))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6307,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s43, s44)) | node3(c_bit1, s43, s44))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6308,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s43, s44)) | node3(c_bit1, s43, s44)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6307, 6306])).
% 35.86/23.71 tff(6309,plain,
% 35.86/23.71 (node3(c_bit1, s43, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6308, 81, 1399])).
% 35.86/23.71 tff(6310,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6311,plain,
% 35.86/23.71 ((node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44))) <=> ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6312,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44))))),
% 35.86/23.71 inference(monotonicity,[status(thm)],[6311])).
% 35.86/23.71 tff(6313,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)) | (~m_counter_cell_v_value(c_bit1, s44)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44)))),
% 35.86/23.71 inference(transitivity,[status(thm)],[6312, 6310])).
% 35.86/23.71 tff(6314,plain,
% 35.86/23.71 ((~![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)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6315,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43) | (~node3(c_bit1, s43, s44))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6314, 6313])).
% 35.86/23.71 tff(6316,plain,
% 35.86/23.71 ((~m_counter_cell_v_value(c_bit1, s44)) | node2(c_bit1, s43)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6315, 234, 6309])).
% 35.86/23.71 tff(6317,plain,
% 35.86/23.71 (~m_counter_cell_v_value(c_bit1, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6316, 6305])).
% 35.86/23.71 tff(6318,plain,
% 35.86/23.71 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s44) | (~node4(c_bit1, s44)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s44) | (~node4(c_bit1, s44)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6319,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s44) | (~node4(c_bit1, s44)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6320,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s44) | (~node4(c_bit1, s44))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6319, 6318])).
% 35.86/23.71 tff(6321,plain,
% 35.86/23.71 (~node4(c_bit1, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6320, 2875, 6317])).
% 35.86/23.71 tff(6322,plain,
% 35.86/23.71 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s44)) | node4(c_bit1, s44))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s44)) | node4(c_bit1, s44))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6323,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s44)) | node4(c_bit1, s44))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6324,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s44)) | node4(c_bit1, s44)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6323, 6322])).
% 35.86/23.71 tff(6325,plain,
% 35.86/23.71 (~m_counter_cell_v_carry_out(c_bit1, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6324, 2887, 6321])).
% 35.86/23.71 tff(6326,assumption,(m_counter_cell_v_carry_in(c_bit2, s44)), introduced(assumption)).
% 35.86/23.71 tff(6327,assumption,(~m_counter_cell_v_carry_out(c_bit1, s44)), introduced(assumption)).
% 35.86/23.71 tff(6328,plain,
% 35.86/23.71 (((~![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, s44)) | m_counter_cell_v_carry_out(c_bit1, s44))) <=> ((~![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, s44)) | m_counter_cell_v_carry_out(c_bit1, s44))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6329,plain,
% 35.86/23.71 ((~![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, s44)) | m_counter_cell_v_carry_out(c_bit1, s44))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6330,plain,
% 35.86/23.71 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s44)) | m_counter_cell_v_carry_out(c_bit1, s44)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6329, 6328])).
% 35.86/23.71 tff(6331,plain,
% 35.86/23.71 ($false),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6330, 3167, 6327, 6326])).
% 35.86/23.71 tff(6332,plain,((~m_counter_cell_v_carry_in(c_bit2, s44)) | m_counter_cell_v_carry_out(c_bit1, s44)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.71 tff(6333,plain,
% 35.86/23.71 (~m_counter_cell_v_carry_in(c_bit2, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6332, 6325])).
% 35.86/23.71 tff(6334,plain,
% 35.86/23.71 (((~![I0: $i, X: $i] : ((~node1(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, s44) | (~m_counter_cell_v_value(c_bit2, s44)) | (~node1(c_bit2, 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_bit2, s44) | (~m_counter_cell_v_value(c_bit2, s44)) | (~node1(c_bit2, s44)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6335,plain,
% 35.86/23.71 (((~node1(c_bit2, s44)) | m_counter_cell_v_carry_in(c_bit2, s44) | (~m_counter_cell_v_value(c_bit2, s44))) <=> (m_counter_cell_v_carry_in(c_bit2, s44) | (~m_counter_cell_v_value(c_bit2, s44)) | (~node1(c_bit2, s44)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6336,plain,
% 35.86/23.71 (((~![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, s44)) | m_counter_cell_v_carry_in(c_bit2, s44) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s44) | (~m_counter_cell_v_value(c_bit2, s44)) | (~node1(c_bit2, s44))))),
% 35.86/23.71 inference(monotonicity,[status(thm)],[6335])).
% 35.86/23.71 tff(6337,plain,
% 35.86/23.71 (((~![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, s44)) | m_counter_cell_v_carry_in(c_bit2, s44) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s44) | (~m_counter_cell_v_value(c_bit2, s44)) | (~node1(c_bit2, s44)))),
% 35.86/23.71 inference(transitivity,[status(thm)],[6336, 6334])).
% 35.86/23.71 tff(6338,plain,
% 35.86/23.71 ((~![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, s44)) | m_counter_cell_v_carry_in(c_bit2, s44) | (~m_counter_cell_v_value(c_bit2, s44)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6339,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~node1(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, s44) | (~m_counter_cell_v_value(c_bit2, s44)) | (~node1(c_bit2, s44))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6338, 6337])).
% 35.86/23.71 tff(6340,plain,
% 35.86/23.71 ((~m_counter_cell_v_value(c_bit2, s44)) | (~node1(c_bit2, s44))),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6339, 3359, 6333])).
% 35.86/23.71 tff(6341,plain,
% 35.86/23.71 (~node1(c_bit2, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6340, 6300])).
% 35.86/23.71 tff(6342,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit2, s44, s45))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit2, s44, s45))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6343,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit2, s44, s45))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6344,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit2, s44, s45)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6343, 6342])).
% 35.86/23.71 tff(6345,plain,
% 35.86/23.71 (node3(c_bit2, s44, s45)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6344, 81, 1430])).
% 35.86/23.71 tff(6346,plain,
% 35.86/23.71 (((~![Y: $i, 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, s45) | node1(c_bit2, s44) | (~node3(c_bit2, 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_bit2, s45) | node1(c_bit2, s44) | (~node3(c_bit2, s44, s45)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6347,plain,
% 35.86/23.71 ((node1(c_bit2, s44) | (~node3(c_bit2, s44, s45)) | m_counter_cell_v_value(c_bit2, s45)) <=> (m_counter_cell_v_value(c_bit2, s45) | node1(c_bit2, s44) | (~node3(c_bit2, s44, s45)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6348,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s44) | (~node3(c_bit2, s44, s45)) | m_counter_cell_v_value(c_bit2, 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_bit2, s45) | node1(c_bit2, s44) | (~node3(c_bit2, s44, s45))))),
% 35.86/23.71 inference(monotonicity,[status(thm)],[6347])).
% 35.86/23.71 tff(6349,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s44) | (~node3(c_bit2, s44, s45)) | m_counter_cell_v_value(c_bit2, 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_bit2, s45) | node1(c_bit2, s44) | (~node3(c_bit2, s44, s45)))),
% 35.86/23.71 inference(transitivity,[status(thm)],[6348, 6346])).
% 35.86/23.71 tff(6350,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s44) | (~node3(c_bit2, s44, s45)) | m_counter_cell_v_value(c_bit2, s45))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6351,plain,
% 35.86/23.71 ((~![Y: $i, 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, s45) | node1(c_bit2, s44) | (~node3(c_bit2, s44, s45))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6350, 6349])).
% 35.86/23.71 tff(6352,plain,
% 35.86/23.71 (m_counter_cell_v_value(c_bit2, s45) | node1(c_bit2, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6351, 199, 6345])).
% 35.86/23.71 tff(6353,plain,
% 35.86/23.71 (m_counter_cell_v_value(c_bit2, s45)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6352, 6341])).
% 35.86/23.71 tff(6354,plain,
% 35.86/23.71 (((~![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)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6355,plain,
% 35.86/23.71 ((~![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)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6356,plain,
% 35.86/23.71 ((~![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))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6355, 6354])).
% 35.86/23.71 tff(6357,plain,
% 35.86/23.71 (~node4(c_bit0, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6356, 2875, 1411])).
% 35.86/23.71 tff(6358,assumption,(~node4(c_bit0, s44)), introduced(assumption)).
% 35.86/23.71 tff(6359,assumption,(m_counter_cell_v_carry_out(c_bit0, s44)), introduced(assumption)).
% 35.86/23.71 tff(6360,plain,
% 35.86/23.71 (((~![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))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6361,plain,
% 35.86/23.71 ((~![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))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6362,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6361, 6360])).
% 35.86/23.71 tff(6363,plain,
% 35.86/23.71 ($false),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6362, 2887, 6359, 6358])).
% 35.86/23.71 tff(6364,plain,((~m_counter_cell_v_carry_out(c_bit0, s44)) | node4(c_bit0, s44)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.71 tff(6365,plain,
% 35.86/23.71 (~m_counter_cell_v_carry_out(c_bit0, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6364, 6357])).
% 35.86/23.71 tff(6366,assumption,(m_counter_cell_v_carry_in(c_bit1, s44)), introduced(assumption)).
% 35.86/23.71 tff(6367,assumption,(~m_counter_cell_v_carry_out(c_bit0, s44)), introduced(assumption)).
% 35.86/23.71 tff(6368,plain,
% 35.86/23.71 (((~![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))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6369,plain,
% 35.86/23.71 ((~![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))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6370,plain,
% 35.86/23.71 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s44)) | m_counter_cell_v_carry_out(c_bit0, s44)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6369, 6368])).
% 35.86/23.71 tff(6371,plain,
% 35.86/23.71 ($false),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6370, 2901, 6367, 6366])).
% 35.86/23.71 tff(6372,plain,(m_counter_cell_v_carry_out(c_bit0, s44) | (~m_counter_cell_v_carry_in(c_bit1, s44))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.71 tff(6373,plain,
% 35.86/23.71 (~m_counter_cell_v_carry_in(c_bit1, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6372, 6365])).
% 35.86/23.71 tff(6374,assumption,(~m_counter_cell_v_carry_in(c_bit1, s44)), introduced(assumption)).
% 35.86/23.71 tff(6375,assumption,(~m_counter_cell_v_value(c_bit1, s44)), introduced(assumption)).
% 35.86/23.71 tff(6376,assumption,(node2(c_bit1, s44)), introduced(assumption)).
% 35.86/23.71 tff(6377,plain,
% 35.86/23.71 (((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6378,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6379,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s44) | m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6378, 6377])).
% 35.86/23.71 tff(6380,plain,
% 35.86/23.71 ($false),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6379, 3291, 6376, 6375, 6374])).
% 35.86/23.71 tff(6381,plain,(m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44)) | m_counter_cell_v_carry_in(c_bit1, s44)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.71 tff(6382,plain,
% 35.86/23.71 (m_counter_cell_v_value(c_bit1, s44) | (~node2(c_bit1, s44))),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6381, 6373])).
% 35.86/23.71 tff(6383,plain,
% 35.86/23.71 (~node2(c_bit1, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6382, 6317])).
% 35.86/23.71 tff(6384,plain,
% 35.86/23.71 (((~![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))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6385,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s44, s45)) | node3(c_bit1, s44, s45))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6386,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s44, s45)) | node3(c_bit1, s44, s45)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6385, 6384])).
% 35.86/23.71 tff(6387,plain,
% 35.86/23.71 (node3(c_bit1, s44, s45)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6386, 81, 1430])).
% 35.86/23.71 tff(6388,plain,
% 35.86/23.71 (((~![Y: $i, I0: $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)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6389,plain,
% 35.86/23.71 ((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)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6390,plain,
% 35.86/23.71 (((~![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))))),
% 35.86/23.71 inference(monotonicity,[status(thm)],[6389])).
% 35.86/23.71 tff(6391,plain,
% 35.86/23.71 (((~![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)))),
% 35.86/23.71 inference(transitivity,[status(thm)],[6390, 6388])).
% 35.86/23.71 tff(6392,plain,
% 35.86/23.71 ((~![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)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6393,plain,
% 35.86/23.71 ((~![Y: $i, I0: $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))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6392, 6391])).
% 35.86/23.71 tff(6394,plain,
% 35.86/23.71 ((~m_counter_cell_v_value(c_bit1, s45)) | node2(c_bit1, s44)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6393, 234, 6387])).
% 35.86/23.71 tff(6395,plain,
% 35.86/23.71 (~m_counter_cell_v_value(c_bit1, s45)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6394, 6383])).
% 35.86/23.71 tff(6396,plain,
% 35.86/23.71 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s45) | (~node4(c_bit1, s45)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s45) | (~node4(c_bit1, s45)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6397,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s45) | (~node4(c_bit1, s45)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6398,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s45) | (~node4(c_bit1, s45))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6397, 6396])).
% 35.86/23.71 tff(6399,plain,
% 35.86/23.71 (~node4(c_bit1, s45)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6398, 2875, 6395])).
% 35.86/23.71 tff(6400,plain,
% 35.86/23.71 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s45)) | node4(c_bit1, s45))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s45)) | node4(c_bit1, s45))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6401,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s45)) | node4(c_bit1, s45))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6402,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s45)) | node4(c_bit1, s45)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6401, 6400])).
% 35.86/23.71 tff(6403,plain,
% 35.86/23.71 (~m_counter_cell_v_carry_out(c_bit1, s45)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6402, 2887, 6399])).
% 35.86/23.71 tff(6404,plain,
% 35.86/23.71 (((~![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, s45)) | m_counter_cell_v_carry_out(c_bit1, s45))) <=> ((~![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, s45)) | m_counter_cell_v_carry_out(c_bit1, s45))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6405,plain,
% 35.86/23.71 ((~![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, s45)) | m_counter_cell_v_carry_out(c_bit1, s45))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6406,plain,
% 35.86/23.71 ((~![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, s45)) | m_counter_cell_v_carry_out(c_bit1, s45)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6405, 6404])).
% 35.86/23.71 tff(6407,plain,
% 35.86/23.71 (~m_counter_cell_v_carry_in(c_bit2, s45)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6406, 3167, 6403])).
% 35.86/23.71 tff(6408,plain,
% 35.86/23.71 (((~![I0: $i, X: $i] : ((~node1(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, s45) | (~m_counter_cell_v_value(c_bit2, s45)) | (~node1(c_bit2, 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_bit2, s45) | (~m_counter_cell_v_value(c_bit2, s45)) | (~node1(c_bit2, s45)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6409,plain,
% 35.86/23.71 (((~node1(c_bit2, s45)) | m_counter_cell_v_carry_in(c_bit2, s45) | (~m_counter_cell_v_value(c_bit2, s45))) <=> (m_counter_cell_v_carry_in(c_bit2, s45) | (~m_counter_cell_v_value(c_bit2, s45)) | (~node1(c_bit2, s45)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6410,plain,
% 35.86/23.71 (((~![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, s45)) | m_counter_cell_v_carry_in(c_bit2, s45) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s45) | (~m_counter_cell_v_value(c_bit2, s45)) | (~node1(c_bit2, s45))))),
% 35.86/23.71 inference(monotonicity,[status(thm)],[6409])).
% 35.86/23.71 tff(6411,plain,
% 35.86/23.71 (((~![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, s45)) | m_counter_cell_v_carry_in(c_bit2, s45) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s45) | (~m_counter_cell_v_value(c_bit2, s45)) | (~node1(c_bit2, s45)))),
% 35.86/23.71 inference(transitivity,[status(thm)],[6410, 6408])).
% 35.86/23.71 tff(6412,plain,
% 35.86/23.71 ((~![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, s45)) | m_counter_cell_v_carry_in(c_bit2, s45) | (~m_counter_cell_v_value(c_bit2, s45)))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6413,plain,
% 35.86/23.71 ((~![I0: $i, X: $i] : ((~node1(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, s45) | (~m_counter_cell_v_value(c_bit2, s45)) | (~node1(c_bit2, s45))),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6412, 6411])).
% 35.86/23.71 tff(6414,plain,
% 35.86/23.71 ((~m_counter_cell_v_value(c_bit2, s45)) | (~node1(c_bit2, s45))),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6413, 3359, 6407])).
% 35.86/23.71 tff(6415,plain,
% 35.86/23.71 (~node1(c_bit2, s45)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6414, 6353])).
% 35.86/23.71 tff(6416,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit2, s45, s46))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit2, s45, s46))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6417,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit2, s45, s46))),
% 35.86/23.71 inference(quant_inst,[status(thm)],[])).
% 35.86/23.71 tff(6418,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit2, s45, s46)),
% 35.86/23.71 inference(modus_ponens,[status(thm)],[6417, 6416])).
% 35.86/23.71 tff(6419,plain,
% 35.86/23.71 (node3(c_bit2, s45, s46)),
% 35.86/23.71 inference(unit_resolution,[status(thm)],[6418, 81, 1456])).
% 35.86/23.71 tff(6420,plain,
% 35.86/23.71 (((~![Y: $i, 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, s46) | node1(c_bit2, s45) | (~node3(c_bit2, 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_bit2, s46) | node1(c_bit2, s45) | (~node3(c_bit2, s45, s46)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6421,plain,
% 35.86/23.71 ((node1(c_bit2, s45) | (~node3(c_bit2, s45, s46)) | m_counter_cell_v_value(c_bit2, s46)) <=> (m_counter_cell_v_value(c_bit2, s46) | node1(c_bit2, s45) | (~node3(c_bit2, s45, s46)))),
% 35.86/23.71 inference(rewrite,[status(thm)],[])).
% 35.86/23.71 tff(6422,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s45) | (~node3(c_bit2, s45, s46)) | m_counter_cell_v_value(c_bit2, 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_bit2, s46) | node1(c_bit2, s45) | (~node3(c_bit2, s45, s46))))),
% 35.86/23.71 inference(monotonicity,[status(thm)],[6421])).
% 35.86/23.71 tff(6423,plain,
% 35.86/23.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s45) | (~node3(c_bit2, s45, s46)) | m_counter_cell_v_value(c_bit2, 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_bit2, s46) | node1(c_bit2, s45) | (~node3(c_bit2, s45, s46)))),
% 35.86/23.71 inference(transitivity,[status(thm)],[6422, 6420])).
% 35.86/23.71 tff(6424,plain,
% 35.86/23.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s45) | (~node3(c_bit2, s45, s46)) | m_counter_cell_v_value(c_bit2, s46))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6425,plain,
% 35.86/23.72 ((~![Y: $i, 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, s46) | node1(c_bit2, s45) | (~node3(c_bit2, s45, s46))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6424, 6423])).
% 35.86/23.72 tff(6426,plain,
% 35.86/23.72 (m_counter_cell_v_value(c_bit2, s46) | node1(c_bit2, s45)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6425, 199, 6419])).
% 35.86/23.72 tff(6427,plain,
% 35.86/23.72 (m_counter_cell_v_value(c_bit2, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6426, 6415])).
% 35.86/23.72 tff(6428,plain,
% 35.86/23.72 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6429,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6430,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6429, 6428])).
% 35.86/23.72 tff(6431,plain,
% 35.86/23.72 ((~m_counter_cell_v_value(c_bit0, s45)) | m_counter_cell_v_carry_out(c_bit0, s45)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6430, 3031, 1444])).
% 35.86/23.72 tff(6432,plain,
% 35.86/23.72 (m_counter_cell_v_carry_out(c_bit0, s45)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6431, 1442])).
% 35.86/23.72 tff(6433,plain,
% 35.86/23.72 (((~![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))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6434,plain,
% 35.86/23.72 ((~![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))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6435,plain,
% 35.86/23.72 ((~![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)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6434, 6433])).
% 35.86/23.72 tff(6436,plain,
% 35.86/23.72 (m_counter_cell_v_carry_in(c_bit1, s45)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6435, 3046, 6432])).
% 35.86/23.72 tff(6437,plain,
% 35.86/23.72 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6438,plain,
% 35.86/23.72 (((~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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6439,plain,
% 35.86/23.72 (((~![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))))),
% 35.86/23.72 inference(monotonicity,[status(thm)],[6438])).
% 35.86/23.72 tff(6440,plain,
% 35.86/23.72 (((~![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)))),
% 35.86/23.72 inference(transitivity,[status(thm)],[6439, 6437])).
% 35.86/23.72 tff(6441,plain,
% 35.86/23.72 ((~![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))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6442,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6441, 6440])).
% 35.86/23.72 tff(6443,plain,
% 35.86/23.72 (m_counter_cell_v_value(c_bit1, s45) | (~node1(c_bit1, s45))),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6442, 170, 6436])).
% 35.86/23.72 tff(6444,plain,
% 35.86/23.72 (~node1(c_bit1, s45)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6443, 6395])).
% 35.86/23.72 tff(6445,plain,
% 35.86/23.72 (((~![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))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6446,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s45, s46)) | node3(c_bit1, s45, s46))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6447,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s45, s46)) | node3(c_bit1, s45, s46)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6446, 6445])).
% 35.86/23.72 tff(6448,plain,
% 35.86/23.72 (node3(c_bit1, s45, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6447, 81, 1456])).
% 35.86/23.72 tff(6449,plain,
% 35.86/23.72 (((~![Y: $i, I0: $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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6450,plain,
% 35.86/23.72 ((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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6451,plain,
% 35.86/23.72 (((~![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))))),
% 35.86/23.72 inference(monotonicity,[status(thm)],[6450])).
% 35.86/23.72 tff(6452,plain,
% 35.86/23.72 (((~![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)))),
% 35.86/23.72 inference(transitivity,[status(thm)],[6451, 6449])).
% 35.86/23.72 tff(6453,plain,
% 35.86/23.72 ((~![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))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6454,plain,
% 35.86/23.72 ((~![Y: $i, I0: $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))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6453, 6452])).
% 35.86/23.72 tff(6455,plain,
% 35.86/23.72 (m_counter_cell_v_value(c_bit1, s46) | node1(c_bit1, s45)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6454, 199, 6448])).
% 35.86/23.72 tff(6456,plain,
% 35.86/23.72 (m_counter_cell_v_value(c_bit1, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6455, 6444])).
% 35.86/23.72 tff(6457,assumption,(~m_counter_cell_v_value(c_bit1, s47)), introduced(assumption)).
% 35.86/23.72 tff(6458,plain,
% 35.86/23.72 (((~![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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6459,plain,
% 35.86/23.72 ((~![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)))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6460,plain,
% 35.86/23.72 ((~![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))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6459, 6458])).
% 35.86/23.72 tff(6461,plain,
% 35.86/23.72 (~node4(c_bit1, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6460, 2875, 6457])).
% 35.86/23.72 tff(6462,assumption,(m_counter_cell_v_value(c_bit1, s46)), introduced(assumption)).
% 35.86/23.72 tff(6463,assumption,(m_counter_cell_v_value(c_bit2, s46)), introduced(assumption)).
% 35.86/23.72 tff(6464,plain,
% 35.86/23.72 (((~![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))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6465,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit1, s46, s47))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6466,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit1, s46, s47)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6465, 6464])).
% 35.86/23.72 tff(6467,plain,
% 35.86/23.72 (node3(c_bit1, s46, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6466, 81, 1487])).
% 35.86/23.72 tff(6468,plain,
% 35.86/23.72 (((~![Y: $i, I0: $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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6469,plain,
% 35.86/23.72 ((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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6470,plain,
% 35.86/23.72 (((~![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))))),
% 35.86/23.72 inference(monotonicity,[status(thm)],[6469])).
% 35.86/23.72 tff(6471,plain,
% 35.86/23.72 (((~![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)))),
% 35.86/23.72 inference(transitivity,[status(thm)],[6470, 6468])).
% 35.86/23.72 tff(6472,plain,
% 35.86/23.72 ((~![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))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6473,plain,
% 35.86/23.72 ((~![Y: $i, I0: $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))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6472, 6471])).
% 35.86/23.72 tff(6474,plain,
% 35.86/23.72 (m_counter_cell_v_value(c_bit1, s47) | node1(c_bit1, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6473, 199, 6467])).
% 35.86/23.72 tff(6475,plain,
% 35.86/23.72 (node1(c_bit1, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6474, 6457])).
% 35.86/23.72 tff(6476,plain,
% 35.86/23.72 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6477,plain,
% 35.86/23.72 (((~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)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6478,plain,
% 35.86/23.72 (((~![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))))),
% 35.86/23.72 inference(monotonicity,[status(thm)],[6477])).
% 35.86/23.72 tff(6479,plain,
% 35.86/23.72 (((~![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)))),
% 35.86/23.72 inference(transitivity,[status(thm)],[6478, 6476])).
% 35.86/23.72 tff(6480,plain,
% 35.86/23.72 ((~![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)))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6481,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6480, 6479])).
% 35.86/23.72 tff(6482,plain,
% 35.86/23.72 (m_counter_cell_v_carry_in(c_bit1, s46) | (~node1(c_bit1, s46))),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6481, 3359, 6462])).
% 35.86/23.72 tff(6483,plain,
% 35.86/23.72 (m_counter_cell_v_carry_in(c_bit1, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6482, 6475])).
% 35.86/23.72 tff(6484,assumption,(~m_counter_cell_v_carry_out(c_bit1, s46)), introduced(assumption)).
% 35.86/23.72 tff(6485,assumption,(m_counter_cell_v_carry_in(c_bit1, s46)), introduced(assumption)).
% 35.86/23.72 tff(6486,plain,
% 35.86/23.72 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6487,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6488,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | (~m_counter_cell_v_value(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit1, s46)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6487, 6486])).
% 35.86/23.72 tff(6489,plain,
% 35.86/23.72 ($false),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6488, 3031, 6462, 6485, 6484])).
% 35.86/23.72 tff(6490,plain,(m_counter_cell_v_carry_out(c_bit1, s46) | (~m_counter_cell_v_value(c_bit1, s46)) | (~m_counter_cell_v_carry_in(c_bit1, s46))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.72 tff(6491,plain,
% 35.86/23.72 (m_counter_cell_v_carry_out(c_bit1, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6490, 6483, 6462])).
% 35.86/23.72 tff(6492,assumption,(~m_counter_cell_v_carry_in(c_bit2, s46)), introduced(assumption)).
% 35.86/23.72 tff(6493,assumption,(m_counter_cell_v_carry_out(c_bit1, s46)), introduced(assumption)).
% 35.86/23.72 tff(6494,plain,
% 35.86/23.72 (((~![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, s46)) | m_counter_cell_v_carry_in(c_bit2, s46))) <=> ((~![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, s46)) | m_counter_cell_v_carry_in(c_bit2, s46))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6495,plain,
% 35.86/23.72 ((~![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, s46)) | m_counter_cell_v_carry_in(c_bit2, s46))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6496,plain,
% 35.86/23.72 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s46)) | m_counter_cell_v_carry_in(c_bit2, s46)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6495, 6494])).
% 35.86/23.72 tff(6497,plain,
% 35.86/23.72 ($false),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6496, 4417, 6493, 6492])).
% 35.86/23.72 tff(6498,plain,(m_counter_cell_v_carry_in(c_bit2, s46) | (~m_counter_cell_v_carry_out(c_bit1, s46))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.72 tff(6499,plain,
% 35.86/23.72 (m_counter_cell_v_carry_in(c_bit2, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6498, 6491])).
% 35.86/23.72 tff(6500,plain,
% 35.86/23.72 (((~![I0: $i, X: $i] : ((~m_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, s46)) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node2(c_bit2, s46)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s46)) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node2(c_bit2, s46)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6501,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~m_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, s46)) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node2(c_bit2, s46)))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6502,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~m_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, s46)) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node2(c_bit2, s46))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6501, 6500])).
% 35.86/23.72 tff(6503,plain,
% 35.86/23.72 ((~m_counter_cell_v_carry_in(c_bit2, s46)) | (~node2(c_bit2, s46))),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6502, 219, 6463])).
% 35.86/23.72 tff(6504,plain,
% 35.86/23.72 (~node2(c_bit2, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6503, 6499])).
% 35.86/23.72 tff(6505,plain,
% 35.86/23.72 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit2, s46, s47))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit2, s46, s47))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6506,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s46, s47)) | node3(c_bit2, s46, s47))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6507,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s46, s47)) | node3(c_bit2, s46, s47)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6506, 6505])).
% 35.86/23.72 tff(6508,plain,
% 35.86/23.72 (node3(c_bit2, s46, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6507, 81, 1487])).
% 35.86/23.72 tff(6509,plain,
% 35.86/23.72 (((~![Y: $i, 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, s47)) | node2(c_bit2, s46) | (~node3(c_bit2, s46, s47)))) <=> ((~![Y: $i, 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, s47)) | node2(c_bit2, s46) | (~node3(c_bit2, s46, s47)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6510,plain,
% 35.86/23.72 ((node2(c_bit2, s46) | (~node3(c_bit2, s46, s47)) | (~m_counter_cell_v_value(c_bit2, s47))) <=> ((~m_counter_cell_v_value(c_bit2, s47)) | node2(c_bit2, s46) | (~node3(c_bit2, s46, s47)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6511,plain,
% 35.86/23.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s46) | (~node3(c_bit2, s46, s47)) | (~m_counter_cell_v_value(c_bit2, s47)))) <=> ((~![Y: $i, 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, s47)) | node2(c_bit2, s46) | (~node3(c_bit2, s46, s47))))),
% 35.86/23.72 inference(monotonicity,[status(thm)],[6510])).
% 35.86/23.72 tff(6512,plain,
% 35.86/23.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s46) | (~node3(c_bit2, s46, s47)) | (~m_counter_cell_v_value(c_bit2, s47)))) <=> ((~![Y: $i, 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, s47)) | node2(c_bit2, s46) | (~node3(c_bit2, s46, s47)))),
% 35.86/23.72 inference(transitivity,[status(thm)],[6511, 6509])).
% 35.86/23.72 tff(6513,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s46) | (~node3(c_bit2, s46, s47)) | (~m_counter_cell_v_value(c_bit2, s47)))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6514,plain,
% 35.86/23.72 ((~![Y: $i, 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, s47)) | node2(c_bit2, s46) | (~node3(c_bit2, s46, s47))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6513, 6512])).
% 35.86/23.72 tff(6515,plain,
% 35.86/23.72 ((~m_counter_cell_v_value(c_bit2, s47)) | node2(c_bit2, s46)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6514, 234, 6508])).
% 35.86/23.72 tff(6516,plain,
% 35.86/23.72 (~m_counter_cell_v_value(c_bit2, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6515, 6504])).
% 35.86/23.72 tff(6517,assumption,(node2(c_bit2, s47)), introduced(assumption)).
% 35.86/23.72 tff(6518,plain,
% 35.86/23.72 (((~![I0: $i, X: $i] : (m_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, s47) | m_counter_cell_v_value(c_bit2, s47) | (~node2(c_bit2, 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_bit2, s47) | m_counter_cell_v_value(c_bit2, s47) | (~node2(c_bit2, s47)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6519,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : (m_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, s47) | m_counter_cell_v_value(c_bit2, s47) | (~node2(c_bit2, s47)))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6520,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : (m_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, s47) | m_counter_cell_v_value(c_bit2, s47) | (~node2(c_bit2, s47))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6519, 6518])).
% 35.86/23.72 tff(6521,plain,
% 35.86/23.72 (m_counter_cell_v_carry_in(c_bit2, s47) | m_counter_cell_v_value(c_bit2, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6520, 3291, 6517])).
% 35.86/23.72 tff(6522,plain,
% 35.86/23.72 (m_counter_cell_v_carry_in(c_bit2, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6521, 6516])).
% 35.86/23.72 tff(6523,plain,
% 35.86/23.72 (((~![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, s47)) | m_counter_cell_v_carry_out(c_bit1, s47))) <=> ((~![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, s47)) | m_counter_cell_v_carry_out(c_bit1, s47))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6524,plain,
% 35.86/23.72 ((~![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, s47)) | m_counter_cell_v_carry_out(c_bit1, s47))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6525,plain,
% 35.86/23.72 ((~![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, s47)) | m_counter_cell_v_carry_out(c_bit1, s47)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6524, 6523])).
% 35.86/23.72 tff(6526,plain,
% 35.86/23.72 (m_counter_cell_v_carry_out(c_bit1, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6525, 3167, 6522])).
% 35.86/23.72 tff(6527,plain,
% 35.86/23.72 (((~![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))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6528,plain,
% 35.86/23.72 ((~![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))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6529,plain,
% 35.86/23.72 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s47)) | node4(c_bit1, s47)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6528, 6527])).
% 35.86/23.72 tff(6530,plain,
% 35.86/23.72 ($false),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6529, 2887, 6526, 6461])).
% 35.86/23.72 tff(6531,plain,(m_counter_cell_v_value(c_bit1, s47) | (~node2(c_bit2, s47)) | (~m_counter_cell_v_value(c_bit2, s46)) | (~m_counter_cell_v_value(c_bit1, s46))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.72 tff(6532,plain,
% 35.86/23.72 (~node2(c_bit2, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6531, 6457, 6463, 6462])).
% 35.86/23.72 tff(6533,plain,
% 35.86/23.72 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit2, s47, s48))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit2, s47, s48))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6534,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit2, s47, s48))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6535,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit2, s47, s48)),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6534, 6533])).
% 35.86/23.72 tff(6536,plain,
% 35.86/23.72 (node3(c_bit2, s47, s48)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6535, 81, 1515])).
% 35.86/23.72 tff(6537,plain,
% 35.86/23.72 (((~![Y: $i, 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, s48)) | node2(c_bit2, s47) | (~node3(c_bit2, 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_bit2, s48)) | node2(c_bit2, s47) | (~node3(c_bit2, s47, s48)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6538,plain,
% 35.86/23.72 ((node2(c_bit2, s47) | (~node3(c_bit2, s47, s48)) | (~m_counter_cell_v_value(c_bit2, s48))) <=> ((~m_counter_cell_v_value(c_bit2, s48)) | node2(c_bit2, s47) | (~node3(c_bit2, s47, s48)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6539,plain,
% 35.86/23.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s47) | (~node3(c_bit2, s47, s48)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s48)) | node2(c_bit2, s47) | (~node3(c_bit2, s47, s48))))),
% 35.86/23.72 inference(monotonicity,[status(thm)],[6538])).
% 35.86/23.72 tff(6540,plain,
% 35.86/23.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s47) | (~node3(c_bit2, s47, s48)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s48)) | node2(c_bit2, s47) | (~node3(c_bit2, s47, s48)))),
% 35.86/23.72 inference(transitivity,[status(thm)],[6539, 6537])).
% 35.86/23.72 tff(6541,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s47) | (~node3(c_bit2, s47, s48)) | (~m_counter_cell_v_value(c_bit2, s48)))),
% 35.86/23.72 inference(quant_inst,[status(thm)],[])).
% 35.86/23.72 tff(6542,plain,
% 35.86/23.72 ((~![Y: $i, 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, s48)) | node2(c_bit2, s47) | (~node3(c_bit2, s47, s48))),
% 35.86/23.72 inference(modus_ponens,[status(thm)],[6541, 6540])).
% 35.86/23.72 tff(6543,plain,
% 35.86/23.72 ((~m_counter_cell_v_value(c_bit2, s48)) | node2(c_bit2, s47)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6542, 234, 6536])).
% 35.86/23.72 tff(6544,plain,
% 35.86/23.72 (~m_counter_cell_v_value(c_bit2, s48)),
% 35.86/23.72 inference(unit_resolution,[status(thm)],[6543, 6532])).
% 35.86/23.72 tff(6545,plain,
% 35.86/23.72 (((~![Y: $i, 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, s48) | node1(c_bit2, s47) | (~node3(c_bit2, s47, 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_bit2, s48) | node1(c_bit2, s47) | (~node3(c_bit2, s47, s48)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6546,plain,
% 35.86/23.72 ((node1(c_bit2, s47) | (~node3(c_bit2, s47, s48)) | m_counter_cell_v_value(c_bit2, s48)) <=> (m_counter_cell_v_value(c_bit2, s48) | node1(c_bit2, s47) | (~node3(c_bit2, s47, s48)))),
% 35.86/23.72 inference(rewrite,[status(thm)],[])).
% 35.86/23.72 tff(6547,plain,
% 35.86/23.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s47) | (~node3(c_bit2, s47, s48)) | m_counter_cell_v_value(c_bit2, 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_bit2, s48) | node1(c_bit2, s47) | (~node3(c_bit2, s47, s48))))),
% 35.86/23.72 inference(monotonicity,[status(thm)],[6546])).
% 35.86/23.72 tff(6548,plain,
% 35.86/23.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s47) | (~node3(c_bit2, s47, s48)) | m_counter_cell_v_value(c_bit2, 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_bit2, s48) | node1(c_bit2, s47) | (~node3(c_bit2, s47, s48)))),
% 35.86/23.72 inference(transitivity,[status(thm)],[6547, 6545])).
% 35.86/23.72 tff(6549,plain,
% 35.86/23.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s47) | (~node3(c_bit2, s47, s48)) | m_counter_cell_v_value(c_bit2, s48))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6550,plain,
% 35.86/23.73 ((~![Y: $i, 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, s48) | node1(c_bit2, s47) | (~node3(c_bit2, s47, s48))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6549, 6548])).
% 35.86/23.73 tff(6551,plain,
% 35.86/23.73 (m_counter_cell_v_value(c_bit2, s48) | node1(c_bit2, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6550, 199, 6536])).
% 35.86/23.73 tff(6552,plain,
% 35.86/23.73 (node1(c_bit2, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6551, 6544])).
% 35.86/23.73 tff(6553,assumption,(node4(c_bit1, s46)), introduced(assumption)).
% 35.86/23.73 tff(6554,plain,
% 35.86/23.73 (((~![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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6555,plain,
% 35.86/23.73 ((~![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)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6556,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6555, 6554])).
% 35.86/23.73 tff(6557,plain,
% 35.86/23.73 (~node4(c_bit0, s46)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6556, 2875, 1468])).
% 35.86/23.73 tff(6558,assumption,(m_counter_cell_v_carry_out(c_bit0, s46)), introduced(assumption)).
% 35.86/23.73 tff(6559,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6560,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6561,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s46)) | node4(c_bit0, s46)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6560, 6559])).
% 35.86/23.73 tff(6562,plain,
% 35.86/23.73 ($false),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6561, 2887, 6558, 6557])).
% 35.86/23.73 tff(6563,plain,(~m_counter_cell_v_carry_out(c_bit0, s46)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.73 tff(6564,assumption,(~m_counter_cell_v_carry_out(c_bit0, s46)), introduced(assumption)).
% 35.86/23.73 tff(6565,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6566,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6567,plain,
% 35.86/23.73 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s46)) | m_counter_cell_v_carry_out(c_bit0, s46)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6566, 6565])).
% 35.86/23.73 tff(6568,plain,
% 35.86/23.73 ($false),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6567, 2901, 6564, 6485])).
% 35.86/23.73 tff(6569,plain,(m_counter_cell_v_carry_out(c_bit0, s46) | (~m_counter_cell_v_carry_in(c_bit1, s46))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.73 tff(6570,plain,
% 35.86/23.73 (~m_counter_cell_v_carry_in(c_bit1, s46)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6569, 6563])).
% 35.86/23.73 tff(6571,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s46) | (~node4(c_bit1, s46)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~node4(c_bit1, s46)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6572,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s46) | (~node4(c_bit1, s46)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6573,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s46) | (~node4(c_bit1, s46))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6572, 6571])).
% 35.86/23.73 tff(6574,plain,
% 35.86/23.73 ($false),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6573, 3076, 6570, 6553])).
% 35.86/23.73 tff(6575,plain,(~node4(c_bit1, s46)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.73 tff(6576,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s46)) | node4(c_bit1, s46))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s46)) | node4(c_bit1, s46))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6577,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s46)) | node4(c_bit1, s46))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6578,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s46)) | node4(c_bit1, s46)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6577, 6576])).
% 35.86/23.73 tff(6579,plain,
% 35.86/23.73 (~m_counter_cell_v_carry_out(c_bit1, s46)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6578, 2887, 6575])).
% 35.86/23.73 tff(6580,plain,
% 35.86/23.73 (((~![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, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))) <=> ((~![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, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6581,plain,
% 35.86/23.73 ((~![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, s46)) | m_counter_cell_v_carry_out(c_bit1, s46))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6582,plain,
% 35.86/23.73 ((~![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, s46)) | m_counter_cell_v_carry_out(c_bit1, s46)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6581, 6580])).
% 35.86/23.73 tff(6583,plain,
% 35.86/23.73 (~m_counter_cell_v_carry_in(c_bit2, s46)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6582, 3167, 6579])).
% 35.86/23.73 tff(6584,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : ((~node1(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, s46) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node1(c_bit2, 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_bit2, s46) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node1(c_bit2, s46)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6585,plain,
% 35.86/23.73 (((~node1(c_bit2, s46)) | m_counter_cell_v_carry_in(c_bit2, s46) | (~m_counter_cell_v_value(c_bit2, s46))) <=> (m_counter_cell_v_carry_in(c_bit2, s46) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node1(c_bit2, s46)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6586,plain,
% 35.86/23.73 (((~![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, s46)) | m_counter_cell_v_carry_in(c_bit2, s46) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s46) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node1(c_bit2, s46))))),
% 35.86/23.73 inference(monotonicity,[status(thm)],[6585])).
% 35.86/23.73 tff(6587,plain,
% 35.86/23.73 (((~![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, s46)) | m_counter_cell_v_carry_in(c_bit2, s46) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s46) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node1(c_bit2, s46)))),
% 35.86/23.73 inference(transitivity,[status(thm)],[6586, 6584])).
% 35.86/23.73 tff(6588,plain,
% 35.86/23.73 ((~![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, s46)) | m_counter_cell_v_carry_in(c_bit2, s46) | (~m_counter_cell_v_value(c_bit2, s46)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6589,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~node1(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, s46) | (~m_counter_cell_v_value(c_bit2, s46)) | (~node1(c_bit2, s46))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6588, 6587])).
% 35.86/23.73 tff(6590,plain,
% 35.86/23.73 ((~m_counter_cell_v_value(c_bit2, s46)) | (~node1(c_bit2, s46))),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6589, 3359, 6583])).
% 35.86/23.73 tff(6591,plain,
% 35.86/23.73 (~node1(c_bit2, s46)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6590, 6463])).
% 35.86/23.73 tff(6592,plain,
% 35.86/23.73 (((~![Y: $i, 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, s47) | node1(c_bit2, s46) | (~node3(c_bit2, 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_bit2, s47) | node1(c_bit2, s46) | (~node3(c_bit2, s46, s47)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6593,plain,
% 35.86/23.73 ((node1(c_bit2, s46) | (~node3(c_bit2, s46, s47)) | m_counter_cell_v_value(c_bit2, s47)) <=> (m_counter_cell_v_value(c_bit2, s47) | node1(c_bit2, s46) | (~node3(c_bit2, s46, s47)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6594,plain,
% 35.86/23.73 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s46) | (~node3(c_bit2, s46, s47)) | m_counter_cell_v_value(c_bit2, 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_bit2, s47) | node1(c_bit2, s46) | (~node3(c_bit2, s46, s47))))),
% 35.86/23.73 inference(monotonicity,[status(thm)],[6593])).
% 35.86/23.73 tff(6595,plain,
% 35.86/23.73 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s46) | (~node3(c_bit2, s46, s47)) | m_counter_cell_v_value(c_bit2, 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_bit2, s47) | node1(c_bit2, s46) | (~node3(c_bit2, s46, s47)))),
% 35.86/23.73 inference(transitivity,[status(thm)],[6594, 6592])).
% 35.86/23.73 tff(6596,plain,
% 35.86/23.73 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s46) | (~node3(c_bit2, s46, s47)) | m_counter_cell_v_value(c_bit2, s47))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6597,plain,
% 35.86/23.73 ((~![Y: $i, 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, s47) | node1(c_bit2, s46) | (~node3(c_bit2, s46, s47))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6596, 6595])).
% 35.86/23.73 tff(6598,plain,
% 35.86/23.73 (m_counter_cell_v_value(c_bit2, s47) | node1(c_bit2, s46)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6597, 199, 6508])).
% 35.86/23.73 tff(6599,plain,
% 35.86/23.73 (m_counter_cell_v_value(c_bit2, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6598, 6591])).
% 35.86/23.73 tff(6600,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : ((~node1(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, s47) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node1(c_bit2, s47)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s47) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node1(c_bit2, s47)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6601,plain,
% 35.86/23.73 (((~node1(c_bit2, s47)) | m_counter_cell_v_carry_in(c_bit2, s47) | (~m_counter_cell_v_value(c_bit2, s47))) <=> (m_counter_cell_v_carry_in(c_bit2, s47) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node1(c_bit2, s47)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6602,plain,
% 35.86/23.73 (((~![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, s47)) | m_counter_cell_v_carry_in(c_bit2, s47) | (~m_counter_cell_v_value(c_bit2, s47)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s47) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node1(c_bit2, s47))))),
% 35.86/23.73 inference(monotonicity,[status(thm)],[6601])).
% 35.86/23.73 tff(6603,plain,
% 35.86/23.73 (((~![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, s47)) | m_counter_cell_v_carry_in(c_bit2, s47) | (~m_counter_cell_v_value(c_bit2, s47)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s47) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node1(c_bit2, s47)))),
% 35.86/23.73 inference(transitivity,[status(thm)],[6602, 6600])).
% 35.86/23.73 tff(6604,plain,
% 35.86/23.73 ((~![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, s47)) | m_counter_cell_v_carry_in(c_bit2, s47) | (~m_counter_cell_v_value(c_bit2, s47)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6605,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s47) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node1(c_bit2, s47))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6604, 6603])).
% 35.86/23.73 tff(6606,plain,
% 35.86/23.73 (m_counter_cell_v_carry_in(c_bit2, s47) | (~node1(c_bit2, s47))),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6605, 3359, 6599])).
% 35.86/23.73 tff(6607,plain,
% 35.86/23.73 (m_counter_cell_v_carry_in(c_bit2, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6606, 6552])).
% 35.86/23.73 tff(6608,plain,
% 35.86/23.73 (m_counter_cell_v_carry_out(c_bit1, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6525, 3167, 6607])).
% 35.86/23.73 tff(6609,plain,
% 35.86/23.73 ($false),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6529, 2887, 6608, 6461])).
% 35.86/23.73 tff(6610,plain,(m_counter_cell_v_value(c_bit1, s47) | (~m_counter_cell_v_value(c_bit2, s46)) | (~m_counter_cell_v_value(c_bit1, s46))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.73 tff(6611,plain,
% 35.86/23.73 (m_counter_cell_v_value(c_bit1, s47) | (~m_counter_cell_v_value(c_bit2, s46))),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6610, 6456])).
% 35.86/23.73 tff(6612,plain,
% 35.86/23.73 (m_counter_cell_v_value(c_bit1, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6611, 6427])).
% 35.86/23.73 tff(6613,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6614,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6615,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6614, 6613])).
% 35.86/23.73 tff(6616,plain,
% 35.86/23.73 ((~m_counter_cell_v_value(c_bit0, s47)) | m_counter_cell_v_carry_out(c_bit0, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6615, 3031, 1503])).
% 35.86/23.73 tff(6617,plain,
% 35.86/23.73 (m_counter_cell_v_carry_out(c_bit0, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6616, 1499])).
% 35.86/23.73 tff(6618,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6619,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6620,plain,
% 35.86/23.73 ((~![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)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6619, 6618])).
% 35.86/23.73 tff(6621,plain,
% 35.86/23.73 (m_counter_cell_v_carry_in(c_bit1, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6620, 3046, 6617])).
% 35.86/23.73 tff(6622,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6623,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6624,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_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))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6623, 6622])).
% 35.86/23.73 tff(6625,plain,
% 35.86/23.73 ((~m_counter_cell_v_value(c_bit1, s47)) | (~node2(c_bit1, s47))),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6624, 219, 6621])).
% 35.86/23.73 tff(6626,plain,
% 35.86/23.73 (~node2(c_bit1, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6625, 6612])).
% 35.86/23.73 tff(6627,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6628,plain,
% 35.86/23.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s47, s48)) | node3(c_bit1, s47, s48))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6629,plain,
% 35.86/23.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s47, s48)) | node3(c_bit1, s47, s48)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6628, 6627])).
% 35.86/23.73 tff(6630,plain,
% 35.86/23.73 (node3(c_bit1, s47, s48)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6629, 81, 1515])).
% 35.86/23.73 tff(6631,plain,
% 35.86/23.73 (((~![Y: $i, I0: $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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6632,plain,
% 35.86/23.73 ((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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6633,plain,
% 35.86/23.73 (((~![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))))),
% 35.86/23.73 inference(monotonicity,[status(thm)],[6632])).
% 35.86/23.73 tff(6634,plain,
% 35.86/23.73 (((~![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)))),
% 35.86/23.73 inference(transitivity,[status(thm)],[6633, 6631])).
% 35.86/23.73 tff(6635,plain,
% 35.86/23.73 ((~![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)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6636,plain,
% 35.86/23.73 ((~![Y: $i, I0: $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))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6635, 6634])).
% 35.86/23.73 tff(6637,plain,
% 35.86/23.73 ((~m_counter_cell_v_value(c_bit1, s48)) | node2(c_bit1, s47)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6636, 234, 6630])).
% 35.86/23.73 tff(6638,plain,
% 35.86/23.73 (~m_counter_cell_v_value(c_bit1, s48)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6637, 6626])).
% 35.86/23.73 tff(6639,plain,
% 35.86/23.73 (((~![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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6640,plain,
% 35.86/23.73 ((~![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)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6641,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6640, 6639])).
% 35.86/23.73 tff(6642,plain,
% 35.86/23.73 (~node4(c_bit0, s48)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6641, 2875, 1527])).
% 35.86/23.73 tff(6643,assumption,(m_counter_cell_v_carry_out(c_bit0, s48)), introduced(assumption)).
% 35.86/23.73 tff(6644,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6645,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6646,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s48)) | node4(c_bit0, s48)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6645, 6644])).
% 35.86/23.73 tff(6647,plain,
% 35.86/23.73 ($false),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6646, 2887, 6643, 6642])).
% 35.86/23.73 tff(6648,plain,(~m_counter_cell_v_carry_out(c_bit0, s48)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.73 tff(6649,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6650,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6651,plain,
% 35.86/23.73 ((~![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)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6650, 6649])).
% 35.86/23.73 tff(6652,plain,
% 35.86/23.73 (~m_counter_cell_v_carry_in(c_bit1, s48)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6651, 2901, 6648])).
% 35.86/23.73 tff(6653,assumption,(node2(c_bit1, s48)), introduced(assumption)).
% 35.86/23.73 tff(6654,assumption,(~m_counter_cell_v_value(c_bit1, s48)), introduced(assumption)).
% 35.86/23.73 tff(6655,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6656,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6657,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s48) | m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6656, 6655])).
% 35.86/23.73 tff(6658,plain,
% 35.86/23.73 ($false),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6657, 3291, 6654, 6653, 6652])).
% 35.86/23.73 tff(6659,plain,(m_counter_cell_v_value(c_bit1, s48) | (~node2(c_bit1, s48))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.73 tff(6660,plain,
% 35.86/23.73 (~node2(c_bit1, s48)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6659, 6638])).
% 35.86/23.73 tff(6661,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6662,plain,
% 35.86/23.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit1, s48, s49))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6663,plain,
% 35.86/23.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit1, s48, s49)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6662, 6661])).
% 35.86/23.73 tff(6664,plain,
% 35.86/23.73 (node3(c_bit1, s48, s49)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6663, 81, 1546])).
% 35.86/23.73 tff(6665,plain,
% 35.86/23.73 (((~![Y: $i, I0: $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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6666,plain,
% 35.86/23.73 ((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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6667,plain,
% 35.86/23.73 (((~![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))))),
% 35.86/23.73 inference(monotonicity,[status(thm)],[6666])).
% 35.86/23.73 tff(6668,plain,
% 35.86/23.73 (((~![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)))),
% 35.86/23.73 inference(transitivity,[status(thm)],[6667, 6665])).
% 35.86/23.73 tff(6669,plain,
% 35.86/23.73 ((~![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)))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6670,plain,
% 35.86/23.73 ((~![Y: $i, I0: $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))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6669, 6668])).
% 35.86/23.73 tff(6671,plain,
% 35.86/23.73 ((~m_counter_cell_v_value(c_bit1, s49)) | node2(c_bit1, s48)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6670, 234, 6664])).
% 35.86/23.73 tff(6672,plain,
% 35.86/23.73 (~m_counter_cell_v_value(c_bit1, s49)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6671, 6660])).
% 35.86/23.73 tff(6673,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6674,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6675,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6674, 6673])).
% 35.86/23.73 tff(6676,plain,
% 35.86/23.73 ((~m_counter_cell_v_value(c_bit0, s49)) | m_counter_cell_v_carry_out(c_bit0, s49)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6675, 3031, 1562])).
% 35.86/23.73 tff(6677,plain,
% 35.86/23.73 (m_counter_cell_v_carry_out(c_bit0, s49)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6676, 1558])).
% 35.86/23.73 tff(6678,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6679,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6680,plain,
% 35.86/23.73 ((~![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)),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6679, 6678])).
% 35.86/23.73 tff(6681,plain,
% 35.86/23.73 (m_counter_cell_v_carry_in(c_bit1, s49)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6680, 3046, 6677])).
% 35.86/23.73 tff(6682,assumption,(~m_counter_cell_v_value(c_bit1, s49)), introduced(assumption)).
% 35.86/23.73 tff(6683,assumption,(m_counter_cell_v_carry_in(c_bit1, s49)), introduced(assumption)).
% 35.86/23.73 tff(6684,assumption,(node1(c_bit1, s49)), introduced(assumption)).
% 35.86/23.73 tff(6685,plain,
% 35.86/23.73 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6686,plain,
% 35.86/23.73 (((~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)))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6687,plain,
% 35.86/23.73 (((~![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))))),
% 35.86/23.73 inference(monotonicity,[status(thm)],[6686])).
% 35.86/23.73 tff(6688,plain,
% 35.86/23.73 (((~![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)))),
% 35.86/23.73 inference(transitivity,[status(thm)],[6687, 6685])).
% 35.86/23.73 tff(6689,plain,
% 35.86/23.73 ((~![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))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6690,plain,
% 35.86/23.73 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49))),
% 35.86/23.73 inference(modus_ponens,[status(thm)],[6689, 6688])).
% 35.86/23.73 tff(6691,plain,
% 35.86/23.73 ($false),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6690, 170, 6684, 6683, 6682])).
% 35.86/23.73 tff(6692,plain,(m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49)) | (~m_counter_cell_v_carry_in(c_bit1, s49))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.73 tff(6693,plain,
% 35.86/23.73 (m_counter_cell_v_value(c_bit1, s49) | (~node1(c_bit1, s49))),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6692, 6681])).
% 35.86/23.73 tff(6694,plain,
% 35.86/23.73 (~node1(c_bit1, s49)),
% 35.86/23.73 inference(unit_resolution,[status(thm)],[6693, 6672])).
% 35.86/23.73 tff(6695,plain,
% 35.86/23.73 (((~![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))),
% 35.86/23.73 inference(rewrite,[status(thm)],[])).
% 35.86/23.73 tff(6696,plain,
% 35.86/23.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit1, s49, s50))),
% 35.86/23.73 inference(quant_inst,[status(thm)],[])).
% 35.86/23.73 tff(6697,plain,
% 35.86/23.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit1, s49, s50)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6696, 6695])).
% 35.86/23.74 tff(6698,plain,
% 35.86/23.74 (node3(c_bit1, s49, s50)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6697, 81, 1574])).
% 35.86/23.74 tff(6699,plain,
% 35.86/23.74 (((~![Y: $i, I0: $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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6700,plain,
% 35.86/23.74 ((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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6701,plain,
% 35.86/23.74 (((~![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))))),
% 35.86/23.74 inference(monotonicity,[status(thm)],[6700])).
% 35.86/23.74 tff(6702,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(transitivity,[status(thm)],[6701, 6699])).
% 35.86/23.74 tff(6703,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6704,plain,
% 35.86/23.74 ((~![Y: $i, I0: $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))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6703, 6702])).
% 35.86/23.74 tff(6705,plain,
% 35.86/23.74 (m_counter_cell_v_value(c_bit1, s50) | node1(c_bit1, s49)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6704, 199, 6698])).
% 35.86/23.74 tff(6706,plain,
% 35.86/23.74 (m_counter_cell_v_value(c_bit1, s50)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6705, 6694])).
% 35.86/23.74 tff(6707,plain,
% 35.86/23.74 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6708,plain,
% 35.86/23.74 (((~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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6709,plain,
% 35.86/23.74 (((~![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))))),
% 35.86/23.74 inference(monotonicity,[status(thm)],[6708])).
% 35.86/23.74 tff(6710,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(transitivity,[status(thm)],[6709, 6707])).
% 35.86/23.74 tff(6711,plain,
% 35.86/23.74 ((~![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)))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6712,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6711, 6710])).
% 35.86/23.74 tff(6713,plain,
% 35.86/23.74 (~node1(c_bit1, s50)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6712, 3359, 6706, 3128])).
% 35.86/23.74 tff(6714,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6715,plain,
% 35.86/23.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit1, s50, s51))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6716,plain,
% 35.86/23.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit1, s50, s51)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6715, 6714])).
% 35.86/23.74 tff(6717,plain,
% 35.86/23.74 (node3(c_bit1, s50, s51)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6716, 81, 1605])).
% 35.86/23.74 tff(6718,plain,
% 35.86/23.74 (((~![Y: $i, I0: $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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6719,plain,
% 35.86/23.74 ((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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6720,plain,
% 35.86/23.74 (((~![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))))),
% 35.86/23.74 inference(monotonicity,[status(thm)],[6719])).
% 35.86/23.74 tff(6721,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(transitivity,[status(thm)],[6720, 6718])).
% 35.86/23.74 tff(6722,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6723,plain,
% 35.86/23.74 ((~![Y: $i, I0: $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))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6722, 6721])).
% 35.86/23.74 tff(6724,plain,
% 35.86/23.74 (m_counter_cell_v_value(c_bit1, s51) | node1(c_bit1, s50)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6723, 199, 6717])).
% 35.86/23.74 tff(6725,plain,
% 35.86/23.74 (m_counter_cell_v_value(c_bit1, s51)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6724, 6713])).
% 35.86/23.74 tff(6726,plain,
% 35.86/23.74 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6727,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6728,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6727, 6726])).
% 35.86/23.74 tff(6729,plain,
% 35.86/23.74 ((~m_counter_cell_v_value(c_bit0, s51)) | m_counter_cell_v_carry_out(c_bit0, s51)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6728, 3031, 1621])).
% 35.86/23.74 tff(6730,plain,
% 35.86/23.74 (m_counter_cell_v_carry_out(c_bit0, s51)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6729, 1617])).
% 35.86/23.74 tff(6731,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6732,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6733,plain,
% 35.86/23.74 ((~![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)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6732, 6731])).
% 35.86/23.74 tff(6734,plain,
% 35.86/23.74 (m_counter_cell_v_carry_in(c_bit1, s51)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6733, 3046, 6730])).
% 35.86/23.74 tff(6735,assumption,(m_counter_cell_v_carry_in(c_bit1, s51)), introduced(assumption)).
% 35.86/23.74 tff(6736,assumption,(m_counter_cell_v_value(c_bit1, s51)), introduced(assumption)).
% 35.86/23.74 tff(6737,assumption,(node2(c_bit1, s51)), introduced(assumption)).
% 35.86/23.74 tff(6738,plain,
% 35.86/23.74 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6739,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6740,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6739, 6738])).
% 35.86/23.74 tff(6741,plain,
% 35.86/23.74 ($false),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6740, 219, 6737, 6736, 6735])).
% 35.86/23.74 tff(6742,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,[]))).
% 35.86/23.74 tff(6743,plain,
% 35.86/23.74 ((~m_counter_cell_v_value(c_bit1, s51)) | (~node2(c_bit1, s51))),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6742, 6734])).
% 35.86/23.74 tff(6744,plain,
% 35.86/23.74 (~node2(c_bit1, s51)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6743, 6725])).
% 35.86/23.74 tff(6745,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6746,plain,
% 35.86/23.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit1, s51, s52))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6747,plain,
% 35.86/23.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit1, s51, s52)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6746, 6745])).
% 35.86/23.74 tff(6748,plain,
% 35.86/23.74 (node3(c_bit1, s51, s52)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6747, 81, 1633])).
% 35.86/23.74 tff(6749,plain,
% 35.86/23.74 (((~![Y: $i, I0: $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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6750,plain,
% 35.86/23.74 ((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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6751,plain,
% 35.86/23.74 (((~![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))))),
% 35.86/23.74 inference(monotonicity,[status(thm)],[6750])).
% 35.86/23.74 tff(6752,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(transitivity,[status(thm)],[6751, 6749])).
% 35.86/23.74 tff(6753,plain,
% 35.86/23.74 ((~![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)))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6754,plain,
% 35.86/23.74 ((~![Y: $i, I0: $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))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6753, 6752])).
% 35.86/23.74 tff(6755,plain,
% 35.86/23.74 ((~m_counter_cell_v_value(c_bit1, s52)) | node2(c_bit1, s51)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6754, 234, 6748])).
% 35.86/23.74 tff(6756,plain,
% 35.86/23.74 (~m_counter_cell_v_value(c_bit1, s52)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6755, 6744])).
% 35.86/23.74 tff(6757,assumption,(node4(c_bit0, s52)), introduced(assumption)).
% 35.86/23.74 tff(6758,assumption,(~m_counter_cell_v_value(c_bit0, s52)), introduced(assumption)).
% 35.86/23.74 tff(6759,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6760,plain,
% 35.86/23.74 ((~![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)))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6761,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6760, 6759])).
% 35.86/23.74 tff(6762,plain,
% 35.86/23.74 ($false),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6761, 2875, 6758, 6757])).
% 35.86/23.74 tff(6763,plain,(m_counter_cell_v_value(c_bit0, s52) | (~node4(c_bit0, s52))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.74 tff(6764,plain,
% 35.86/23.74 (~node4(c_bit0, s52)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6763, 1645])).
% 35.86/23.74 tff(6765,assumption,(~node4(c_bit0, s52)), introduced(assumption)).
% 35.86/23.74 tff(6766,assumption,(m_counter_cell_v_carry_out(c_bit0, s52)), introduced(assumption)).
% 35.86/23.74 tff(6767,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6768,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6769,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6768, 6767])).
% 35.86/23.74 tff(6770,plain,
% 35.86/23.74 ($false),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6769, 2887, 6766, 6765])).
% 35.86/23.74 tff(6771,plain,((~m_counter_cell_v_carry_out(c_bit0, s52)) | node4(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.74 tff(6772,plain,
% 35.86/23.74 (~m_counter_cell_v_carry_out(c_bit0, s52)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6771, 6764])).
% 35.86/23.74 tff(6773,assumption,(m_counter_cell_v_carry_in(c_bit1, s52)), introduced(assumption)).
% 35.86/23.74 tff(6774,assumption,(~m_counter_cell_v_carry_out(c_bit0, s52)), introduced(assumption)).
% 35.86/23.74 tff(6775,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6776,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6777,plain,
% 35.86/23.74 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6776, 6775])).
% 35.86/23.74 tff(6778,plain,
% 35.86/23.74 ($false),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6777, 2901, 6774, 6773])).
% 35.86/23.74 tff(6779,plain,((~m_counter_cell_v_carry_in(c_bit1, s52)) | m_counter_cell_v_carry_out(c_bit0, s52)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.74 tff(6780,plain,
% 35.86/23.74 (~m_counter_cell_v_carry_in(c_bit1, s52)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6779, 6772])).
% 35.86/23.74 tff(6781,plain,
% 35.86/23.74 (((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6782,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6783,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : (m_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))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6782, 6781])).
% 35.86/23.74 tff(6784,plain,
% 35.86/23.74 (~node2(c_bit1, s52)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6783, 3291, 6780, 6756])).
% 35.86/23.74 tff(6785,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6786,plain,
% 35.86/23.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit1, s52, s53))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6787,plain,
% 35.86/23.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit1, s52, s53)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6786, 6785])).
% 35.86/23.74 tff(6788,plain,
% 35.86/23.74 (node3(c_bit1, s52, s53)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6787, 81, 1664])).
% 35.86/23.74 tff(6789,plain,
% 35.86/23.74 (((~![Y: $i, I0: $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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6790,plain,
% 35.86/23.74 ((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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6791,plain,
% 35.86/23.74 (((~![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))))),
% 35.86/23.74 inference(monotonicity,[status(thm)],[6790])).
% 35.86/23.74 tff(6792,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(transitivity,[status(thm)],[6791, 6789])).
% 35.86/23.74 tff(6793,plain,
% 35.86/23.74 ((~![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)))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6794,plain,
% 35.86/23.74 ((~![Y: $i, I0: $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))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6793, 6792])).
% 35.86/23.74 tff(6795,plain,
% 35.86/23.74 ((~m_counter_cell_v_value(c_bit1, s53)) | node2(c_bit1, s52)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6794, 234, 6788])).
% 35.86/23.74 tff(6796,plain,
% 35.86/23.74 (~m_counter_cell_v_value(c_bit1, s53)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6795, 6784])).
% 35.86/23.74 tff(6797,plain,
% 35.86/23.74 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6798,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6799,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6798, 6797])).
% 35.86/23.74 tff(6800,plain,
% 35.86/23.74 ((~m_counter_cell_v_value(c_bit0, s53)) | m_counter_cell_v_carry_out(c_bit0, s53)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6799, 3031, 1680])).
% 35.86/23.74 tff(6801,plain,
% 35.86/23.74 (m_counter_cell_v_carry_out(c_bit0, s53)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6800, 1676])).
% 35.86/23.74 tff(6802,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6803,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6804,plain,
% 35.86/23.74 ((~![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)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6803, 6802])).
% 35.86/23.74 tff(6805,plain,
% 35.86/23.74 (m_counter_cell_v_carry_in(c_bit1, s53)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6804, 3046, 6801])).
% 35.86/23.74 tff(6806,assumption,(node1(c_bit1, s53)), introduced(assumption)).
% 35.86/23.74 tff(6807,assumption,(~m_counter_cell_v_value(c_bit1, s53)), introduced(assumption)).
% 35.86/23.74 tff(6808,plain,
% 35.86/23.74 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6809,plain,
% 35.86/23.74 (((~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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6810,plain,
% 35.86/23.74 (((~![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))))),
% 35.86/23.74 inference(monotonicity,[status(thm)],[6809])).
% 35.86/23.74 tff(6811,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(transitivity,[status(thm)],[6810, 6808])).
% 35.86/23.74 tff(6812,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6813,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53) | (~node1(c_bit1, s53))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6812, 6811])).
% 35.86/23.74 tff(6814,plain,
% 35.86/23.74 ($false),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6813, 170, 6807, 6806, 6805])).
% 35.86/23.74 tff(6815,plain,((~node1(c_bit1, s53)) | m_counter_cell_v_value(c_bit1, s53)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.74 tff(6816,plain,
% 35.86/23.74 (~node1(c_bit1, s53)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6815, 6796])).
% 35.86/23.74 tff(6817,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6818,plain,
% 35.86/23.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit1, s53, s54))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6819,plain,
% 35.86/23.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit1, s53, s54)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6818, 6817])).
% 35.86/23.74 tff(6820,plain,
% 35.86/23.74 (node3(c_bit1, s53, s54)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6819, 81, 1692])).
% 35.86/23.74 tff(6821,plain,
% 35.86/23.74 (((~![Y: $i, I0: $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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6822,plain,
% 35.86/23.74 ((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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6823,plain,
% 35.86/23.74 (((~![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))))),
% 35.86/23.74 inference(monotonicity,[status(thm)],[6822])).
% 35.86/23.74 tff(6824,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(transitivity,[status(thm)],[6823, 6821])).
% 35.86/23.74 tff(6825,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6826,plain,
% 35.86/23.74 ((~![Y: $i, I0: $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))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6825, 6824])).
% 35.86/23.74 tff(6827,plain,
% 35.86/23.74 (m_counter_cell_v_value(c_bit1, s54) | node1(c_bit1, s53)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6826, 199, 6820])).
% 35.86/23.74 tff(6828,plain,
% 35.86/23.74 (m_counter_cell_v_value(c_bit1, s54)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6827, 6816])).
% 35.86/23.74 tff(6829,assumption,(m_counter_cell_v_carry_in(c_bit1, s54)), introduced(assumption)).
% 35.86/23.74 tff(6830,plain,
% 35.86/23.74 (((~![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)))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6831,plain,
% 35.86/23.74 ((~![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)))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6832,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6831, 6830])).
% 35.86/23.74 tff(6833,plain,
% 35.86/23.74 (~node4(c_bit0, s54)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6832, 2875, 1704])).
% 35.86/23.74 tff(6834,assumption,(~node4(c_bit0, s54)), introduced(assumption)).
% 35.86/23.74 tff(6835,assumption,(m_counter_cell_v_carry_out(c_bit0, s54)), introduced(assumption)).
% 35.86/23.74 tff(6836,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6837,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.74 inference(quant_inst,[status(thm)],[])).
% 35.86/23.74 tff(6838,plain,
% 35.86/23.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54)),
% 35.86/23.74 inference(modus_ponens,[status(thm)],[6837, 6836])).
% 35.86/23.74 tff(6839,plain,
% 35.86/23.74 ($false),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6838, 2887, 6835, 6834])).
% 35.86/23.74 tff(6840,plain,((~m_counter_cell_v_carry_out(c_bit0, s54)) | node4(c_bit0, s54)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.74 tff(6841,plain,
% 35.86/23.74 (~m_counter_cell_v_carry_out(c_bit0, s54)),
% 35.86/23.74 inference(unit_resolution,[status(thm)],[6840, 6833])).
% 35.86/23.74 tff(6842,plain,
% 35.86/23.74 (((~![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))),
% 35.86/23.74 inference(rewrite,[status(thm)],[])).
% 35.86/23.74 tff(6843,plain,
% 35.86/23.74 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6844,plain,
% 35.86/23.75 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s54)) | m_counter_cell_v_carry_out(c_bit0, s54)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6843, 6842])).
% 35.86/23.75 tff(6845,plain,
% 35.86/23.75 ($false),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6844, 2901, 6841, 6829])).
% 35.86/23.75 tff(6846,plain,(~m_counter_cell_v_carry_in(c_bit1, s54)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.75 tff(6847,plain,
% 35.86/23.75 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6848,plain,
% 35.86/23.75 (((~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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6849,plain,
% 35.86/23.75 (((~![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))))),
% 35.86/23.75 inference(monotonicity,[status(thm)],[6848])).
% 35.86/23.75 tff(6850,plain,
% 35.86/23.75 (((~![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)))),
% 35.86/23.75 inference(transitivity,[status(thm)],[6849, 6847])).
% 35.86/23.75 tff(6851,plain,
% 35.86/23.75 ((~![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)))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6852,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6851, 6850])).
% 35.86/23.75 tff(6853,plain,
% 35.86/23.75 ((~m_counter_cell_v_value(c_bit1, s54)) | (~node1(c_bit1, s54))),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6852, 3359, 6846])).
% 35.86/23.75 tff(6854,plain,
% 35.86/23.75 (~node1(c_bit1, s54)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6853, 6828])).
% 35.86/23.75 tff(6855,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6856,plain,
% 35.86/23.75 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit1, s54, s55))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6857,plain,
% 35.86/23.75 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit1, s54, s55)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6856, 6855])).
% 35.86/23.75 tff(6858,plain,
% 35.86/23.75 (node3(c_bit1, s54, s55)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6857, 81, 1723])).
% 35.86/23.75 tff(6859,plain,
% 35.86/23.75 (((~![Y: $i, I0: $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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6860,plain,
% 35.86/23.75 ((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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6861,plain,
% 35.86/23.75 (((~![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))))),
% 35.86/23.75 inference(monotonicity,[status(thm)],[6860])).
% 35.86/23.75 tff(6862,plain,
% 35.86/23.75 (((~![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)))),
% 35.86/23.75 inference(transitivity,[status(thm)],[6861, 6859])).
% 35.86/23.75 tff(6863,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6864,plain,
% 35.86/23.75 ((~![Y: $i, I0: $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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6863, 6862])).
% 35.86/23.75 tff(6865,plain,
% 35.86/23.75 (m_counter_cell_v_value(c_bit1, s55) | node1(c_bit1, s54)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6864, 199, 6858])).
% 35.86/23.75 tff(6866,plain,
% 35.86/23.75 (m_counter_cell_v_value(c_bit1, s55)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6865, 6854])).
% 35.86/23.75 tff(6867,plain,
% 35.86/23.75 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6868,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6869,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6868, 6867])).
% 35.86/23.75 tff(6870,plain,
% 35.86/23.75 ((~m_counter_cell_v_value(c_bit0, s55)) | m_counter_cell_v_carry_out(c_bit0, s55)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6869, 3031, 1739])).
% 35.86/23.75 tff(6871,plain,
% 35.86/23.75 (m_counter_cell_v_carry_out(c_bit0, s55)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6870, 1735])).
% 35.86/23.75 tff(6872,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6873,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6874,plain,
% 35.86/23.75 ((~![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)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6873, 6872])).
% 35.86/23.75 tff(6875,plain,
% 35.86/23.75 (m_counter_cell_v_carry_in(c_bit1, s55)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6874, 3046, 6871])).
% 35.86/23.75 tff(6876,plain,
% 35.86/23.75 (((~![I0: $i, X: $i] : ((~m_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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6877,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~m_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)))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6878,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~m_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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6877, 6876])).
% 35.86/23.75 tff(6879,plain,
% 35.86/23.75 ((~m_counter_cell_v_value(c_bit1, s55)) | (~node2(c_bit1, s55))),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6878, 219, 6875])).
% 35.86/23.75 tff(6880,plain,
% 35.86/23.75 (~node2(c_bit1, s55)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6879, 6866])).
% 35.86/23.75 tff(6881,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6882,plain,
% 35.86/23.75 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s55, s56)) | node3(c_bit1, s55, s56))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6883,plain,
% 35.86/23.75 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s55, s56)) | node3(c_bit1, s55, s56)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6882, 6881])).
% 35.86/23.75 tff(6884,plain,
% 35.86/23.75 (node3(c_bit1, s55, s56)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6883, 81, 1751])).
% 35.86/23.75 tff(6885,plain,
% 35.86/23.75 (((~![Y: $i, I0: $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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6886,plain,
% 35.86/23.75 ((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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6887,plain,
% 35.86/23.75 (((~![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))))),
% 35.86/23.75 inference(monotonicity,[status(thm)],[6886])).
% 35.86/23.75 tff(6888,plain,
% 35.86/23.75 (((~![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)))),
% 35.86/23.75 inference(transitivity,[status(thm)],[6887, 6885])).
% 35.86/23.75 tff(6889,plain,
% 35.86/23.75 ((~![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)))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6890,plain,
% 35.86/23.75 ((~![Y: $i, I0: $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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6889, 6888])).
% 35.86/23.75 tff(6891,plain,
% 35.86/23.75 ((~m_counter_cell_v_value(c_bit1, s56)) | node2(c_bit1, s55)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6890, 234, 6884])).
% 35.86/23.75 tff(6892,plain,
% 35.86/23.75 (~m_counter_cell_v_value(c_bit1, s56)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6891, 6880])).
% 35.86/23.75 tff(6893,plain,
% 35.86/23.75 (((~![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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6894,plain,
% 35.86/23.75 ((~![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)))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6895,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6894, 6893])).
% 35.86/23.75 tff(6896,plain,
% 35.86/23.75 (~node4(c_bit0, s56)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6895, 2875, 1763])).
% 35.86/23.75 tff(6897,assumption,(m_counter_cell_v_carry_out(c_bit0, s56)), introduced(assumption)).
% 35.86/23.75 tff(6898,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6899,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6900,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s56)) | node4(c_bit0, s56)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6899, 6898])).
% 35.86/23.75 tff(6901,plain,
% 35.86/23.75 ($false),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6900, 2887, 6897, 6896])).
% 35.86/23.75 tff(6902,plain,(~m_counter_cell_v_carry_out(c_bit0, s56)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.75 tff(6903,assumption,(m_counter_cell_v_carry_in(c_bit1, s56)), introduced(assumption)).
% 35.86/23.75 tff(6904,assumption,(~m_counter_cell_v_carry_out(c_bit0, s56)), introduced(assumption)).
% 35.86/23.75 tff(6905,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6906,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6907,plain,
% 35.86/23.75 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s56)) | m_counter_cell_v_carry_out(c_bit0, s56)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6906, 6905])).
% 35.86/23.75 tff(6908,plain,
% 35.86/23.75 ($false),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6907, 2901, 6904, 6903])).
% 35.86/23.75 tff(6909,plain,(m_counter_cell_v_carry_out(c_bit0, s56) | (~m_counter_cell_v_carry_in(c_bit1, s56))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.75 tff(6910,plain,
% 35.86/23.75 (~m_counter_cell_v_carry_in(c_bit1, s56)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6909, 6902])).
% 35.86/23.75 tff(6911,assumption,(node2(c_bit1, s56)), introduced(assumption)).
% 35.86/23.75 tff(6912,assumption,(~m_counter_cell_v_value(c_bit1, s56)), introduced(assumption)).
% 35.86/23.75 tff(6913,plain,
% 35.86/23.75 (((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6914,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : (m_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)))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6915,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s56) | m_counter_cell_v_value(c_bit1, s56) | (~node2(c_bit1, s56))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6914, 6913])).
% 35.86/23.75 tff(6916,plain,
% 35.86/23.75 ($false),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6915, 3291, 6912, 6911, 6910])).
% 35.86/23.75 tff(6917,plain,((~node2(c_bit1, s56)) | m_counter_cell_v_value(c_bit1, s56)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.75 tff(6918,plain,
% 35.86/23.75 (~node2(c_bit1, s56)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6917, 6892])).
% 35.86/23.75 tff(6919,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6920,plain,
% 35.86/23.75 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s56, s57)) | node3(c_bit1, s56, s57))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6921,plain,
% 35.86/23.75 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s56, s57)) | node3(c_bit1, s56, s57)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6920, 6919])).
% 35.86/23.75 tff(6922,plain,
% 35.86/23.75 (node3(c_bit1, s56, s57)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6921, 81, 1782])).
% 35.86/23.75 tff(6923,plain,
% 35.86/23.75 (((~![Y: $i, I0: $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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6924,plain,
% 35.86/23.75 ((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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6925,plain,
% 35.86/23.75 (((~![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))))),
% 35.86/23.75 inference(monotonicity,[status(thm)],[6924])).
% 35.86/23.75 tff(6926,plain,
% 35.86/23.75 (((~![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)))),
% 35.86/23.75 inference(transitivity,[status(thm)],[6925, 6923])).
% 35.86/23.75 tff(6927,plain,
% 35.86/23.75 ((~![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)))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6928,plain,
% 35.86/23.75 ((~![Y: $i, I0: $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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6927, 6926])).
% 35.86/23.75 tff(6929,plain,
% 35.86/23.75 ((~m_counter_cell_v_value(c_bit1, s57)) | node2(c_bit1, s56)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6928, 234, 6922])).
% 35.86/23.75 tff(6930,plain,
% 35.86/23.75 (~m_counter_cell_v_value(c_bit1, s57)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6929, 6918])).
% 35.86/23.75 tff(6931,plain,
% 35.86/23.75 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6932,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6933,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6932, 6931])).
% 35.86/23.75 tff(6934,plain,
% 35.86/23.75 ((~m_counter_cell_v_value(c_bit0, s57)) | m_counter_cell_v_carry_out(c_bit0, s57)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6933, 3031, 1798])).
% 35.86/23.75 tff(6935,plain,
% 35.86/23.75 (m_counter_cell_v_carry_out(c_bit0, s57)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6934, 1794])).
% 35.86/23.75 tff(6936,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6937,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6938,plain,
% 35.86/23.75 ((~![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)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6937, 6936])).
% 35.86/23.75 tff(6939,plain,
% 35.86/23.75 (m_counter_cell_v_carry_in(c_bit1, s57)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6938, 3046, 6935])).
% 35.86/23.75 tff(6940,plain,
% 35.86/23.75 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6941,plain,
% 35.86/23.75 (((~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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6942,plain,
% 35.86/23.75 (((~![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))))),
% 35.86/23.75 inference(monotonicity,[status(thm)],[6941])).
% 35.86/23.75 tff(6943,plain,
% 35.86/23.75 (((~![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)))),
% 35.86/23.75 inference(transitivity,[status(thm)],[6942, 6940])).
% 35.86/23.75 tff(6944,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6945,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~node1(I0, 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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6944, 6943])).
% 35.86/23.75 tff(6946,plain,
% 35.86/23.75 (m_counter_cell_v_value(c_bit1, s57) | (~node1(c_bit1, s57))),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6945, 170, 6939])).
% 35.86/23.75 tff(6947,plain,
% 35.86/23.75 (~node1(c_bit1, s57)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6946, 6930])).
% 35.86/23.75 tff(6948,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6949,plain,
% 35.86/23.75 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s57, s58)) | node3(c_bit1, s57, s58))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6950,plain,
% 35.86/23.75 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s57, s58)) | node3(c_bit1, s57, s58)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6949, 6948])).
% 35.86/23.75 tff(6951,plain,
% 35.86/23.75 (node3(c_bit1, s57, s58)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6950, 81, 1810])).
% 35.86/23.75 tff(6952,plain,
% 35.86/23.75 (((~![Y: $i, I0: $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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6953,plain,
% 35.86/23.75 ((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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6954,plain,
% 35.86/23.75 (((~![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))))),
% 35.86/23.75 inference(monotonicity,[status(thm)],[6953])).
% 35.86/23.75 tff(6955,plain,
% 35.86/23.75 (((~![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)))),
% 35.86/23.75 inference(transitivity,[status(thm)],[6954, 6952])).
% 35.86/23.75 tff(6956,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6957,plain,
% 35.86/23.75 ((~![Y: $i, I0: $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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6956, 6955])).
% 35.86/23.75 tff(6958,plain,
% 35.86/23.75 (m_counter_cell_v_value(c_bit1, s58) | node1(c_bit1, s57)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6957, 199, 6951])).
% 35.86/23.75 tff(6959,plain,
% 35.86/23.75 (m_counter_cell_v_value(c_bit1, s58)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6958, 6947])).
% 35.86/23.75 tff(6960,plain,
% 35.86/23.75 (((~![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)))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6961,plain,
% 35.86/23.75 ((~![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)))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6962,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6961, 6960])).
% 35.86/23.75 tff(6963,plain,
% 35.86/23.75 (~node4(c_bit0, s58)),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6962, 2875, 1822])).
% 35.86/23.75 tff(6964,assumption,(m_counter_cell_v_carry_out(c_bit0, s58)), introduced(assumption)).
% 35.86/23.75 tff(6965,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6966,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6967,plain,
% 35.86/23.75 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s58)) | node4(c_bit0, s58)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6966, 6965])).
% 35.86/23.75 tff(6968,plain,
% 35.86/23.75 ($false),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6967, 2887, 6964, 6963])).
% 35.86/23.75 tff(6969,plain,(~m_counter_cell_v_carry_out(c_bit0, s58)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.75 tff(6970,assumption,(m_counter_cell_v_carry_in(c_bit1, s58)), introduced(assumption)).
% 35.86/23.75 tff(6971,assumption,(~m_counter_cell_v_carry_out(c_bit0, s58)), introduced(assumption)).
% 35.86/23.75 tff(6972,plain,
% 35.86/23.75 (((~![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))),
% 35.86/23.75 inference(rewrite,[status(thm)],[])).
% 35.86/23.75 tff(6973,plain,
% 35.86/23.75 ((~![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))),
% 35.86/23.75 inference(quant_inst,[status(thm)],[])).
% 35.86/23.75 tff(6974,plain,
% 35.86/23.75 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s58)) | m_counter_cell_v_carry_out(c_bit0, s58)),
% 35.86/23.75 inference(modus_ponens,[status(thm)],[6973, 6972])).
% 35.86/23.75 tff(6975,plain,
% 35.86/23.75 ($false),
% 35.86/23.75 inference(unit_resolution,[status(thm)],[6974, 2901, 6971, 6970])).
% 35.86/23.75 tff(6976,plain,(m_counter_cell_v_carry_out(c_bit0, s58) | (~m_counter_cell_v_carry_in(c_bit1, s58))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.75 tff(6977,plain,
% 35.86/23.75 (~m_counter_cell_v_carry_in(c_bit1, s58)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[6976, 6969])).
% 35.86/23.76 tff(6978,assumption,(~m_counter_cell_v_carry_in(c_bit1, s58)), introduced(assumption)).
% 35.86/23.76 tff(6979,assumption,(m_counter_cell_v_value(c_bit1, s58)), introduced(assumption)).
% 35.86/23.76 tff(6980,assumption,(node1(c_bit1, s58)), introduced(assumption)).
% 35.86/23.76 tff(6981,plain,
% 35.86/23.76 (((~![I0: $i, X: $i] : ((~node1(I0, 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)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(6982,plain,
% 35.86/23.76 (((~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)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(6983,plain,
% 35.86/23.76 (((~![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))))),
% 35.86/23.76 inference(monotonicity,[status(thm)],[6982])).
% 35.86/23.76 tff(6984,plain,
% 35.86/23.76 (((~![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)))),
% 35.86/23.76 inference(transitivity,[status(thm)],[6983, 6981])).
% 35.86/23.76 tff(6985,plain,
% 35.86/23.76 ((~![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)))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(6986,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s58) | (~m_counter_cell_v_value(c_bit1, s58)) | (~node1(c_bit1, s58))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[6985, 6984])).
% 35.86/23.76 tff(6987,plain,
% 35.86/23.76 ($false),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[6986, 3359, 6980, 6979, 6978])).
% 35.86/23.76 tff(6988,plain,(m_counter_cell_v_carry_in(c_bit1, s58) | (~node1(c_bit1, s58)) | (~m_counter_cell_v_value(c_bit1, s58))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.76 tff(6989,plain,
% 35.86/23.76 ((~node1(c_bit1, s58)) | (~m_counter_cell_v_value(c_bit1, s58))),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[6988, 6977])).
% 35.86/23.76 tff(6990,plain,
% 35.86/23.76 (~node1(c_bit1, s58)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[6989, 6959])).
% 35.86/23.76 tff(6991,plain,
% 35.86/23.76 (((~![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))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(6992,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s58, s59)) | node3(c_bit1, s58, s59))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(6993,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s58, s59)) | node3(c_bit1, s58, s59)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[6992, 6991])).
% 35.86/23.76 tff(6994,plain,
% 35.86/23.76 (node3(c_bit1, s58, s59)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[6993, 81, 1841])).
% 35.86/23.76 tff(6995,plain,
% 35.86/23.76 (((~![Y: $i, I0: $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)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(6996,plain,
% 35.86/23.76 ((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)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(6997,plain,
% 35.86/23.76 (((~![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))))),
% 35.86/23.76 inference(monotonicity,[status(thm)],[6996])).
% 35.86/23.76 tff(6998,plain,
% 35.86/23.76 (((~![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)))),
% 35.86/23.76 inference(transitivity,[status(thm)],[6997, 6995])).
% 35.86/23.76 tff(6999,plain,
% 35.86/23.76 ((~![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))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7000,plain,
% 35.86/23.76 ((~![Y: $i, I0: $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))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[6999, 6998])).
% 35.86/23.76 tff(7001,plain,
% 35.86/23.76 (m_counter_cell_v_value(c_bit1, s59) | node1(c_bit1, s58)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7000, 199, 6994])).
% 35.86/23.76 tff(7002,plain,
% 35.86/23.76 (m_counter_cell_v_value(c_bit1, s59)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7001, 6990])).
% 35.86/23.76 tff(7003,assumption,(node2(c_bit1, s59)), introduced(assumption)).
% 35.86/23.76 tff(7004,plain,
% 35.86/23.76 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7005,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7006,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7005, 7004])).
% 35.86/23.76 tff(7007,plain,
% 35.86/23.76 ((~m_counter_cell_v_value(c_bit0, s59)) | m_counter_cell_v_carry_out(c_bit0, s59)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7006, 3031, 1857])).
% 35.86/23.76 tff(7008,plain,
% 35.86/23.76 (m_counter_cell_v_carry_out(c_bit0, s59)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7007, 1853])).
% 35.86/23.76 tff(7009,plain,
% 35.86/23.76 (((~![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))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7010,plain,
% 35.86/23.76 ((~![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))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7011,plain,
% 35.86/23.76 ((~![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)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7010, 7009])).
% 35.86/23.76 tff(7012,plain,
% 35.86/23.76 (m_counter_cell_v_carry_in(c_bit1, s59)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7011, 3046, 7008])).
% 35.86/23.76 tff(7013,assumption,(m_counter_cell_v_value(c_bit1, s59)), introduced(assumption)).
% 35.86/23.76 tff(7014,plain,
% 35.86/23.76 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7015,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59)))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7016,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59)) | (~node2(c_bit1, s59))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7015, 7014])).
% 35.86/23.76 tff(7017,plain,
% 35.86/23.76 ($false),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7016, 219, 7013, 7012, 7003])).
% 35.86/23.76 tff(7018,plain,((~node2(c_bit1, s59)) | (~m_counter_cell_v_value(c_bit1, s59))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.76 tff(7019,plain,
% 35.86/23.76 (~node2(c_bit1, s59)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7018, 7002])).
% 35.86/23.76 tff(7020,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s60)) | node3(c_bit1, s59, s60))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s60)) | node3(c_bit1, s59, s60))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7021,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s59, s60)) | node3(c_bit1, s59, s60))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7022,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s59, s60)) | node3(c_bit1, s59, s60)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7021, 7020])).
% 35.86/23.76 tff(7023,plain,
% 35.86/23.76 (node3(c_bit1, s59, s60)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7022, 81, 74])).
% 35.86/23.76 tff(7024,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7025,plain,
% 35.86/23.76 ((node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)) | (~m_counter_cell_v_value(c_bit1, s60))) <=> ((~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7026,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)) | (~m_counter_cell_v_value(c_bit1, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60))))),
% 35.86/23.76 inference(monotonicity,[status(thm)],[7025])).
% 35.86/23.76 tff(7027,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)) | (~m_counter_cell_v_value(c_bit1, s60)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)))),
% 35.86/23.76 inference(transitivity,[status(thm)],[7026, 7024])).
% 35.86/23.76 tff(7028,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s59) | (~node3(c_bit1, s59, s60)) | (~m_counter_cell_v_value(c_bit1, s60)))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7029,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59) | (~node3(c_bit1, s59, s60))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7028, 7027])).
% 35.86/23.76 tff(7030,plain,
% 35.86/23.76 ((~m_counter_cell_v_value(c_bit1, s60)) | node2(c_bit1, s59)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7029, 234, 7023])).
% 35.86/23.76 tff(7031,plain,
% 35.86/23.76 (~m_counter_cell_v_value(c_bit1, s60)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7030, 7019])).
% 35.86/23.76 tff(7032,assumption,(node2(c_bit1, s60)), introduced(assumption)).
% 35.86/23.76 tff(7033,plain,
% 35.86/23.76 (((~![I0: $i, X: $i] : (m_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, s60) | m_counter_cell_v_value(c_bit1, s60) | (~node2(c_bit1, s60)))) <=> ((~![I0: $i, X: $i] : (m_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, s60) | m_counter_cell_v_value(c_bit1, s60) | (~node2(c_bit1, s60)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7034,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : (m_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, s60) | m_counter_cell_v_value(c_bit1, s60) | (~node2(c_bit1, s60)))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7035,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s60) | m_counter_cell_v_value(c_bit1, s60) | (~node2(c_bit1, s60))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7034, 7033])).
% 35.86/23.76 tff(7036,plain,
% 35.86/23.76 ($false),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7035, 3291, 7032, 7031, 3108])).
% 35.86/23.76 tff(7037,plain,(m_counter_cell_v_carry_in(c_bit1, s60) | (~node2(c_bit1, s60))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.76 tff(7038,plain,
% 35.86/23.76 (~node2(c_bit1, s60)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7037, 3107])).
% 35.86/23.76 tff(7039,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s60, s61)) | node3(c_bit1, s60, s61))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s60, s61)) | node3(c_bit1, s60, s61))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7040,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s60, s61)) | node3(c_bit1, s60, s61))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7041,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s60, s61)) | node3(c_bit1, s60, s61)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7040, 7039])).
% 35.86/23.76 tff(7042,plain,
% 35.86/23.76 (node3(c_bit1, s60, s61)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7041, 81, 1888])).
% 35.86/23.76 tff(7043,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7044,plain,
% 35.86/23.76 ((node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)) | (~m_counter_cell_v_value(c_bit1, s61))) <=> ((~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7045,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)) | (~m_counter_cell_v_value(c_bit1, s61)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61))))),
% 35.86/23.76 inference(monotonicity,[status(thm)],[7044])).
% 35.86/23.76 tff(7046,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)) | (~m_counter_cell_v_value(c_bit1, s61)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)))),
% 35.86/23.76 inference(transitivity,[status(thm)],[7045, 7043])).
% 35.86/23.76 tff(7047,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s60) | (~node3(c_bit1, s60, s61)) | (~m_counter_cell_v_value(c_bit1, s61)))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7048,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60) | (~node3(c_bit1, s60, s61))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7047, 7046])).
% 35.86/23.76 tff(7049,plain,
% 35.86/23.76 ((~m_counter_cell_v_value(c_bit1, s61)) | node2(c_bit1, s60)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7048, 234, 7042])).
% 35.86/23.76 tff(7050,plain,
% 35.86/23.76 (~m_counter_cell_v_value(c_bit1, s61)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7049, 7038])).
% 35.86/23.76 tff(7051,plain,
% 35.86/23.76 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7052,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7053,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s61)) | (~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7052, 7051])).
% 35.86/23.76 tff(7054,plain,
% 35.86/23.76 ((~m_counter_cell_v_value(c_bit0, s61)) | m_counter_cell_v_carry_out(c_bit0, s61)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7053, 3031, 1904])).
% 35.86/23.76 tff(7055,plain,
% 35.86/23.76 (m_counter_cell_v_carry_out(c_bit0, s61)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7054, 1900])).
% 35.86/23.76 tff(7056,plain,
% 35.86/23.76 (((~![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, s61)) | m_counter_cell_v_carry_in(c_bit1, s61))) <=> ((~![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, s61)) | m_counter_cell_v_carry_in(c_bit1, s61))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7057,plain,
% 35.86/23.76 ((~![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, s61)) | m_counter_cell_v_carry_in(c_bit1, s61))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7058,plain,
% 35.86/23.76 ((~![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, s61)) | m_counter_cell_v_carry_in(c_bit1, s61)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7057, 7056])).
% 35.86/23.76 tff(7059,plain,
% 35.86/23.76 (m_counter_cell_v_carry_in(c_bit1, s61)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7058, 3046, 7055])).
% 35.86/23.76 tff(7060,plain,
% 35.86/23.76 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7061,plain,
% 35.86/23.76 (((~node1(c_bit1, s61)) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7062,plain,
% 35.86/23.76 (((~![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, s61)) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61))))),
% 35.86/23.76 inference(monotonicity,[status(thm)],[7061])).
% 35.86/23.76 tff(7063,plain,
% 35.86/23.76 (((~![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, s61)) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61)))),
% 35.86/23.76 inference(transitivity,[status(thm)],[7062, 7060])).
% 35.86/23.76 tff(7064,plain,
% 35.86/23.76 ((~![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, s61)) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7065,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s61)) | m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7064, 7063])).
% 35.86/23.76 tff(7066,plain,
% 35.86/23.76 (m_counter_cell_v_value(c_bit1, s61) | (~node1(c_bit1, s61))),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7065, 170, 7059])).
% 35.86/23.76 tff(7067,plain,
% 35.86/23.76 (~node1(c_bit1, s61)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7066, 7050])).
% 35.86/23.76 tff(7068,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s61, s62)) | node3(c_bit1, s61, s62))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s61, s62)) | node3(c_bit1, s61, s62))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7069,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s61, s62)) | node3(c_bit1, s61, s62))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7070,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s61, s62)) | node3(c_bit1, s61, s62)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7069, 7068])).
% 35.86/23.76 tff(7071,plain,
% 35.86/23.76 (node3(c_bit1, s61, s62)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7070, 81, 1916])).
% 35.86/23.76 tff(7072,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7073,plain,
% 35.86/23.76 ((node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)) | m_counter_cell_v_value(c_bit1, s62)) <=> (m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7074,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)) | m_counter_cell_v_value(c_bit1, s62))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62))))),
% 35.86/23.76 inference(monotonicity,[status(thm)],[7073])).
% 35.86/23.76 tff(7075,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)) | m_counter_cell_v_value(c_bit1, s62))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)))),
% 35.86/23.76 inference(transitivity,[status(thm)],[7074, 7072])).
% 35.86/23.76 tff(7076,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s61) | (~node3(c_bit1, s61, s62)) | m_counter_cell_v_value(c_bit1, s62))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7077,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61) | (~node3(c_bit1, s61, s62))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7076, 7075])).
% 35.86/23.76 tff(7078,plain,
% 35.86/23.76 (m_counter_cell_v_value(c_bit1, s62) | node1(c_bit1, s61)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7077, 199, 7071])).
% 35.86/23.76 tff(7079,plain,
% 35.86/23.76 (m_counter_cell_v_value(c_bit1, s62)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7078, 7067])).
% 35.86/23.76 tff(7080,assumption,(m_counter_cell_v_value(c_bit1, s62)), introduced(assumption)).
% 35.86/23.76 tff(7081,assumption,(node1(c_bit1, s62)), introduced(assumption)).
% 35.86/23.76 tff(7082,plain,
% 35.86/23.76 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7083,plain,
% 35.86/23.76 (((~node1(c_bit1, s62)) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62))) <=> (m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62)))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7084,plain,
% 35.86/23.76 (((~![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, s62)) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62))))),
% 35.86/23.76 inference(monotonicity,[status(thm)],[7083])).
% 35.86/23.76 tff(7085,plain,
% 35.86/23.76 (((~![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, s62)) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62)))),
% 35.86/23.76 inference(transitivity,[status(thm)],[7084, 7082])).
% 35.86/23.76 tff(7086,plain,
% 35.86/23.76 ((~![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, s62)) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7087,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62)) | (~node1(c_bit1, s62))),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7086, 7085])).
% 35.86/23.76 tff(7088,plain,
% 35.86/23.76 (m_counter_cell_v_carry_in(c_bit1, s62) | (~m_counter_cell_v_value(c_bit1, s62))),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7087, 3359, 7081])).
% 35.86/23.76 tff(7089,plain,
% 35.86/23.76 (m_counter_cell_v_carry_in(c_bit1, s62)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7088, 7080])).
% 35.86/23.76 tff(7090,assumption,(~m_counter_cell_v_carry_out(c_bit1, s62)), introduced(assumption)).
% 35.86/23.76 tff(7091,plain,
% 35.86/23.76 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s62)) | (~m_counter_cell_v_value(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit1, s62))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s62)) | (~m_counter_cell_v_value(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit1, s62))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7092,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s62)) | (~m_counter_cell_v_value(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit1, s62))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7093,plain,
% 35.86/23.76 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s62)) | (~m_counter_cell_v_value(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit1, s62)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7092, 7091])).
% 35.86/23.76 tff(7094,plain,
% 35.86/23.76 ((~m_counter_cell_v_carry_in(c_bit1, s62)) | (~m_counter_cell_v_value(c_bit1, s62))),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7093, 3031, 7090])).
% 35.86/23.76 tff(7095,plain,
% 35.86/23.76 ($false),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7094, 7089, 7080])).
% 35.86/23.76 tff(7096,plain,((~m_counter_cell_v_value(c_bit1, s62)) | m_counter_cell_v_carry_out(c_bit1, s62) | (~node1(c_bit1, s62))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.76 tff(7097,plain,
% 35.86/23.76 (m_counter_cell_v_carry_out(c_bit1, s62) | (~node1(c_bit1, s62))),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7096, 7079])).
% 35.86/23.76 tff(7098,plain,
% 35.86/23.76 (~node1(c_bit1, s62)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7097, 3089])).
% 35.86/23.76 tff(7099,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s62, s63)) | node3(c_bit1, s62, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s62, s63)) | node3(c_bit1, s62, s63))),
% 35.86/23.76 inference(rewrite,[status(thm)],[])).
% 35.86/23.76 tff(7100,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s62, s63)) | node3(c_bit1, s62, s63))),
% 35.86/23.76 inference(quant_inst,[status(thm)],[])).
% 35.86/23.76 tff(7101,plain,
% 35.86/23.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s62, s63)) | node3(c_bit1, s62, s63)),
% 35.86/23.76 inference(modus_ponens,[status(thm)],[7100, 7099])).
% 35.86/23.76 tff(7102,plain,
% 35.86/23.76 (node3(c_bit1, s62, s63)),
% 35.86/23.76 inference(unit_resolution,[status(thm)],[7101, 81, 1947])).
% 35.86/23.76 tff(7103,plain,
% 35.86/23.76 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7104,plain,
% 35.86/23.77 ((node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)) | m_counter_cell_v_value(c_bit1, s63)) <=> (m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7105,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)) | m_counter_cell_v_value(c_bit1, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63))))),
% 35.86/23.77 inference(monotonicity,[status(thm)],[7104])).
% 35.86/23.77 tff(7106,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)) | m_counter_cell_v_value(c_bit1, s63))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)))),
% 35.86/23.77 inference(transitivity,[status(thm)],[7105, 7103])).
% 35.86/23.77 tff(7107,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s62) | (~node3(c_bit1, s62, s63)) | m_counter_cell_v_value(c_bit1, s63))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7108,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62) | (~node3(c_bit1, s62, s63))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7107, 7106])).
% 35.86/23.77 tff(7109,plain,
% 35.86/23.77 (m_counter_cell_v_value(c_bit1, s63) | node1(c_bit1, s62)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7108, 199, 7102])).
% 35.86/23.77 tff(7110,plain,
% 35.86/23.77 (m_counter_cell_v_value(c_bit1, s63)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7109, 7098])).
% 35.86/23.77 tff(7111,plain,
% 35.86/23.77 (((~![I0: $i, X: $i] : ((~m_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, s63)) | (~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s63)) | (~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7112,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : ((~m_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, s63)) | (~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63)))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7113,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s63)) | (~m_counter_cell_v_value(c_bit1, s63)) | (~node2(c_bit1, s63))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7112, 7111])).
% 35.86/23.77 tff(7114,plain,
% 35.86/23.77 ($false),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7113, 219, 7110, 3050, 3021])).
% 35.86/23.77 tff(7115,plain,(~node2(c_bit1, s63)), inference(lemma,lemma(discharge,[]))).
% 35.86/23.77 tff(7116,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s63, s64)) | node3(c_bit1, s63, s64))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s63, s64)) | node3(c_bit1, s63, s64))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7117,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s63, s64)) | node3(c_bit1, s63, s64))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7118,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s63, s64)) | node3(c_bit1, s63, s64)),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7117, 7116])).
% 35.86/23.77 tff(7119,plain,
% 35.86/23.77 (node3(c_bit1, s63, s64)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7118, 81, 1975])).
% 35.86/23.77 tff(7120,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7121,plain,
% 35.86/23.77 ((node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)) | (~m_counter_cell_v_value(c_bit1, s64))) <=> ((~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7122,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)) | (~m_counter_cell_v_value(c_bit1, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64))))),
% 35.86/23.77 inference(monotonicity,[status(thm)],[7121])).
% 35.86/23.77 tff(7123,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)) | (~m_counter_cell_v_value(c_bit1, s64)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)))),
% 35.86/23.77 inference(transitivity,[status(thm)],[7122, 7120])).
% 35.86/23.77 tff(7124,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s63) | (~node3(c_bit1, s63, s64)) | (~m_counter_cell_v_value(c_bit1, s64)))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7125,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63) | (~node3(c_bit1, s63, s64))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7124, 7123])).
% 35.86/23.77 tff(7126,plain,
% 35.86/23.77 ((~m_counter_cell_v_value(c_bit1, s64)) | node2(c_bit1, s63)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7125, 234, 7119])).
% 35.86/23.77 tff(7127,plain,
% 35.86/23.77 (~m_counter_cell_v_value(c_bit1, s64)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7126, 7115])).
% 35.86/23.77 tff(7128,plain,
% 35.86/23.77 (((~![I0: $i, X: $i] : (m_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, s64) | m_counter_cell_v_value(c_bit1, s64) | (~node2(c_bit1, s64)))) <=> ((~![I0: $i, X: $i] : (m_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, s64) | m_counter_cell_v_value(c_bit1, s64) | (~node2(c_bit1, s64)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7129,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : (m_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, s64) | m_counter_cell_v_value(c_bit1, s64) | (~node2(c_bit1, s64)))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7130,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : (m_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, s64) | m_counter_cell_v_value(c_bit1, s64) | (~node2(c_bit1, s64))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7129, 7128])).
% 35.86/23.77 tff(7131,plain,
% 35.86/23.77 (m_counter_cell_v_carry_in(c_bit1, s64) | (~node2(c_bit1, s64))),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7130, 3291, 7127])).
% 35.86/23.77 tff(7132,plain,
% 35.86/23.77 (~node2(c_bit1, s64)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7131, 3020])).
% 35.86/23.77 tff(7133,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s64, s65)) | node3(c_bit1, s64, s65))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s64, s65)) | node3(c_bit1, s64, s65))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7134,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s64, s65)) | node3(c_bit1, s64, s65))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7135,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s64, s65)) | node3(c_bit1, s64, s65)),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7134, 7133])).
% 35.86/23.77 tff(7136,plain,
% 35.86/23.77 (node3(c_bit1, s64, s65)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7135, 81, 2006])).
% 35.86/23.77 tff(7137,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7138,plain,
% 35.86/23.77 ((node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)) | (~m_counter_cell_v_value(c_bit1, s65))) <=> ((~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7139,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)) | (~m_counter_cell_v_value(c_bit1, s65)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65))))),
% 35.86/23.77 inference(monotonicity,[status(thm)],[7138])).
% 35.86/23.77 tff(7140,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)) | (~m_counter_cell_v_value(c_bit1, s65)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)))),
% 35.86/23.77 inference(transitivity,[status(thm)],[7139, 7137])).
% 35.86/23.77 tff(7141,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s64) | (~node3(c_bit1, s64, s65)) | (~m_counter_cell_v_value(c_bit1, s65)))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7142,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64) | (~node3(c_bit1, s64, s65))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7141, 7140])).
% 35.86/23.77 tff(7143,plain,
% 35.86/23.77 ((~m_counter_cell_v_value(c_bit1, s65)) | node2(c_bit1, s64)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7142, 234, 7136])).
% 35.86/23.77 tff(7144,plain,
% 35.86/23.77 (~m_counter_cell_v_value(c_bit1, s65)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7143, 7132])).
% 35.86/23.77 tff(7145,plain,
% 35.86/23.77 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7146,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7147,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s65)) | (~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65)),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7146, 7145])).
% 35.86/23.77 tff(7148,plain,
% 35.86/23.77 ((~m_counter_cell_v_value(c_bit0, s65)) | m_counter_cell_v_carry_out(c_bit0, s65)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7147, 3031, 2022])).
% 35.86/23.77 tff(7149,plain,
% 35.86/23.77 (m_counter_cell_v_carry_out(c_bit0, s65)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7148, 2018])).
% 35.86/23.77 tff(7150,plain,
% 35.86/23.77 (((~![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, s65)) | m_counter_cell_v_carry_in(c_bit1, s65))) <=> ((~![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, s65)) | m_counter_cell_v_carry_in(c_bit1, s65))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7151,plain,
% 35.86/23.77 ((~![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, s65)) | m_counter_cell_v_carry_in(c_bit1, s65))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7152,plain,
% 35.86/23.77 ((~![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, s65)) | m_counter_cell_v_carry_in(c_bit1, s65)),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7151, 7150])).
% 35.86/23.77 tff(7153,plain,
% 35.86/23.77 (m_counter_cell_v_carry_in(c_bit1, s65)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7152, 3046, 7149])).
% 35.86/23.77 tff(7154,assumption,(~m_counter_cell_v_value(c_bit1, s65)), introduced(assumption)).
% 35.86/23.77 tff(7155,assumption,(m_counter_cell_v_carry_in(c_bit1, s65)), introduced(assumption)).
% 35.86/23.77 tff(7156,assumption,(node1(c_bit1, s65)), introduced(assumption)).
% 35.86/23.77 tff(7157,plain,
% 35.86/23.77 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7158,plain,
% 35.86/23.77 (((~node1(c_bit1, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7159,plain,
% 35.86/23.77 (((~![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, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65))))),
% 35.86/23.77 inference(monotonicity,[status(thm)],[7158])).
% 35.86/23.77 tff(7160,plain,
% 35.86/23.77 (((~![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, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)))),
% 35.86/23.77 inference(transitivity,[status(thm)],[7159, 7157])).
% 35.86/23.77 tff(7161,plain,
% 35.86/23.77 ((~![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, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7162,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s65)) | m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7161, 7160])).
% 35.86/23.77 tff(7163,plain,
% 35.86/23.77 ($false),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7162, 170, 7156, 7155, 7154])).
% 35.86/23.77 tff(7164,plain,(m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65)) | (~m_counter_cell_v_carry_in(c_bit1, s65))), inference(lemma,lemma(discharge,[]))).
% 35.86/23.77 tff(7165,plain,
% 35.86/23.77 (m_counter_cell_v_value(c_bit1, s65) | (~node1(c_bit1, s65))),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7164, 7153])).
% 35.86/23.77 tff(7166,plain,
% 35.86/23.77 (~node1(c_bit1, s65)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7165, 7144])).
% 35.86/23.77 tff(7167,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s65, s66)) | node3(c_bit1, s65, s66))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s65, s66)) | node3(c_bit1, s65, s66))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7168,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s65, s66)) | node3(c_bit1, s65, s66))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7169,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s65, s66)) | node3(c_bit1, s65, s66)),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7168, 7167])).
% 35.86/23.77 tff(7170,plain,
% 35.86/23.77 (node3(c_bit1, s65, s66)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7169, 81, 2034])).
% 35.86/23.77 tff(7171,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7172,plain,
% 35.86/23.77 ((node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)) | m_counter_cell_v_value(c_bit1, s66)) <=> (m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7173,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)) | m_counter_cell_v_value(c_bit1, s66))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66))))),
% 35.86/23.77 inference(monotonicity,[status(thm)],[7172])).
% 35.86/23.77 tff(7174,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)) | m_counter_cell_v_value(c_bit1, s66))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)))),
% 35.86/23.77 inference(transitivity,[status(thm)],[7173, 7171])).
% 35.86/23.77 tff(7175,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s65) | (~node3(c_bit1, s65, s66)) | m_counter_cell_v_value(c_bit1, s66))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7176,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65) | (~node3(c_bit1, s65, s66))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7175, 7174])).
% 35.86/23.77 tff(7177,plain,
% 35.86/23.77 (m_counter_cell_v_value(c_bit1, s66) | node1(c_bit1, s65)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7176, 199, 7170])).
% 35.86/23.77 tff(7178,plain,
% 35.86/23.77 (m_counter_cell_v_value(c_bit1, s66)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7177, 7166])).
% 35.86/23.77 tff(7179,plain,
% 35.86/23.77 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7180,plain,
% 35.86/23.77 (((~node1(c_bit1, s66)) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66))) <=> (m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7181,plain,
% 35.86/23.77 (((~![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, s66)) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66))))),
% 35.86/23.77 inference(monotonicity,[status(thm)],[7180])).
% 35.86/23.77 tff(7182,plain,
% 35.86/23.77 (((~![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, s66)) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66)))),
% 35.86/23.77 inference(transitivity,[status(thm)],[7181, 7179])).
% 35.86/23.77 tff(7183,plain,
% 35.86/23.77 ((~![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, s66)) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7184,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s66) | (~m_counter_cell_v_value(c_bit1, s66)) | (~node1(c_bit1, s66))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7183, 7182])).
% 35.86/23.77 tff(7185,plain,
% 35.86/23.77 (m_counter_cell_v_carry_in(c_bit1, s66) | (~node1(c_bit1, s66))),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7184, 3359, 7178])).
% 35.86/23.77 tff(7186,plain,
% 35.86/23.77 (~node1(c_bit1, s66)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7185, 3002])).
% 35.86/23.77 tff(7187,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s66, s67)) | node3(c_bit1, s66, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s66, s67)) | node3(c_bit1, s66, s67))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7188,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s66, s67)) | node3(c_bit1, s66, s67))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7189,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s66, s67)) | node3(c_bit1, s66, s67)),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7188, 7187])).
% 35.86/23.77 tff(7190,plain,
% 35.86/23.77 (node3(c_bit1, s66, s67)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7189, 81, 2065])).
% 35.86/23.77 tff(7191,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7192,plain,
% 35.86/23.77 ((node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)) | m_counter_cell_v_value(c_bit1, s67)) <=> (m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7193,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)) | m_counter_cell_v_value(c_bit1, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67))))),
% 35.86/23.77 inference(monotonicity,[status(thm)],[7192])).
% 35.86/23.77 tff(7194,plain,
% 35.86/23.77 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)) | m_counter_cell_v_value(c_bit1, s67))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)))),
% 35.86/23.77 inference(transitivity,[status(thm)],[7193, 7191])).
% 35.86/23.77 tff(7195,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s66) | (~node3(c_bit1, s66, s67)) | m_counter_cell_v_value(c_bit1, s67))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7196,plain,
% 35.86/23.77 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66) | (~node3(c_bit1, s66, s67))),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7195, 7194])).
% 35.86/23.77 tff(7197,plain,
% 35.86/23.77 (m_counter_cell_v_value(c_bit1, s67) | node1(c_bit1, s66)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7196, 199, 7190])).
% 35.86/23.77 tff(7198,plain,
% 35.86/23.77 (m_counter_cell_v_value(c_bit1, s67)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7197, 7186])).
% 35.86/23.77 tff(7199,assumption,(m_counter_cell_v_value(c_bit1, s67)), introduced(assumption)).
% 35.86/23.77 tff(7200,plain,
% 35.86/23.77 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7201,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7202,plain,
% 35.86/23.77 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s67)) | (~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67)),
% 35.86/23.77 inference(modus_ponens,[status(thm)],[7201, 7200])).
% 35.86/23.77 tff(7203,plain,
% 35.86/23.77 ((~m_counter_cell_v_value(c_bit0, s67)) | m_counter_cell_v_carry_out(c_bit0, s67)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7202, 3031, 2081])).
% 35.86/23.77 tff(7204,plain,
% 35.86/23.77 (m_counter_cell_v_carry_out(c_bit0, s67)),
% 35.86/23.77 inference(unit_resolution,[status(thm)],[7203, 2077])).
% 35.86/23.77 tff(7205,plain,
% 35.86/23.77 (((~![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, s67)) | m_counter_cell_v_carry_in(c_bit1, s67))) <=> ((~![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, s67)) | m_counter_cell_v_carry_in(c_bit1, s67))),
% 35.86/23.77 inference(rewrite,[status(thm)],[])).
% 35.86/23.77 tff(7206,plain,
% 35.86/23.77 ((~![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, s67)) | m_counter_cell_v_carry_in(c_bit1, s67))),
% 35.86/23.77 inference(quant_inst,[status(thm)],[])).
% 35.86/23.77 tff(7207,plain,
% 35.86/23.77 ((~![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, s67)) | m_counter_cell_v_carry_in(c_bit1, s67)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7206, 7205])).
% 35.97/23.78 tff(7208,plain,
% 35.97/23.78 (m_counter_cell_v_carry_in(c_bit1, s67)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7207, 3046, 7204])).
% 35.97/23.78 tff(7209,assumption,(node2(c_bit1, s67)), introduced(assumption)).
% 35.97/23.78 tff(7210,plain,
% 35.97/23.78 (((~![I0: $i, X: $i] : ((~m_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, s67)) | (~m_counter_cell_v_value(c_bit1, s67)) | (~node2(c_bit1, s67)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s67)) | (~m_counter_cell_v_value(c_bit1, s67)) | (~node2(c_bit1, s67)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7211,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~m_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, s67)) | (~m_counter_cell_v_value(c_bit1, s67)) | (~node2(c_bit1, s67)))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7212,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s67)) | (~m_counter_cell_v_value(c_bit1, s67)) | (~node2(c_bit1, s67))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7211, 7210])).
% 35.97/23.78 tff(7213,plain,
% 35.97/23.78 ($false),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7212, 219, 7209, 7208, 7199])).
% 35.97/23.78 tff(7214,plain,((~node2(c_bit1, s67)) | (~m_counter_cell_v_value(c_bit1, s67))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.78 tff(7215,plain,
% 35.97/23.78 (~node2(c_bit1, s67)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7214, 7198])).
% 35.97/23.78 tff(7216,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s67, s68)) | node3(c_bit1, s67, s68))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s67, s68)) | node3(c_bit1, s67, s68))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7217,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s67, s68)) | node3(c_bit1, s67, s68))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7218,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s67, s68)) | node3(c_bit1, s67, s68)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7217, 7216])).
% 35.97/23.78 tff(7219,plain,
% 35.97/23.78 (node3(c_bit1, s67, s68)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7218, 81, 2093])).
% 35.97/23.78 tff(7220,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7221,plain,
% 35.97/23.78 ((node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)) | (~m_counter_cell_v_value(c_bit1, s68))) <=> ((~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7222,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)) | (~m_counter_cell_v_value(c_bit1, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68))))),
% 35.97/23.78 inference(monotonicity,[status(thm)],[7221])).
% 35.97/23.78 tff(7223,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)) | (~m_counter_cell_v_value(c_bit1, s68)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)))),
% 35.97/23.78 inference(transitivity,[status(thm)],[7222, 7220])).
% 35.97/23.78 tff(7224,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s67) | (~node3(c_bit1, s67, s68)) | (~m_counter_cell_v_value(c_bit1, s68)))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7225,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67) | (~node3(c_bit1, s67, s68))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7224, 7223])).
% 35.97/23.78 tff(7226,plain,
% 35.97/23.78 ((~m_counter_cell_v_value(c_bit1, s68)) | node2(c_bit1, s67)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7225, 234, 7219])).
% 35.97/23.78 tff(7227,plain,
% 35.97/23.78 (~m_counter_cell_v_value(c_bit1, s68)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7226, 7215])).
% 35.97/23.78 tff(7228,plain,
% 35.97/23.78 (((~![I0: $i, X: $i] : (m_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, s68) | m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68)))) <=> ((~![I0: $i, X: $i] : (m_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, s68) | m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7229,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : (m_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, s68) | m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68)))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7230,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s68) | m_counter_cell_v_value(c_bit1, s68) | (~node2(c_bit1, s68))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7229, 7228])).
% 35.97/23.78 tff(7231,plain,
% 35.97/23.78 ($false),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7230, 3291, 7227, 2984, 2983])).
% 35.97/23.78 tff(7232,plain,(~node2(c_bit1, s68)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.78 tff(7233,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s68, s69)) | node3(c_bit1, s68, s69))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s68, s69)) | node3(c_bit1, s68, s69))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7234,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s68, s69)) | node3(c_bit1, s68, s69))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7235,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s68, s69)) | node3(c_bit1, s68, s69)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7234, 7233])).
% 35.97/23.78 tff(7236,plain,
% 35.97/23.78 (node3(c_bit1, s68, s69)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7235, 81, 2124])).
% 35.97/23.78 tff(7237,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7238,plain,
% 35.97/23.78 ((node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)) | (~m_counter_cell_v_value(c_bit1, s69))) <=> ((~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7239,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)) | (~m_counter_cell_v_value(c_bit1, s69)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69))))),
% 35.97/23.78 inference(monotonicity,[status(thm)],[7238])).
% 35.97/23.78 tff(7240,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)) | (~m_counter_cell_v_value(c_bit1, s69)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)))),
% 35.97/23.78 inference(transitivity,[status(thm)],[7239, 7237])).
% 35.97/23.78 tff(7241,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s68) | (~node3(c_bit1, s68, s69)) | (~m_counter_cell_v_value(c_bit1, s69)))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7242,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68) | (~node3(c_bit1, s68, s69))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7241, 7240])).
% 35.97/23.78 tff(7243,plain,
% 35.97/23.78 ((~m_counter_cell_v_value(c_bit1, s69)) | node2(c_bit1, s68)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7242, 234, 7236])).
% 35.97/23.78 tff(7244,plain,
% 35.97/23.78 (~m_counter_cell_v_value(c_bit1, s69)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7243, 7232])).
% 35.97/23.78 tff(7245,plain,
% 35.97/23.78 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7246,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7247,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s69)) | (~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7246, 7245])).
% 35.97/23.78 tff(7248,plain,
% 35.97/23.78 ((~m_counter_cell_v_value(c_bit0, s69)) | m_counter_cell_v_carry_out(c_bit0, s69)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7247, 3031, 2140])).
% 35.97/23.78 tff(7249,plain,
% 35.97/23.78 (m_counter_cell_v_carry_out(c_bit0, s69)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7248, 2136])).
% 35.97/23.78 tff(7250,plain,
% 35.97/23.78 (((~![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, s69)) | m_counter_cell_v_carry_in(c_bit1, s69))) <=> ((~![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, s69)) | m_counter_cell_v_carry_in(c_bit1, s69))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7251,plain,
% 35.97/23.78 ((~![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, s69)) | m_counter_cell_v_carry_in(c_bit1, s69))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7252,plain,
% 35.97/23.78 ((~![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, s69)) | m_counter_cell_v_carry_in(c_bit1, s69)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7251, 7250])).
% 35.97/23.78 tff(7253,plain,
% 35.97/23.78 (m_counter_cell_v_carry_in(c_bit1, s69)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7252, 3046, 7249])).
% 35.97/23.78 tff(7254,plain,
% 35.97/23.78 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7255,plain,
% 35.97/23.78 (((~node1(c_bit1, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7256,plain,
% 35.97/23.78 (((~![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, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69))))),
% 35.97/23.78 inference(monotonicity,[status(thm)],[7255])).
% 35.97/23.78 tff(7257,plain,
% 35.97/23.78 (((~![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, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69)))),
% 35.97/23.78 inference(transitivity,[status(thm)],[7256, 7254])).
% 35.97/23.78 tff(7258,plain,
% 35.97/23.78 ((~![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, s69)) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7259,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s69)) | m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7258, 7257])).
% 35.97/23.78 tff(7260,plain,
% 35.97/23.78 (m_counter_cell_v_value(c_bit1, s69) | (~node1(c_bit1, s69))),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7259, 170, 7253])).
% 35.97/23.78 tff(7261,plain,
% 35.97/23.78 (~node1(c_bit1, s69)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7260, 7244])).
% 35.97/23.78 tff(7262,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s69, s70)) | node3(c_bit1, s69, s70))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s69, s70)) | node3(c_bit1, s69, s70))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7263,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s69, s70)) | node3(c_bit1, s69, s70))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7264,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s69, s70)) | node3(c_bit1, s69, s70)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7263, 7262])).
% 35.97/23.78 tff(7265,plain,
% 35.97/23.78 (node3(c_bit1, s69, s70)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7264, 81, 2152])).
% 35.97/23.78 tff(7266,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7267,plain,
% 35.97/23.78 ((node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)) | m_counter_cell_v_value(c_bit1, s70)) <=> (m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7268,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)) | m_counter_cell_v_value(c_bit1, s70))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70))))),
% 35.97/23.78 inference(monotonicity,[status(thm)],[7267])).
% 35.97/23.78 tff(7269,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)) | m_counter_cell_v_value(c_bit1, s70))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)))),
% 35.97/23.78 inference(transitivity,[status(thm)],[7268, 7266])).
% 35.97/23.78 tff(7270,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s69) | (~node3(c_bit1, s69, s70)) | m_counter_cell_v_value(c_bit1, s70))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7271,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69) | (~node3(c_bit1, s69, s70))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7270, 7269])).
% 35.97/23.78 tff(7272,plain,
% 35.97/23.78 (m_counter_cell_v_value(c_bit1, s70) | node1(c_bit1, s69)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7271, 199, 7265])).
% 35.97/23.78 tff(7273,plain,
% 35.97/23.78 (m_counter_cell_v_value(c_bit1, s70)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7272, 7261])).
% 35.97/23.78 tff(7274,plain,
% 35.97/23.78 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7275,plain,
% 35.97/23.78 (((~node1(c_bit1, s70)) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70))) <=> (m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7276,plain,
% 35.97/23.78 (((~![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, s70)) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70))))),
% 35.97/23.78 inference(monotonicity,[status(thm)],[7275])).
% 35.97/23.78 tff(7277,plain,
% 35.97/23.78 (((~![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, s70)) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70)))),
% 35.97/23.78 inference(transitivity,[status(thm)],[7276, 7274])).
% 35.97/23.78 tff(7278,plain,
% 35.97/23.78 ((~![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, s70)) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7279,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s70) | (~m_counter_cell_v_value(c_bit1, s70)) | (~node1(c_bit1, s70))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7278, 7277])).
% 35.97/23.78 tff(7280,plain,
% 35.97/23.78 (m_counter_cell_v_carry_in(c_bit1, s70) | (~node1(c_bit1, s70))),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7279, 3359, 7273])).
% 35.97/23.78 tff(7281,plain,
% 35.97/23.78 (~node1(c_bit1, s70)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7280, 2965])).
% 35.97/23.78 tff(7282,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s70, s71)) | node3(c_bit1, s70, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s70, s71)) | node3(c_bit1, s70, s71))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7283,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s70, s71)) | node3(c_bit1, s70, s71))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7284,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s70, s71)) | node3(c_bit1, s70, s71)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7283, 7282])).
% 35.97/23.78 tff(7285,plain,
% 35.97/23.78 (node3(c_bit1, s70, s71)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7284, 81, 2183])).
% 35.97/23.78 tff(7286,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7287,plain,
% 35.97/23.78 ((node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)) | m_counter_cell_v_value(c_bit1, s71)) <=> (m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7288,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)) | m_counter_cell_v_value(c_bit1, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71))))),
% 35.97/23.78 inference(monotonicity,[status(thm)],[7287])).
% 35.97/23.78 tff(7289,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)) | m_counter_cell_v_value(c_bit1, s71))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)))),
% 35.97/23.78 inference(transitivity,[status(thm)],[7288, 7286])).
% 35.97/23.78 tff(7290,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s70) | (~node3(c_bit1, s70, s71)) | m_counter_cell_v_value(c_bit1, s71))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7291,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70) | (~node3(c_bit1, s70, s71))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7290, 7289])).
% 35.97/23.78 tff(7292,plain,
% 35.97/23.78 (m_counter_cell_v_value(c_bit1, s71) | node1(c_bit1, s70)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7291, 199, 7285])).
% 35.97/23.78 tff(7293,plain,
% 35.97/23.78 (m_counter_cell_v_value(c_bit1, s71)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7292, 7281])).
% 35.97/23.78 tff(7294,plain,
% 35.97/23.78 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7295,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7296,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s71)) | (~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7295, 7294])).
% 35.97/23.78 tff(7297,plain,
% 35.97/23.78 ((~m_counter_cell_v_value(c_bit0, s71)) | m_counter_cell_v_carry_out(c_bit0, s71)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7296, 3031, 2199])).
% 35.97/23.78 tff(7298,plain,
% 35.97/23.78 (m_counter_cell_v_carry_out(c_bit0, s71)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7297, 2195])).
% 35.97/23.78 tff(7299,plain,
% 35.97/23.78 (((~![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, s71)) | m_counter_cell_v_carry_in(c_bit1, s71))) <=> ((~![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, s71)) | m_counter_cell_v_carry_in(c_bit1, s71))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7300,plain,
% 35.97/23.78 ((~![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, s71)) | m_counter_cell_v_carry_in(c_bit1, s71))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7301,plain,
% 35.97/23.78 ((~![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, s71)) | m_counter_cell_v_carry_in(c_bit1, s71)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7300, 7299])).
% 35.97/23.78 tff(7302,plain,
% 35.97/23.78 (m_counter_cell_v_carry_in(c_bit1, s71)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7301, 3046, 7298])).
% 35.97/23.78 tff(7303,assumption,(m_counter_cell_v_carry_in(c_bit1, s71)), introduced(assumption)).
% 35.97/23.78 tff(7304,assumption,(m_counter_cell_v_value(c_bit1, s71)), introduced(assumption)).
% 35.97/23.78 tff(7305,assumption,(node2(c_bit1, s71)), introduced(assumption)).
% 35.97/23.78 tff(7306,plain,
% 35.97/23.78 (((~![I0: $i, X: $i] : ((~m_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, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7307,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~m_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, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71)))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7308,plain,
% 35.97/23.78 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~node2(c_bit1, s71))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7307, 7306])).
% 35.97/23.78 tff(7309,plain,
% 35.97/23.78 ($false),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7308, 219, 7305, 7304, 7303])).
% 35.97/23.78 tff(7310,plain,((~node2(c_bit1, s71)) | (~m_counter_cell_v_value(c_bit1, s71)) | (~m_counter_cell_v_carry_in(c_bit1, s71))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.78 tff(7311,plain,
% 35.97/23.78 ((~node2(c_bit1, s71)) | (~m_counter_cell_v_value(c_bit1, s71))),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7310, 7302])).
% 35.97/23.78 tff(7312,plain,
% 35.97/23.78 (~node2(c_bit1, s71)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7311, 7293])).
% 35.97/23.78 tff(7313,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s71, s72)) | node3(c_bit1, s71, s72))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s71, s72)) | node3(c_bit1, s71, s72))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7314,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s71, s72)) | node3(c_bit1, s71, s72))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7315,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s71, s72)) | node3(c_bit1, s71, s72)),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7314, 7313])).
% 35.97/23.78 tff(7316,plain,
% 35.97/23.78 (node3(c_bit1, s71, s72)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7315, 81, 2211])).
% 35.97/23.78 tff(7317,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7318,plain,
% 35.97/23.78 ((node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)) | (~m_counter_cell_v_value(c_bit1, s72))) <=> ((~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7319,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)) | (~m_counter_cell_v_value(c_bit1, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72))))),
% 35.97/23.78 inference(monotonicity,[status(thm)],[7318])).
% 35.97/23.78 tff(7320,plain,
% 35.97/23.78 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)) | (~m_counter_cell_v_value(c_bit1, s72)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)))),
% 35.97/23.78 inference(transitivity,[status(thm)],[7319, 7317])).
% 35.97/23.78 tff(7321,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s71) | (~node3(c_bit1, s71, s72)) | (~m_counter_cell_v_value(c_bit1, s72)))),
% 35.97/23.78 inference(quant_inst,[status(thm)],[])).
% 35.97/23.78 tff(7322,plain,
% 35.97/23.78 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71) | (~node3(c_bit1, s71, s72))),
% 35.97/23.78 inference(modus_ponens,[status(thm)],[7321, 7320])).
% 35.97/23.78 tff(7323,plain,
% 35.97/23.78 ((~m_counter_cell_v_value(c_bit1, s72)) | node2(c_bit1, s71)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7322, 234, 7316])).
% 35.97/23.78 tff(7324,plain,
% 35.97/23.78 (~m_counter_cell_v_value(c_bit1, s72)),
% 35.97/23.78 inference(unit_resolution,[status(thm)],[7323, 7312])).
% 35.97/23.78 tff(7325,assumption,(node1(c_bit1, s73)), introduced(assumption)).
% 35.97/23.78 tff(7326,assumption,(~m_counter_cell_v_value(c_bit1, s72)), introduced(assumption)).
% 35.97/23.78 tff(7327,assumption,(~m_counter_cell_v_carry_in(c_bit1, s73)), introduced(assumption)).
% 35.97/23.78 tff(7328,plain,
% 35.97/23.78 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node1(c_bit1, s73)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node1(c_bit1, s73)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7329,plain,
% 35.97/23.78 (((~node1(c_bit1, s73)) | m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73))) <=> (m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node1(c_bit1, s73)))),
% 35.97/23.78 inference(rewrite,[status(thm)],[])).
% 35.97/23.78 tff(7330,plain,
% 35.97/23.78 (((~![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, s73)) | m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node1(c_bit1, s73))))),
% 35.97/23.79 inference(monotonicity,[status(thm)],[7329])).
% 35.97/23.79 tff(7331,plain,
% 35.97/23.79 (((~![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, s73)) | m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node1(c_bit1, s73)))),
% 35.97/23.79 inference(transitivity,[status(thm)],[7330, 7328])).
% 35.97/23.79 tff(7332,plain,
% 35.97/23.79 ((~![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, s73)) | m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7333,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node1(c_bit1, s73))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7332, 7331])).
% 35.97/23.79 tff(7334,plain,
% 35.97/23.79 (m_counter_cell_v_carry_in(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73))),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7333, 3359, 7325])).
% 35.97/23.79 tff(7335,plain,
% 35.97/23.79 (~m_counter_cell_v_value(c_bit1, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7334, 7327])).
% 35.97/23.79 tff(7336,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s72, s73)) | node3(c_bit1, s72, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s72, s73)) | node3(c_bit1, s72, s73))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7337,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s72, s73)) | node3(c_bit1, s72, s73))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7338,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s72, s73)) | node3(c_bit1, s72, s73)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7337, 7336])).
% 35.97/23.79 tff(7339,plain,
% 35.97/23.79 (node3(c_bit1, s72, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7338, 81, 2242])).
% 35.97/23.79 tff(7340,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s73) | node1(c_bit1, s72) | (~node3(c_bit1, s72, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s73) | node1(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7341,plain,
% 35.97/23.79 ((node1(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | m_counter_cell_v_value(c_bit1, s73)) <=> (m_counter_cell_v_value(c_bit1, s73) | node1(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7342,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | m_counter_cell_v_value(c_bit1, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s73) | node1(c_bit1, s72) | (~node3(c_bit1, s72, s73))))),
% 35.97/23.79 inference(monotonicity,[status(thm)],[7341])).
% 35.97/23.79 tff(7343,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | m_counter_cell_v_value(c_bit1, s73))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s73) | node1(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 35.97/23.79 inference(transitivity,[status(thm)],[7342, 7340])).
% 35.97/23.79 tff(7344,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | m_counter_cell_v_value(c_bit1, s73))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7345,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s73) | node1(c_bit1, s72) | (~node3(c_bit1, s72, s73))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7344, 7343])).
% 35.97/23.79 tff(7346,plain,
% 35.97/23.79 (m_counter_cell_v_value(c_bit1, s73) | node1(c_bit1, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7345, 199, 7339])).
% 35.97/23.79 tff(7347,plain,
% 35.97/23.79 (node1(c_bit1, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7346, 7335])).
% 35.97/23.79 tff(7348,assumption,(m_counter_cell_v_carry_in(c_bit1, s72)), introduced(assumption)).
% 35.97/23.79 tff(7349,assumption,(node1(c_bit1, s72)), introduced(assumption)).
% 35.97/23.79 tff(7350,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72) | (~node1(c_bit1, s72)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72) | (~node1(c_bit1, s72)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7351,plain,
% 35.97/23.79 (((~node1(c_bit1, s72)) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72) | (~node1(c_bit1, s72)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7352,plain,
% 35.97/23.79 (((~![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, s72)) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72) | (~node1(c_bit1, s72))))),
% 35.97/23.79 inference(monotonicity,[status(thm)],[7351])).
% 35.97/23.79 tff(7353,plain,
% 35.97/23.79 (((~![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, s72)) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72) | (~node1(c_bit1, s72)))),
% 35.97/23.79 inference(transitivity,[status(thm)],[7352, 7350])).
% 35.97/23.79 tff(7354,plain,
% 35.97/23.79 ((~![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, s72)) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7355,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_value(c_bit1, s72) | (~node1(c_bit1, s72))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7354, 7353])).
% 35.97/23.79 tff(7356,plain,
% 35.97/23.79 ($false),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7355, 170, 7349, 7326, 7348])).
% 35.97/23.79 tff(7357,plain,(m_counter_cell_v_value(c_bit1, s72) | (~node1(c_bit1, s72)) | (~m_counter_cell_v_carry_in(c_bit1, s72))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.79 tff(7358,plain,
% 35.97/23.79 (~m_counter_cell_v_carry_in(c_bit1, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7357, 7347, 7326])).
% 35.97/23.79 tff(7359,assumption,(~m_counter_cell_v_carry_in(c_bit1, s72)), introduced(assumption)).
% 35.97/23.79 tff(7360,assumption,(m_counter_cell_v_carry_out(c_bit0, s72)), introduced(assumption)).
% 35.97/23.79 tff(7361,plain,
% 35.97/23.79 (((~![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, s72)) | m_counter_cell_v_carry_in(c_bit1, s72))) <=> ((~![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, s72)) | m_counter_cell_v_carry_in(c_bit1, s72))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7362,plain,
% 35.97/23.79 ((~![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, s72)) | m_counter_cell_v_carry_in(c_bit1, s72))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7363,plain,
% 35.97/23.79 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s72)) | m_counter_cell_v_carry_in(c_bit1, s72)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7362, 7361])).
% 35.97/23.79 tff(7364,plain,
% 35.97/23.79 ($false),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7363, 3046, 7360, 7359])).
% 35.97/23.79 tff(7365,plain,((~m_counter_cell_v_carry_out(c_bit0, s72)) | m_counter_cell_v_carry_in(c_bit1, s72)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.79 tff(7366,plain,
% 35.97/23.79 (~m_counter_cell_v_carry_out(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7365, 7358])).
% 35.97/23.79 tff(7367,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s72)) | (~m_counter_cell_v_value(c_bit0, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s72)) | (~m_counter_cell_v_value(c_bit0, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7368,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s72)) | (~m_counter_cell_v_value(c_bit0, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7369,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s72)) | (~m_counter_cell_v_value(c_bit0, s72)) | m_counter_cell_v_carry_out(c_bit0, s72)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7368, 7367])).
% 35.97/23.79 tff(7370,plain,
% 35.97/23.79 ((~m_counter_cell_v_value(c_bit0, s72)) | m_counter_cell_v_carry_out(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7369, 3031, 2227])).
% 35.97/23.79 tff(7371,plain,
% 35.97/23.79 (~m_counter_cell_v_value(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7370, 7366])).
% 35.97/23.79 tff(7372,plain,
% 35.97/23.79 (~node1(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[2234, 7371])).
% 35.97/23.79 tff(7373,plain,
% 35.97/23.79 (m_counter_cell_v_value(c_bit0, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[2253, 7372])).
% 35.97/23.79 tff(7374,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7375,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7376,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s73)) | (~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7375, 7374])).
% 35.97/23.79 tff(7377,plain,
% 35.97/23.79 ((~m_counter_cell_v_value(c_bit0, s73)) | m_counter_cell_v_carry_out(c_bit0, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7376, 3031, 2258])).
% 35.97/23.79 tff(7378,plain,
% 35.97/23.79 (m_counter_cell_v_carry_out(c_bit0, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7377, 7373])).
% 35.97/23.79 tff(7379,plain,
% 35.97/23.79 (((~![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, s73)) | m_counter_cell_v_carry_in(c_bit1, s73))) <=> ((~![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, s73)) | m_counter_cell_v_carry_in(c_bit1, s73))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7380,plain,
% 35.97/23.79 ((~![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, s73)) | m_counter_cell_v_carry_in(c_bit1, s73))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7381,plain,
% 35.97/23.79 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s73)) | m_counter_cell_v_carry_in(c_bit1, s73)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7380, 7379])).
% 35.97/23.79 tff(7382,plain,
% 35.97/23.79 ($false),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7381, 3046, 7378, 7327])).
% 35.97/23.79 tff(7383,plain,(m_counter_cell_v_carry_in(c_bit1, s73) | m_counter_cell_v_value(c_bit1, s72) | (~node1(c_bit1, s73))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.79 tff(7384,plain,
% 35.97/23.79 (m_counter_cell_v_carry_in(c_bit1, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7383, 7325, 7326])).
% 35.97/23.79 tff(7385,assumption,(m_counter_cell_v_carry_in(c_bit1, s73)), introduced(assumption)).
% 35.97/23.79 tff(7386,assumption,(~m_counter_cell_v_value(c_bit1, s73)), introduced(assumption)).
% 35.97/23.79 tff(7387,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7388,plain,
% 35.97/23.79 (((~node1(c_bit1, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7389,plain,
% 35.97/23.79 (((~![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, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73))))),
% 35.97/23.79 inference(monotonicity,[status(thm)],[7388])).
% 35.97/23.79 tff(7390,plain,
% 35.97/23.79 (((~![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, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73)))),
% 35.97/23.79 inference(transitivity,[status(thm)],[7389, 7387])).
% 35.97/23.79 tff(7391,plain,
% 35.97/23.79 ((~![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, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7392,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~node1(c_bit1, s73))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7391, 7390])).
% 35.97/23.79 tff(7393,plain,
% 35.97/23.79 ($false),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7392, 170, 7386, 7385, 7325])).
% 35.97/23.79 tff(7394,plain,((~node1(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s73) | (~m_counter_cell_v_carry_in(c_bit1, s73))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.79 tff(7395,plain,
% 35.97/23.79 (m_counter_cell_v_value(c_bit1, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7394, 7384, 7325])).
% 35.97/23.79 tff(7396,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7397,plain,
% 35.97/23.79 ((node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | (~m_counter_cell_v_value(c_bit1, s73))) <=> ((~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7398,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | (~m_counter_cell_v_value(c_bit1, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73))))),
% 35.97/23.79 inference(monotonicity,[status(thm)],[7397])).
% 35.97/23.79 tff(7399,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | (~m_counter_cell_v_value(c_bit1, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)))),
% 35.97/23.79 inference(transitivity,[status(thm)],[7398, 7396])).
% 35.97/23.79 tff(7400,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s72) | (~node3(c_bit1, s72, s73)) | (~m_counter_cell_v_value(c_bit1, s73)))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7401,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72) | (~node3(c_bit1, s72, s73))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7400, 7399])).
% 35.97/23.79 tff(7402,plain,
% 35.97/23.79 ((~m_counter_cell_v_value(c_bit1, s73)) | node2(c_bit1, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7401, 234, 7339])).
% 35.97/23.79 tff(7403,plain,
% 35.97/23.79 (node2(c_bit1, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7402, 7395])).
% 35.97/23.79 tff(7404,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : (m_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, s72) | m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72)))) <=> ((~![I0: $i, X: $i] : (m_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, s72) | m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7405,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : (m_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, s72) | m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72)))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7406,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : (m_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, s72) | m_counter_cell_v_value(c_bit1, s72) | (~node2(c_bit1, s72))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7405, 7404])).
% 35.97/23.79 tff(7407,plain,
% 35.97/23.79 (m_counter_cell_v_carry_in(c_bit1, s72) | (~node2(c_bit1, s72))),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7406, 3291, 7326])).
% 35.97/23.79 tff(7408,plain,
% 35.97/23.79 (m_counter_cell_v_carry_in(c_bit1, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7407, 7403])).
% 35.97/23.79 tff(7409,assumption,(~m_counter_cell_v_carry_out(c_bit0, s73)), introduced(assumption)).
% 35.97/23.79 tff(7410,plain,
% 35.97/23.79 (((~![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, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))) <=> ((~![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, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7411,plain,
% 35.97/23.79 ((~![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, s73)) | m_counter_cell_v_carry_out(c_bit0, s73))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7412,plain,
% 35.97/23.79 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | m_counter_cell_v_carry_out(c_bit0, s73)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7411, 7410])).
% 35.97/23.79 tff(7413,plain,
% 35.97/23.79 ($false),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7412, 2901, 7409, 7385])).
% 35.97/23.79 tff(7414,plain,(m_counter_cell_v_carry_out(c_bit0, s73) | (~m_counter_cell_v_carry_in(c_bit1, s73))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.79 tff(7415,plain,
% 35.97/23.79 (m_counter_cell_v_carry_out(c_bit0, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7414, 7384])).
% 35.97/23.79 tff(7416,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s73)) | node4(c_bit0, s73))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s73)) | node4(c_bit0, s73))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7417,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s73)) | node4(c_bit0, s73))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7418,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s73)) | node4(c_bit0, s73)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7417, 7416])).
% 35.97/23.79 tff(7419,plain,
% 35.97/23.79 (node4(c_bit0, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7418, 2887, 7415])).
% 35.97/23.79 tff(7420,assumption,(node4(c_bit0, s73)), introduced(assumption)).
% 35.97/23.79 tff(7421,assumption,(~m_counter_cell_v_value(c_bit0, s73)), introduced(assumption)).
% 35.97/23.79 tff(7422,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s73) | (~node4(c_bit0, s73)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s73) | (~node4(c_bit0, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7423,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s73) | (~node4(c_bit0, s73)))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7424,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s73) | (~node4(c_bit0, s73))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7423, 7422])).
% 35.97/23.79 tff(7425,plain,
% 35.97/23.79 ($false),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7424, 2875, 7421, 7420])).
% 35.97/23.79 tff(7426,plain,(m_counter_cell_v_value(c_bit0, s73) | (~node4(c_bit0, s73))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.79 tff(7427,plain,
% 35.97/23.79 (m_counter_cell_v_value(c_bit0, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7426, 7419])).
% 35.97/23.79 tff(7428,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s73)) | node2(c_bit0, s72) | (~node3(c_bit0, s72, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s73)) | node2(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7429,plain,
% 35.97/23.79 ((node2(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | (~m_counter_cell_v_value(c_bit0, s73))) <=> ((~m_counter_cell_v_value(c_bit0, s73)) | node2(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7430,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | (~m_counter_cell_v_value(c_bit0, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s73)) | node2(c_bit0, s72) | (~node3(c_bit0, s72, s73))))),
% 35.97/23.79 inference(monotonicity,[status(thm)],[7429])).
% 35.97/23.79 tff(7431,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | (~m_counter_cell_v_value(c_bit0, s73)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s73)) | node2(c_bit0, s72) | (~node3(c_bit0, s72, s73)))),
% 35.97/23.79 inference(transitivity,[status(thm)],[7430, 7428])).
% 35.97/23.79 tff(7432,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s72) | (~node3(c_bit0, s72, s73)) | (~m_counter_cell_v_value(c_bit0, s73)))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7433,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s73)) | node2(c_bit0, s72) | (~node3(c_bit0, s72, s73))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7432, 7431])).
% 35.97/23.79 tff(7434,plain,
% 35.97/23.79 ((~m_counter_cell_v_value(c_bit0, s73)) | node2(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7433, 234, 2246])).
% 35.97/23.79 tff(7435,plain,
% 35.97/23.79 (node2(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7434, 7427])).
% 35.97/23.79 tff(7436,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : ((~m_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, s72)) | (~m_counter_cell_v_value(c_bit0, s72)) | (~node2(c_bit0, s72)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s72)) | (~m_counter_cell_v_value(c_bit0, s72)) | (~node2(c_bit0, s72)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7437,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_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, s72)) | (~m_counter_cell_v_value(c_bit0, s72)) | (~node2(c_bit0, s72)))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7438,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_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, s72)) | (~m_counter_cell_v_value(c_bit0, s72)) | (~node2(c_bit0, s72))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7437, 7436])).
% 35.97/23.79 tff(7439,plain,
% 35.97/23.79 ((~m_counter_cell_v_value(c_bit0, s72)) | (~node2(c_bit0, s72))),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7438, 219, 2227])).
% 35.97/23.79 tff(7440,plain,
% 35.97/23.79 (~m_counter_cell_v_value(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7439, 7435])).
% 35.97/23.79 tff(7441,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s72) | (~node4(c_bit0, s72)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s72) | (~node4(c_bit0, s72)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7442,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s72) | (~node4(c_bit0, s72)))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7443,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s72) | (~node4(c_bit0, s72))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7442, 7441])).
% 35.97/23.79 tff(7444,plain,
% 35.97/23.79 (~node4(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7443, 2875, 7440])).
% 35.97/23.79 tff(7445,assumption,(~node4(c_bit0, s72)), introduced(assumption)).
% 35.97/23.79 tff(7446,plain,
% 35.97/23.79 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7447,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7448,plain,
% 35.97/23.79 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7447, 7446])).
% 35.97/23.79 tff(7449,plain,
% 35.97/23.79 ($false),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7448, 2887, 7360, 7445])).
% 35.97/23.79 tff(7450,plain,((~m_counter_cell_v_carry_out(c_bit0, s72)) | node4(c_bit0, s72)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.79 tff(7451,plain,
% 35.97/23.79 (~m_counter_cell_v_carry_out(c_bit0, s72)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7450, 7444])).
% 35.97/23.79 tff(7452,plain,
% 35.97/23.79 (((~![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, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))) <=> ((~![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, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7453,plain,
% 35.97/23.79 ((~![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, s72)) | m_counter_cell_v_carry_out(c_bit0, s72))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7454,plain,
% 35.97/23.79 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s72)) | m_counter_cell_v_carry_out(c_bit0, s72)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7453, 7452])).
% 35.97/23.79 tff(7455,plain,
% 35.97/23.79 ($false),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7454, 2901, 7451, 7408])).
% 35.97/23.79 tff(7456,plain,((~node1(c_bit1, s73)) | m_counter_cell_v_value(c_bit1, s72)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.79 tff(7457,plain,
% 35.97/23.79 (~node1(c_bit1, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7456, 7324])).
% 35.97/23.79 tff(7458,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s73, s74)) | node3(c_bit1, s73, s74))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s73, s74)) | node3(c_bit1, s73, s74))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7459,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s73, s74)) | node3(c_bit1, s73, s74))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7460,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s73, s74)) | node3(c_bit1, s73, s74)),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7459, 7458])).
% 35.97/23.79 tff(7461,plain,
% 35.97/23.79 (node3(c_bit1, s73, s74)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7460, 81, 2270])).
% 35.97/23.79 tff(7462,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7463,plain,
% 35.97/23.79 ((node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | m_counter_cell_v_value(c_bit1, s74)) <=> (m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7464,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | m_counter_cell_v_value(c_bit1, s74))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74))))),
% 35.97/23.79 inference(monotonicity,[status(thm)],[7463])).
% 35.97/23.79 tff(7465,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | m_counter_cell_v_value(c_bit1, s74))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 35.97/23.79 inference(transitivity,[status(thm)],[7464, 7462])).
% 35.97/23.79 tff(7466,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | m_counter_cell_v_value(c_bit1, s74))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7467,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73) | (~node3(c_bit1, s73, s74))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7466, 7465])).
% 35.97/23.79 tff(7468,plain,
% 35.97/23.79 (m_counter_cell_v_value(c_bit1, s74) | node1(c_bit1, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7467, 199, 7461])).
% 35.97/23.79 tff(7469,plain,
% 35.97/23.79 (m_counter_cell_v_value(c_bit1, s74)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7468, 7457])).
% 35.97/23.79 tff(7470,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s74)) | node2(c_bit1, s73) | (~node3(c_bit1, s73, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s74)) | node2(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7471,plain,
% 35.97/23.79 ((node2(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | (~m_counter_cell_v_value(c_bit1, s74))) <=> ((~m_counter_cell_v_value(c_bit1, s74)) | node2(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 35.97/23.79 inference(rewrite,[status(thm)],[])).
% 35.97/23.79 tff(7472,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | (~m_counter_cell_v_value(c_bit1, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s74)) | node2(c_bit1, s73) | (~node3(c_bit1, s73, s74))))),
% 35.97/23.79 inference(monotonicity,[status(thm)],[7471])).
% 35.97/23.79 tff(7473,plain,
% 35.97/23.79 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | (~m_counter_cell_v_value(c_bit1, s74)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s74)) | node2(c_bit1, s73) | (~node3(c_bit1, s73, s74)))),
% 35.97/23.79 inference(transitivity,[status(thm)],[7472, 7470])).
% 35.97/23.79 tff(7474,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s73) | (~node3(c_bit1, s73, s74)) | (~m_counter_cell_v_value(c_bit1, s74)))),
% 35.97/23.79 inference(quant_inst,[status(thm)],[])).
% 35.97/23.79 tff(7475,plain,
% 35.97/23.79 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s74)) | node2(c_bit1, s73) | (~node3(c_bit1, s73, s74))),
% 35.97/23.79 inference(modus_ponens,[status(thm)],[7474, 7473])).
% 35.97/23.79 tff(7476,plain,
% 35.97/23.79 ((~m_counter_cell_v_value(c_bit1, s74)) | node2(c_bit1, s73)),
% 35.97/23.79 inference(unit_resolution,[status(thm)],[7475, 234, 7461])).
% 35.97/23.79 tff(7477,plain,
% 35.97/23.80 (node2(c_bit1, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7476, 7469])).
% 35.97/23.80 tff(7478,plain,
% 35.97/23.80 (m_counter_cell_v_carry_out(c_bit0, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7377, 2254])).
% 35.97/23.80 tff(7479,plain,
% 35.97/23.80 (m_counter_cell_v_carry_in(c_bit1, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7381, 3046, 7478])).
% 35.97/23.80 tff(7480,assumption,(m_counter_cell_v_value(c_bit1, s73)), introduced(assumption)).
% 35.97/23.80 tff(7481,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~m_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, s73)) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node2(c_bit1, s73)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s73)) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node2(c_bit1, s73)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7482,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_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, s73)) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node2(c_bit1, s73)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7483,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | (~m_counter_cell_v_value(c_bit1, s73)) | (~node2(c_bit1, s73))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7482, 7481])).
% 35.97/23.80 tff(7484,plain,
% 35.97/23.80 ($false),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7483, 219, 7480, 7479, 7477])).
% 35.97/23.80 tff(7485,plain,(~m_counter_cell_v_value(c_bit1, s73)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.80 tff(7486,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s73) | (~node4(c_bit1, s73)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s73) | (~node4(c_bit1, s73)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7487,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s73) | (~node4(c_bit1, s73)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7488,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s73) | (~node4(c_bit1, s73))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7487, 7486])).
% 35.97/23.80 tff(7489,plain,
% 35.97/23.80 (~node4(c_bit1, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7488, 2875, 7485])).
% 35.97/23.80 tff(7490,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s73)) | node4(c_bit1, s73))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s73)) | node4(c_bit1, s73))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7491,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s73)) | node4(c_bit1, s73))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7492,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s73)) | node4(c_bit1, s73)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7491, 7490])).
% 35.97/23.80 tff(7493,plain,
% 35.97/23.80 (~m_counter_cell_v_carry_out(c_bit1, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7492, 2887, 7489])).
% 35.97/23.80 tff(7494,assumption,(m_counter_cell_v_value(c_bit0, s73)), introduced(assumption)).
% 35.97/23.80 tff(7495,plain,
% 35.97/23.80 (~node2(c_bit0, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[2262, 7494])).
% 35.97/23.80 tff(7496,plain,
% 35.97/23.80 (~m_counter_cell_v_value(c_bit0, s74)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[2281, 7495])).
% 35.97/23.80 tff(7497,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s74) | (~node4(c_bit0, s74)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s74) | (~node4(c_bit0, s74)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7498,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s74) | (~node4(c_bit0, s74)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7499,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s74) | (~node4(c_bit0, s74))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7498, 7497])).
% 35.97/23.80 tff(7500,plain,
% 35.97/23.80 (~node4(c_bit0, s74)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7499, 2875, 7496])).
% 35.97/23.80 tff(7501,plain,
% 35.97/23.80 (m_counter_cell_v_carry_out(c_bit0, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7377, 7494])).
% 35.97/23.80 tff(7502,plain,
% 35.97/23.80 (m_counter_cell_v_carry_in(c_bit1, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7381, 3046, 7501])).
% 35.97/23.80 tff(7503,assumption,(~m_counter_cell_v_carry_out(c_bit1, s73)), introduced(assumption)).
% 35.97/23.80 tff(7504,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s73)) | (~m_counter_cell_v_value(c_bit1, s73)) | m_counter_cell_v_carry_out(c_bit1, s73))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s73)) | (~m_counter_cell_v_value(c_bit1, s73)) | m_counter_cell_v_carry_out(c_bit1, s73))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7505,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s73)) | (~m_counter_cell_v_value(c_bit1, s73)) | m_counter_cell_v_carry_out(c_bit1, s73))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7506,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s73)) | (~m_counter_cell_v_value(c_bit1, s73)) | m_counter_cell_v_carry_out(c_bit1, s73)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7505, 7504])).
% 35.97/23.80 tff(7507,plain,
% 35.97/23.80 ($false),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7506, 3031, 7480, 7385, 7503])).
% 35.97/23.80 tff(7508,plain,(m_counter_cell_v_carry_out(c_bit1, s73) | (~m_counter_cell_v_value(c_bit1, s73)) | (~m_counter_cell_v_carry_in(c_bit1, s73))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.80 tff(7509,plain,
% 35.97/23.80 (~m_counter_cell_v_value(c_bit1, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7508, 7502, 7503])).
% 35.97/23.80 tff(7510,plain,
% 35.97/23.80 (~node1(c_bit1, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7394, 7509, 7502])).
% 35.97/23.80 tff(7511,plain,
% 35.97/23.80 (m_counter_cell_v_value(c_bit1, s74)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7468, 7510])).
% 35.97/23.80 tff(7512,assumption,(node1(c_bit1, s74)), introduced(assumption)).
% 35.97/23.80 tff(7513,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7514,plain,
% 35.97/23.80 (((~node1(c_bit1, s74)) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74))) <=> (m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7515,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s74)) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74))))),
% 35.97/23.80 inference(monotonicity,[status(thm)],[7514])).
% 35.97/23.80 tff(7516,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s74)) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74)))),
% 35.97/23.80 inference(transitivity,[status(thm)],[7515, 7513])).
% 35.97/23.80 tff(7517,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s74)) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7518,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74)) | (~node1(c_bit1, s74))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7517, 7516])).
% 35.97/23.80 tff(7519,plain,
% 35.97/23.80 (m_counter_cell_v_carry_in(c_bit1, s74) | (~m_counter_cell_v_value(c_bit1, s74))),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7518, 3359, 7512])).
% 35.97/23.80 tff(7520,plain,
% 35.97/23.80 (m_counter_cell_v_carry_in(c_bit1, s74)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7519, 7511])).
% 35.97/23.80 tff(7521,plain,
% 35.97/23.80 (((~![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, s74)) | m_counter_cell_v_carry_out(c_bit0, s74))) <=> ((~![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, s74)) | m_counter_cell_v_carry_out(c_bit0, s74))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7522,plain,
% 35.97/23.80 ((~![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, s74)) | m_counter_cell_v_carry_out(c_bit0, s74))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7523,plain,
% 35.97/23.80 ((~![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, s74)) | m_counter_cell_v_carry_out(c_bit0, s74)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7522, 7521])).
% 35.97/23.80 tff(7524,plain,
% 35.97/23.80 (m_counter_cell_v_carry_out(c_bit0, s74)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7523, 2901, 7520])).
% 35.97/23.80 tff(7525,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s74)) | node4(c_bit0, s74))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s74)) | node4(c_bit0, s74))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7526,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s74)) | node4(c_bit0, s74))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7527,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s74)) | node4(c_bit0, s74)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7526, 7525])).
% 35.97/23.80 tff(7528,plain,
% 35.97/23.80 ($false),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7527, 2887, 7524, 7500])).
% 35.97/23.80 tff(7529,plain,((~m_counter_cell_v_value(c_bit0, s73)) | (~node1(c_bit1, s74)) | m_counter_cell_v_carry_out(c_bit1, s73)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.80 tff(7530,plain,
% 35.97/23.80 ((~node1(c_bit1, s74)) | m_counter_cell_v_carry_out(c_bit1, s73)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7529, 2254])).
% 35.97/23.80 tff(7531,plain,
% 35.97/23.80 (~node1(c_bit1, s74)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7530, 7493])).
% 35.97/23.80 tff(7532,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s74, s75)) | node3(c_bit1, s74, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s74, s75)) | node3(c_bit1, s74, s75))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7533,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s74, s75)) | node3(c_bit1, s74, s75))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7534,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s74, s75)) | node3(c_bit1, s74, s75)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7533, 7532])).
% 35.97/23.80 tff(7535,plain,
% 35.97/23.80 (node3(c_bit1, s74, s75)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7534, 81, 2301])).
% 35.97/23.80 tff(7536,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7537,plain,
% 35.97/23.80 ((node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)) | m_counter_cell_v_value(c_bit1, s75)) <=> (m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7538,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)) | m_counter_cell_v_value(c_bit1, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75))))),
% 35.97/23.80 inference(monotonicity,[status(thm)],[7537])).
% 35.97/23.80 tff(7539,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)) | m_counter_cell_v_value(c_bit1, s75))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)))),
% 35.97/23.80 inference(transitivity,[status(thm)],[7538, 7536])).
% 35.97/23.80 tff(7540,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s74) | (~node3(c_bit1, s74, s75)) | m_counter_cell_v_value(c_bit1, s75))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7541,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74) | (~node3(c_bit1, s74, s75))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7540, 7539])).
% 35.97/23.80 tff(7542,plain,
% 35.97/23.80 (m_counter_cell_v_value(c_bit1, s75) | node1(c_bit1, s74)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7541, 199, 7535])).
% 35.97/23.80 tff(7543,plain,
% 35.97/23.80 (m_counter_cell_v_value(c_bit1, s75)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7542, 7531])).
% 35.97/23.80 tff(7544,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7545,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7546,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s75)) | (~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7545, 7544])).
% 35.97/23.80 tff(7547,plain,
% 35.97/23.80 ((~m_counter_cell_v_value(c_bit0, s75)) | m_counter_cell_v_carry_out(c_bit0, s75)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7546, 3031, 2317])).
% 35.97/23.80 tff(7548,plain,
% 35.97/23.80 (m_counter_cell_v_carry_out(c_bit0, s75)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7547, 2313])).
% 35.97/23.80 tff(7549,assumption,(~m_counter_cell_v_carry_in(c_bit1, s75)), introduced(assumption)).
% 35.97/23.80 tff(7550,assumption,(m_counter_cell_v_carry_out(c_bit0, s75)), introduced(assumption)).
% 35.97/23.80 tff(7551,plain,
% 35.97/23.80 (((~![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, s75)) | m_counter_cell_v_carry_in(c_bit1, s75))) <=> ((~![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, s75)) | m_counter_cell_v_carry_in(c_bit1, s75))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7552,plain,
% 35.97/23.80 ((~![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, s75)) | m_counter_cell_v_carry_in(c_bit1, s75))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7553,plain,
% 35.97/23.80 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s75)) | m_counter_cell_v_carry_in(c_bit1, s75)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7552, 7551])).
% 35.97/23.80 tff(7554,plain,
% 35.97/23.80 ($false),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7553, 3046, 7550, 7549])).
% 35.97/23.80 tff(7555,plain,((~m_counter_cell_v_carry_out(c_bit0, s75)) | m_counter_cell_v_carry_in(c_bit1, s75)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.80 tff(7556,plain,
% 35.97/23.80 (m_counter_cell_v_carry_in(c_bit1, s75)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7555, 7548])).
% 35.97/23.80 tff(7557,assumption,(m_counter_cell_v_carry_in(c_bit1, s75)), introduced(assumption)).
% 35.97/23.80 tff(7558,assumption,(m_counter_cell_v_value(c_bit1, s75)), introduced(assumption)).
% 35.97/23.80 tff(7559,assumption,(node2(c_bit1, s75)), introduced(assumption)).
% 35.97/23.80 tff(7560,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~m_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, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~node2(c_bit1, s75)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~node2(c_bit1, s75)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7561,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_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, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~node2(c_bit1, s75)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7562,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~node2(c_bit1, s75))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7561, 7560])).
% 35.97/23.80 tff(7563,plain,
% 35.97/23.80 ($false),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7562, 219, 7559, 7558, 7557])).
% 35.97/23.80 tff(7564,plain,((~node2(c_bit1, s75)) | (~m_counter_cell_v_value(c_bit1, s75)) | (~m_counter_cell_v_carry_in(c_bit1, s75))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.80 tff(7565,plain,
% 35.97/23.80 ((~node2(c_bit1, s75)) | (~m_counter_cell_v_value(c_bit1, s75))),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7564, 7556])).
% 35.97/23.80 tff(7566,plain,
% 35.97/23.80 (~node2(c_bit1, s75)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7565, 7543])).
% 35.97/23.80 tff(7567,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s75, s76)) | node3(c_bit1, s75, s76))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s75, s76)) | node3(c_bit1, s75, s76))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7568,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s75, s76)) | node3(c_bit1, s75, s76))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7569,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s75, s76)) | node3(c_bit1, s75, s76)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7568, 7567])).
% 35.97/23.80 tff(7570,plain,
% 35.97/23.80 (node3(c_bit1, s75, s76)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7569, 81, 2329])).
% 35.97/23.80 tff(7571,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7572,plain,
% 35.97/23.80 ((node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)) | (~m_counter_cell_v_value(c_bit1, s76))) <=> ((~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7573,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)) | (~m_counter_cell_v_value(c_bit1, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76))))),
% 35.97/23.80 inference(monotonicity,[status(thm)],[7572])).
% 35.97/23.80 tff(7574,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)) | (~m_counter_cell_v_value(c_bit1, s76)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)))),
% 35.97/23.80 inference(transitivity,[status(thm)],[7573, 7571])).
% 35.97/23.80 tff(7575,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s75) | (~node3(c_bit1, s75, s76)) | (~m_counter_cell_v_value(c_bit1, s76)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7576,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75) | (~node3(c_bit1, s75, s76))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7575, 7574])).
% 35.97/23.80 tff(7577,plain,
% 35.97/23.80 ((~m_counter_cell_v_value(c_bit1, s76)) | node2(c_bit1, s75)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7576, 234, 7570])).
% 35.97/23.80 tff(7578,plain,
% 35.97/23.80 (~m_counter_cell_v_value(c_bit1, s76)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7577, 7566])).
% 35.97/23.80 tff(7579,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s76) | (~node4(c_bit0, s76)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s76) | (~node4(c_bit0, s76)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7580,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s76) | (~node4(c_bit0, s76)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7581,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s76) | (~node4(c_bit0, s76))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7580, 7579])).
% 35.97/23.80 tff(7582,plain,
% 35.97/23.80 (~node4(c_bit0, s76)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7581, 2875, 2341])).
% 35.97/23.80 tff(7583,assumption,(~node4(c_bit0, s76)), introduced(assumption)).
% 35.97/23.80 tff(7584,assumption,(m_counter_cell_v_carry_out(c_bit0, s76)), introduced(assumption)).
% 35.97/23.80 tff(7585,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7586,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7587,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7586, 7585])).
% 35.97/23.80 tff(7588,plain,
% 35.97/23.80 ($false),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7587, 2887, 7584, 7583])).
% 35.97/23.80 tff(7589,plain,((~m_counter_cell_v_carry_out(c_bit0, s76)) | node4(c_bit0, s76)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.80 tff(7590,plain,
% 35.97/23.80 (~m_counter_cell_v_carry_out(c_bit0, s76)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7589, 7582])).
% 35.97/23.80 tff(7591,assumption,(m_counter_cell_v_carry_in(c_bit1, s76)), introduced(assumption)).
% 35.97/23.80 tff(7592,assumption,(~m_counter_cell_v_carry_out(c_bit0, s76)), introduced(assumption)).
% 35.97/23.80 tff(7593,plain,
% 35.97/23.80 (((~![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, s76)) | m_counter_cell_v_carry_out(c_bit0, s76))) <=> ((~![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, s76)) | m_counter_cell_v_carry_out(c_bit0, s76))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7594,plain,
% 35.97/23.80 ((~![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, s76)) | m_counter_cell_v_carry_out(c_bit0, s76))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7595,plain,
% 35.97/23.80 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s76)) | m_counter_cell_v_carry_out(c_bit0, s76)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7594, 7593])).
% 35.97/23.80 tff(7596,plain,
% 35.97/23.80 ($false),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7595, 2901, 7592, 7591])).
% 35.97/23.80 tff(7597,plain,((~m_counter_cell_v_carry_in(c_bit1, s76)) | m_counter_cell_v_carry_out(c_bit0, s76)), inference(lemma,lemma(discharge,[]))).
% 35.97/23.80 tff(7598,plain,
% 35.97/23.80 (~m_counter_cell_v_carry_in(c_bit1, s76)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7597, 7590])).
% 35.97/23.80 tff(7599,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : (m_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, s76) | m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76)))) <=> ((~![I0: $i, X: $i] : (m_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, s76) | m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7600,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : (m_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, s76) | m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7601,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : (m_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, s76) | m_counter_cell_v_value(c_bit1, s76) | (~node2(c_bit1, s76))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7600, 7599])).
% 35.97/23.80 tff(7602,plain,
% 35.97/23.80 (~node2(c_bit1, s76)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7601, 3291, 7598, 7578])).
% 35.97/23.80 tff(7603,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s76, s77)) | node3(c_bit1, s76, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s76, s77)) | node3(c_bit1, s76, s77))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7604,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s76, s77)) | node3(c_bit1, s76, s77))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7605,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s76, s77)) | node3(c_bit1, s76, s77)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7604, 7603])).
% 35.97/23.80 tff(7606,plain,
% 35.97/23.80 (node3(c_bit1, s76, s77)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7605, 81, 2360])).
% 35.97/23.80 tff(7607,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7608,plain,
% 35.97/23.80 ((node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)) | (~m_counter_cell_v_value(c_bit1, s77))) <=> ((~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7609,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)) | (~m_counter_cell_v_value(c_bit1, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77))))),
% 35.97/23.80 inference(monotonicity,[status(thm)],[7608])).
% 35.97/23.80 tff(7610,plain,
% 35.97/23.80 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)) | (~m_counter_cell_v_value(c_bit1, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)))),
% 35.97/23.80 inference(transitivity,[status(thm)],[7609, 7607])).
% 35.97/23.80 tff(7611,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s76) | (~node3(c_bit1, s76, s77)) | (~m_counter_cell_v_value(c_bit1, s77)))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7612,plain,
% 35.97/23.80 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76) | (~node3(c_bit1, s76, s77))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7611, 7610])).
% 35.97/23.80 tff(7613,plain,
% 35.97/23.80 ((~m_counter_cell_v_value(c_bit1, s77)) | node2(c_bit1, s76)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7612, 234, 7606])).
% 35.97/23.80 tff(7614,plain,
% 35.97/23.80 (~m_counter_cell_v_value(c_bit1, s77)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7613, 7602])).
% 35.97/23.80 tff(7615,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7616,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7617,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7616, 7615])).
% 35.97/23.80 tff(7618,plain,
% 35.97/23.80 ((~m_counter_cell_v_value(c_bit0, s77)) | m_counter_cell_v_carry_out(c_bit0, s77)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7617, 3031, 2376])).
% 35.97/23.80 tff(7619,plain,
% 35.97/23.80 (m_counter_cell_v_carry_out(c_bit0, s77)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7618, 2372])).
% 35.97/23.80 tff(7620,plain,
% 35.97/23.80 (((~![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, s77)) | m_counter_cell_v_carry_in(c_bit1, s77))) <=> ((~![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, s77)) | m_counter_cell_v_carry_in(c_bit1, s77))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7621,plain,
% 35.97/23.80 ((~![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, s77)) | m_counter_cell_v_carry_in(c_bit1, s77))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7622,plain,
% 35.97/23.80 ((~![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, s77)) | m_counter_cell_v_carry_in(c_bit1, s77)),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7621, 7620])).
% 35.97/23.80 tff(7623,plain,
% 35.97/23.80 (m_counter_cell_v_carry_in(c_bit1, s77)),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7622, 3046, 7619])).
% 35.97/23.80 tff(7624,assumption,(m_counter_cell_v_carry_in(c_bit1, s77)), introduced(assumption)).
% 35.97/23.80 tff(7625,assumption,(node1(c_bit1, s77)), introduced(assumption)).
% 35.97/23.80 tff(7626,assumption,(~m_counter_cell_v_value(c_bit1, s77)), introduced(assumption)).
% 35.97/23.80 tff(7627,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7628,plain,
% 35.97/23.80 (((~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)))),
% 35.97/23.80 inference(rewrite,[status(thm)],[])).
% 35.97/23.80 tff(7629,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77))))),
% 35.97/23.80 inference(monotonicity,[status(thm)],[7628])).
% 35.97/23.80 tff(7630,plain,
% 35.97/23.80 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)))),
% 35.97/23.80 inference(transitivity,[status(thm)],[7629, 7627])).
% 35.97/23.80 tff(7631,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77))),
% 35.97/23.80 inference(quant_inst,[status(thm)],[])).
% 35.97/23.80 tff(7632,plain,
% 35.97/23.80 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s77)) | m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77))),
% 35.97/23.80 inference(modus_ponens,[status(thm)],[7631, 7630])).
% 35.97/23.80 tff(7633,plain,
% 35.97/23.80 ($false),
% 35.97/23.80 inference(unit_resolution,[status(thm)],[7632, 170, 7626, 7625, 7624])).
% 35.97/23.81 tff(7634,plain,(m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77)) | (~m_counter_cell_v_carry_in(c_bit1, s77))), inference(lemma,lemma(discharge,[]))).
% 35.97/23.81 tff(7635,plain,
% 35.97/23.81 (m_counter_cell_v_value(c_bit1, s77) | (~node1(c_bit1, s77))),
% 35.97/23.81 inference(unit_resolution,[status(thm)],[7634, 7623])).
% 35.97/23.81 tff(7636,plain,
% 35.97/23.81 (~node1(c_bit1, s77)),
% 35.97/23.81 inference(unit_resolution,[status(thm)],[7635, 7614])).
% 35.97/23.81 tff(7637,plain,
% 35.97/23.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s77, s78)) | node3(c_bit1, s77, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s77, s78)) | node3(c_bit1, s77, s78))),
% 35.97/23.81 inference(rewrite,[status(thm)],[])).
% 35.97/23.81 tff(7638,plain,
% 35.97/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s77, s78)) | node3(c_bit1, s77, s78))),
% 35.97/23.81 inference(quant_inst,[status(thm)],[])).
% 35.97/23.81 tff(7639,plain,
% 35.97/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s77, s78)) | node3(c_bit1, s77, s78)),
% 35.97/23.81 inference(modus_ponens,[status(thm)],[7638, 7637])).
% 35.97/23.81 tff(7640,plain,
% 35.97/23.81 (node3(c_bit1, s77, s78)),
% 35.97/23.81 inference(unit_resolution,[status(thm)],[7639, 81, 2388])).
% 35.97/23.81 tff(7641,plain,
% 35.97/23.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)))),
% 35.97/23.81 inference(rewrite,[status(thm)],[])).
% 35.97/23.81 tff(7642,plain,
% 35.97/23.81 ((node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)) | m_counter_cell_v_value(c_bit1, s78)) <=> (m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)))),
% 35.97/23.81 inference(rewrite,[status(thm)],[])).
% 35.97/23.81 tff(7643,plain,
% 35.97/23.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)) | m_counter_cell_v_value(c_bit1, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78))))),
% 35.97/23.81 inference(monotonicity,[status(thm)],[7642])).
% 35.97/23.81 tff(7644,plain,
% 35.97/23.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)) | m_counter_cell_v_value(c_bit1, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)))),
% 35.97/23.81 inference(transitivity,[status(thm)],[7643, 7641])).
% 35.97/23.81 tff(7645,plain,
% 35.97/23.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s77) | (~node3(c_bit1, s77, s78)) | m_counter_cell_v_value(c_bit1, s78))),
% 35.97/23.81 inference(quant_inst,[status(thm)],[])).
% 35.97/23.81 tff(7646,plain,
% 35.97/23.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77) | (~node3(c_bit1, s77, s78))),
% 35.97/23.81 inference(modus_ponens,[status(thm)],[7645, 7644])).
% 35.97/23.81 tff(7647,plain,
% 35.97/23.81 (m_counter_cell_v_value(c_bit1, s78) | node1(c_bit1, s77)),
% 35.97/23.81 inference(unit_resolution,[status(thm)],[7646, 199, 7640])).
% 35.97/23.81 tff(7648,plain,
% 35.97/23.81 (m_counter_cell_v_value(c_bit1, s78)),
% 35.97/23.81 inference(unit_resolution,[status(thm)],[7647, 7636])).
% 35.97/23.81 tff(7649,plain,
% 35.97/23.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78)))),
% 35.97/23.81 inference(rewrite,[status(thm)],[])).
% 35.97/23.81 tff(7650,plain,
% 35.97/23.81 (((~node1(c_bit1, s78)) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78))) <=> (m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78)))),
% 35.97/23.81 inference(rewrite,[status(thm)],[])).
% 35.97/23.81 tff(7651,plain,
% 35.97/23.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s78)) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78))))),
% 35.97/23.81 inference(monotonicity,[status(thm)],[7650])).
% 35.97/23.81 tff(7652,plain,
% 35.97/23.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s78)) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78)))),
% 35.97/23.81 inference(transitivity,[status(thm)],[7651, 7649])).
% 35.97/23.81 tff(7653,plain,
% 35.97/23.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s78)) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)))),
% 35.97/23.81 inference(quant_inst,[status(thm)],[])).
% 35.97/23.81 tff(7654,plain,
% 35.97/23.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s78) | (~m_counter_cell_v_value(c_bit1, s78)) | (~node1(c_bit1, s78))),
% 35.97/23.81 inference(modus_ponens,[status(thm)],[7653, 7652])).
% 35.97/23.81 tff(7655,plain,
% 35.97/23.81 (~node1(c_bit1, s78)),
% 35.97/23.81 inference(unit_resolution,[status(thm)],[7654, 3359, 7648, 2947])).
% 35.97/23.81 tff(7656,plain,
% 35.97/23.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s78, s79)) | node3(c_bit1, s78, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s78, s79)) | node3(c_bit1, s78, s79))),
% 35.97/23.81 inference(rewrite,[status(thm)],[])).
% 35.97/23.81 tff(7657,plain,
% 35.97/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s78, s79)) | node3(c_bit1, s78, s79))),
% 35.97/23.81 inference(quant_inst,[status(thm)],[])).
% 35.97/23.81 tff(7658,plain,
% 35.97/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s78, s79)) | node3(c_bit1, s78, s79)),
% 35.97/23.81 inference(modus_ponens,[status(thm)],[7657, 7656])).
% 35.97/23.81 tff(7659,plain,
% 35.97/23.81 (node3(c_bit1, s78, s79)),
% 35.97/23.81 inference(unit_resolution,[status(thm)],[7658, 81, 2419])).
% 35.97/23.81 tff(7660,plain,
% 35.97/23.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)))),
% 35.97/23.81 inference(rewrite,[status(thm)],[])).
% 35.97/23.81 tff(7661,plain,
% 35.97/23.81 ((node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)) | m_counter_cell_v_value(c_bit1, s79)) <=> (m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)))),
% 35.97/23.81 inference(rewrite,[status(thm)],[])).
% 35.97/23.81 tff(7662,plain,
% 35.97/23.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)) | m_counter_cell_v_value(c_bit1, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79))))),
% 35.97/23.81 inference(monotonicity,[status(thm)],[7661])).
% 35.97/23.81 tff(7663,plain,
% 35.97/23.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)) | m_counter_cell_v_value(c_bit1, s79))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)))),
% 36.00/23.81 inference(transitivity,[status(thm)],[7662, 7660])).
% 36.00/23.81 tff(7664,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s78) | (~node3(c_bit1, s78, s79)) | m_counter_cell_v_value(c_bit1, s79))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7665,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78) | (~node3(c_bit1, s78, s79))),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7664, 7663])).
% 36.00/23.81 tff(7666,plain,
% 36.00/23.81 (m_counter_cell_v_value(c_bit1, s79) | node1(c_bit1, s78)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7665, 199, 7659])).
% 36.00/23.81 tff(7667,plain,
% 36.00/23.81 (m_counter_cell_v_value(c_bit1, s79)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7666, 7655])).
% 36.00/23.81 tff(7668,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7669,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7670,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | (~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7669, 7668])).
% 36.00/23.81 tff(7671,plain,
% 36.00/23.81 ((~m_counter_cell_v_value(c_bit0, s79)) | m_counter_cell_v_carry_out(c_bit0, s79)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7670, 3031, 2435])).
% 36.00/23.81 tff(7672,plain,
% 36.00/23.81 (m_counter_cell_v_carry_out(c_bit0, s79)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7671, 2431])).
% 36.00/23.81 tff(7673,plain,
% 36.00/23.81 (((~![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, s79)) | m_counter_cell_v_carry_in(c_bit1, s79))) <=> ((~![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, s79)) | m_counter_cell_v_carry_in(c_bit1, s79))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7674,plain,
% 36.00/23.81 ((~![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, s79)) | m_counter_cell_v_carry_in(c_bit1, s79))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7675,plain,
% 36.00/23.81 ((~![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, s79)) | m_counter_cell_v_carry_in(c_bit1, s79)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7674, 7673])).
% 36.00/23.81 tff(7676,plain,
% 36.00/23.81 (m_counter_cell_v_carry_in(c_bit1, s79)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7675, 3046, 7672])).
% 36.00/23.81 tff(7677,assumption,(m_counter_cell_v_carry_in(c_bit1, s79)), introduced(assumption)).
% 36.00/23.81 tff(7678,assumption,(node2(c_bit1, s79)), introduced(assumption)).
% 36.00/23.81 tff(7679,assumption,(m_counter_cell_v_value(c_bit1, s79)), introduced(assumption)).
% 36.00/23.81 tff(7680,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : ((~m_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, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7681,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~m_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, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79)))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7682,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~node2(c_bit1, s79))),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7681, 7680])).
% 36.00/23.81 tff(7683,plain,
% 36.00/23.81 ($false),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7682, 219, 7679, 7678, 7677])).
% 36.00/23.81 tff(7684,plain,((~node2(c_bit1, s79)) | (~m_counter_cell_v_value(c_bit1, s79)) | (~m_counter_cell_v_carry_in(c_bit1, s79))), inference(lemma,lemma(discharge,[]))).
% 36.00/23.81 tff(7685,plain,
% 36.00/23.81 ((~node2(c_bit1, s79)) | (~m_counter_cell_v_value(c_bit1, s79))),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7684, 7676])).
% 36.00/23.81 tff(7686,plain,
% 36.00/23.81 (~node2(c_bit1, s79)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7685, 7667])).
% 36.00/23.81 tff(7687,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s79, s80)) | node3(c_bit1, s79, s80))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s79, s80)) | node3(c_bit1, s79, s80))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7688,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s79, s80)) | node3(c_bit1, s79, s80))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7689,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s79, s80)) | node3(c_bit1, s79, s80)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7688, 7687])).
% 36.00/23.81 tff(7690,plain,
% 36.00/23.81 (node3(c_bit1, s79, s80)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7689, 81, 2447])).
% 36.00/23.81 tff(7691,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7692,plain,
% 36.00/23.81 ((node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)) | (~m_counter_cell_v_value(c_bit1, s80))) <=> ((~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7693,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)) | (~m_counter_cell_v_value(c_bit1, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80))))),
% 36.00/23.81 inference(monotonicity,[status(thm)],[7692])).
% 36.00/23.81 tff(7694,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)) | (~m_counter_cell_v_value(c_bit1, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)))),
% 36.00/23.81 inference(transitivity,[status(thm)],[7693, 7691])).
% 36.00/23.81 tff(7695,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s79) | (~node3(c_bit1, s79, s80)) | (~m_counter_cell_v_value(c_bit1, s80)))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7696,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79) | (~node3(c_bit1, s79, s80))),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7695, 7694])).
% 36.00/23.81 tff(7697,plain,
% 36.00/23.81 ((~m_counter_cell_v_value(c_bit1, s80)) | node2(c_bit1, s79)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7696, 234, 7690])).
% 36.00/23.81 tff(7698,plain,
% 36.00/23.81 (~m_counter_cell_v_value(c_bit1, s80)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7697, 7686])).
% 36.00/23.81 tff(7699,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s80) | (~node4(c_bit0, s80)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s80) | (~node4(c_bit0, s80)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7700,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s80) | (~node4(c_bit0, s80)))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7701,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s80) | (~node4(c_bit0, s80))),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7700, 7699])).
% 36.00/23.81 tff(7702,plain,
% 36.00/23.81 (~node4(c_bit0, s80)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7701, 2875, 2459])).
% 36.00/23.81 tff(7703,assumption,(m_counter_cell_v_carry_out(c_bit0, s80)), introduced(assumption)).
% 36.00/23.81 tff(7704,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7705,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7706,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s80)) | node4(c_bit0, s80)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7705, 7704])).
% 36.00/23.81 tff(7707,plain,
% 36.00/23.81 ($false),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7706, 2887, 7703, 7702])).
% 36.00/23.81 tff(7708,plain,(~m_counter_cell_v_carry_out(c_bit0, s80)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.81 tff(7709,assumption,(m_counter_cell_v_carry_in(c_bit1, s80)), introduced(assumption)).
% 36.00/23.81 tff(7710,assumption,(~m_counter_cell_v_carry_out(c_bit0, s80)), introduced(assumption)).
% 36.00/23.81 tff(7711,plain,
% 36.00/23.81 (((~![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, s80)) | m_counter_cell_v_carry_out(c_bit0, s80))) <=> ((~![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, s80)) | m_counter_cell_v_carry_out(c_bit0, s80))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7712,plain,
% 36.00/23.81 ((~![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, s80)) | m_counter_cell_v_carry_out(c_bit0, s80))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7713,plain,
% 36.00/23.81 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s80)) | m_counter_cell_v_carry_out(c_bit0, s80)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7712, 7711])).
% 36.00/23.81 tff(7714,plain,
% 36.00/23.81 ($false),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7713, 2901, 7710, 7709])).
% 36.00/23.81 tff(7715,plain,((~m_counter_cell_v_carry_in(c_bit1, s80)) | m_counter_cell_v_carry_out(c_bit0, s80)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.81 tff(7716,plain,
% 36.00/23.81 (~m_counter_cell_v_carry_in(c_bit1, s80)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7715, 7708])).
% 36.00/23.81 tff(7717,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : (m_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, s80) | m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80)))) <=> ((~![I0: $i, X: $i] : (m_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, s80) | m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7718,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : (m_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, s80) | m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80)))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7719,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : (m_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, s80) | m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80))),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7718, 7717])).
% 36.00/23.81 tff(7720,plain,
% 36.00/23.81 (m_counter_cell_v_value(c_bit1, s80) | (~node2(c_bit1, s80))),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7719, 3291, 7716])).
% 36.00/23.81 tff(7721,plain,
% 36.00/23.81 (~node2(c_bit1, s80)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7720, 7698])).
% 36.00/23.81 tff(7722,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s80, s81)) | node3(c_bit1, s80, s81))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s80, s81)) | node3(c_bit1, s80, s81))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7723,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s80, s81)) | node3(c_bit1, s80, s81))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7724,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s80, s81)) | node3(c_bit1, s80, s81)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7723, 7722])).
% 36.00/23.81 tff(7725,plain,
% 36.00/23.81 (node3(c_bit1, s80, s81)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7724, 81, 2478])).
% 36.00/23.81 tff(7726,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7727,plain,
% 36.00/23.81 ((node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)) | (~m_counter_cell_v_value(c_bit1, s81))) <=> ((~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7728,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)) | (~m_counter_cell_v_value(c_bit1, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81))))),
% 36.00/23.81 inference(monotonicity,[status(thm)],[7727])).
% 36.00/23.81 tff(7729,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)) | (~m_counter_cell_v_value(c_bit1, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)))),
% 36.00/23.81 inference(transitivity,[status(thm)],[7728, 7726])).
% 36.00/23.81 tff(7730,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s80) | (~node3(c_bit1, s80, s81)) | (~m_counter_cell_v_value(c_bit1, s81)))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7731,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80) | (~node3(c_bit1, s80, s81))),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7730, 7729])).
% 36.00/23.81 tff(7732,plain,
% 36.00/23.81 ((~m_counter_cell_v_value(c_bit1, s81)) | node2(c_bit1, s80)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7731, 234, 7725])).
% 36.00/23.81 tff(7733,plain,
% 36.00/23.81 (~m_counter_cell_v_value(c_bit1, s81)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7732, 7721])).
% 36.00/23.81 tff(7734,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7735,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7736,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | (~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7735, 7734])).
% 36.00/23.81 tff(7737,plain,
% 36.00/23.81 ((~m_counter_cell_v_value(c_bit0, s81)) | m_counter_cell_v_carry_out(c_bit0, s81)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7736, 3031, 2494])).
% 36.00/23.81 tff(7738,plain,
% 36.00/23.81 (m_counter_cell_v_carry_out(c_bit0, s81)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7737, 2490])).
% 36.00/23.81 tff(7739,assumption,(~m_counter_cell_v_carry_in(c_bit1, s81)), introduced(assumption)).
% 36.00/23.81 tff(7740,assumption,(m_counter_cell_v_carry_out(c_bit0, s81)), introduced(assumption)).
% 36.00/23.81 tff(7741,plain,
% 36.00/23.81 (((~![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, s81)) | m_counter_cell_v_carry_in(c_bit1, s81))) <=> ((~![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, s81)) | m_counter_cell_v_carry_in(c_bit1, s81))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7742,plain,
% 36.00/23.81 ((~![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, s81)) | m_counter_cell_v_carry_in(c_bit1, s81))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7743,plain,
% 36.00/23.81 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s81)) | m_counter_cell_v_carry_in(c_bit1, s81)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7742, 7741])).
% 36.00/23.81 tff(7744,plain,
% 36.00/23.81 ($false),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7743, 3046, 7740, 7739])).
% 36.00/23.81 tff(7745,plain,((~m_counter_cell_v_carry_out(c_bit0, s81)) | m_counter_cell_v_carry_in(c_bit1, s81)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.81 tff(7746,plain,
% 36.00/23.81 (m_counter_cell_v_carry_in(c_bit1, s81)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7745, 7738])).
% 36.00/23.81 tff(7747,assumption,(~m_counter_cell_v_value(c_bit1, s81)), introduced(assumption)).
% 36.00/23.81 tff(7748,assumption,(m_counter_cell_v_carry_in(c_bit1, s81)), introduced(assumption)).
% 36.00/23.81 tff(7749,assumption,(node1(c_bit1, s81)), introduced(assumption)).
% 36.00/23.81 tff(7750,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7751,plain,
% 36.00/23.81 (((~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7752,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81))))),
% 36.00/23.81 inference(monotonicity,[status(thm)],[7751])).
% 36.00/23.81 tff(7753,plain,
% 36.00/23.81 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)))),
% 36.00/23.81 inference(transitivity,[status(thm)],[7752, 7750])).
% 36.00/23.81 tff(7754,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7755,plain,
% 36.00/23.81 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s81)) | m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81))),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7754, 7753])).
% 36.00/23.81 tff(7756,plain,
% 36.00/23.81 ($false),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7755, 170, 7749, 7748, 7747])).
% 36.00/23.81 tff(7757,plain,(m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81)) | (~m_counter_cell_v_carry_in(c_bit1, s81))), inference(lemma,lemma(discharge,[]))).
% 36.00/23.81 tff(7758,plain,
% 36.00/23.81 (m_counter_cell_v_value(c_bit1, s81) | (~node1(c_bit1, s81))),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7757, 7746])).
% 36.00/23.81 tff(7759,plain,
% 36.00/23.81 (~node1(c_bit1, s81)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7758, 7733])).
% 36.00/23.81 tff(7760,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s81, s82)) | node3(c_bit1, s81, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s81, s82)) | node3(c_bit1, s81, s82))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7761,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s81, s82)) | node3(c_bit1, s81, s82))),
% 36.00/23.81 inference(quant_inst,[status(thm)],[])).
% 36.00/23.81 tff(7762,plain,
% 36.00/23.81 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s81, s82)) | node3(c_bit1, s81, s82)),
% 36.00/23.81 inference(modus_ponens,[status(thm)],[7761, 7760])).
% 36.00/23.81 tff(7763,plain,
% 36.00/23.81 (node3(c_bit1, s81, s82)),
% 36.00/23.81 inference(unit_resolution,[status(thm)],[7762, 81, 2506])).
% 36.00/23.81 tff(7764,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7765,plain,
% 36.00/23.81 ((node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)) | m_counter_cell_v_value(c_bit1, s82)) <=> (m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)))),
% 36.00/23.81 inference(rewrite,[status(thm)],[])).
% 36.00/23.81 tff(7766,plain,
% 36.00/23.81 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)) | m_counter_cell_v_value(c_bit1, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82))))),
% 36.00/23.82 inference(monotonicity,[status(thm)],[7765])).
% 36.00/23.82 tff(7767,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)) | m_counter_cell_v_value(c_bit1, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)))),
% 36.00/23.82 inference(transitivity,[status(thm)],[7766, 7764])).
% 36.00/23.82 tff(7768,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s81) | (~node3(c_bit1, s81, s82)) | m_counter_cell_v_value(c_bit1, s82))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7769,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81) | (~node3(c_bit1, s81, s82))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7768, 7767])).
% 36.00/23.82 tff(7770,plain,
% 36.00/23.82 (m_counter_cell_v_value(c_bit1, s82) | node1(c_bit1, s81)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7769, 199, 7763])).
% 36.00/23.82 tff(7771,plain,
% 36.00/23.82 (m_counter_cell_v_value(c_bit1, s82)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7770, 7759])).
% 36.00/23.82 tff(7772,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s82) | (~node4(c_bit0, s82)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s82) | (~node4(c_bit0, s82)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7773,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s82) | (~node4(c_bit0, s82)))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7774,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s82) | (~node4(c_bit0, s82))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7773, 7772])).
% 36.00/23.82 tff(7775,plain,
% 36.00/23.82 (~node4(c_bit0, s82)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7774, 2875, 2518])).
% 36.00/23.82 tff(7776,assumption,(m_counter_cell_v_carry_out(c_bit0, s82)), introduced(assumption)).
% 36.00/23.82 tff(7777,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s82)) | node4(c_bit0, s82))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s82)) | node4(c_bit0, s82))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7778,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s82)) | node4(c_bit0, s82))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7779,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s82)) | node4(c_bit0, s82)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7778, 7777])).
% 36.00/23.82 tff(7780,plain,
% 36.00/23.82 ($false),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7779, 2887, 7776, 7775])).
% 36.00/23.82 tff(7781,plain,(~m_counter_cell_v_carry_out(c_bit0, s82)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.82 tff(7782,assumption,(m_counter_cell_v_carry_in(c_bit1, s82)), introduced(assumption)).
% 36.00/23.82 tff(7783,assumption,(~m_counter_cell_v_carry_out(c_bit0, s82)), introduced(assumption)).
% 36.00/23.82 tff(7784,plain,
% 36.00/23.82 (((~![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, s82)) | m_counter_cell_v_carry_out(c_bit0, s82))) <=> ((~![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, s82)) | m_counter_cell_v_carry_out(c_bit0, s82))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7785,plain,
% 36.00/23.82 ((~![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, s82)) | m_counter_cell_v_carry_out(c_bit0, s82))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7786,plain,
% 36.00/23.82 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s82)) | m_counter_cell_v_carry_out(c_bit0, s82)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7785, 7784])).
% 36.00/23.82 tff(7787,plain,
% 36.00/23.82 ($false),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7786, 2901, 7783, 7782])).
% 36.00/23.82 tff(7788,plain,((~m_counter_cell_v_carry_in(c_bit1, s82)) | m_counter_cell_v_carry_out(c_bit0, s82)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.82 tff(7789,plain,
% 36.00/23.82 (~m_counter_cell_v_carry_in(c_bit1, s82)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7788, 7781])).
% 36.00/23.82 tff(7790,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7791,plain,
% 36.00/23.82 (((~node1(c_bit1, s82)) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82))) <=> (m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7792,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s82)) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82))))),
% 36.00/23.82 inference(monotonicity,[status(thm)],[7791])).
% 36.00/23.82 tff(7793,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s82)) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82)))),
% 36.00/23.82 inference(transitivity,[status(thm)],[7792, 7790])).
% 36.00/23.82 tff(7794,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s82)) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7795,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s82) | (~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7794, 7793])).
% 36.00/23.82 tff(7796,plain,
% 36.00/23.82 ((~m_counter_cell_v_value(c_bit1, s82)) | (~node1(c_bit1, s82))),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7795, 3359, 7789])).
% 36.00/23.82 tff(7797,plain,
% 36.00/23.82 (~node1(c_bit1, s82)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7796, 7771])).
% 36.00/23.82 tff(7798,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s82, s83)) | node3(c_bit1, s82, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s82, s83)) | node3(c_bit1, s82, s83))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7799,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s82, s83)) | node3(c_bit1, s82, s83))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7800,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s82, s83)) | node3(c_bit1, s82, s83)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7799, 7798])).
% 36.00/23.82 tff(7801,plain,
% 36.00/23.82 (node3(c_bit1, s82, s83)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7800, 81, 2537])).
% 36.00/23.82 tff(7802,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7803,plain,
% 36.00/23.82 ((node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)) | m_counter_cell_v_value(c_bit1, s83)) <=> (m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7804,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)) | m_counter_cell_v_value(c_bit1, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83))))),
% 36.00/23.82 inference(monotonicity,[status(thm)],[7803])).
% 36.00/23.82 tff(7805,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)) | m_counter_cell_v_value(c_bit1, s83))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)))),
% 36.00/23.82 inference(transitivity,[status(thm)],[7804, 7802])).
% 36.00/23.82 tff(7806,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s82) | (~node3(c_bit1, s82, s83)) | m_counter_cell_v_value(c_bit1, s83))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7807,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82) | (~node3(c_bit1, s82, s83))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7806, 7805])).
% 36.00/23.82 tff(7808,plain,
% 36.00/23.82 (m_counter_cell_v_value(c_bit1, s83) | node1(c_bit1, s82)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7807, 199, 7801])).
% 36.00/23.82 tff(7809,plain,
% 36.00/23.82 (m_counter_cell_v_value(c_bit1, s83)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7808, 7797])).
% 36.00/23.82 tff(7810,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7811,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7812,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | (~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7811, 7810])).
% 36.00/23.82 tff(7813,plain,
% 36.00/23.82 ((~m_counter_cell_v_value(c_bit0, s83)) | m_counter_cell_v_carry_out(c_bit0, s83)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7812, 3031, 2553])).
% 36.00/23.82 tff(7814,plain,
% 36.00/23.82 (m_counter_cell_v_carry_out(c_bit0, s83)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7813, 2549])).
% 36.00/23.82 tff(7815,plain,
% 36.00/23.82 (((~![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, s83)) | m_counter_cell_v_carry_in(c_bit1, s83))) <=> ((~![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, s83)) | m_counter_cell_v_carry_in(c_bit1, s83))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7816,plain,
% 36.00/23.82 ((~![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, s83)) | m_counter_cell_v_carry_in(c_bit1, s83))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7817,plain,
% 36.00/23.82 ((~![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, s83)) | m_counter_cell_v_carry_in(c_bit1, s83)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7816, 7815])).
% 36.00/23.82 tff(7818,plain,
% 36.00/23.82 (m_counter_cell_v_carry_in(c_bit1, s83)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7817, 3046, 7814])).
% 36.00/23.82 tff(7819,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s83)) | (~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s83)) | (~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7820,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s83)) | (~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83)))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7821,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s83)) | (~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7820, 7819])).
% 36.00/23.82 tff(7822,plain,
% 36.00/23.82 ((~m_counter_cell_v_value(c_bit1, s83)) | (~node2(c_bit1, s83))),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7821, 219, 7818])).
% 36.00/23.82 tff(7823,plain,
% 36.00/23.82 (~node2(c_bit1, s83)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7822, 7809])).
% 36.00/23.82 tff(7824,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s83, s84)) | node3(c_bit1, s83, s84))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s83, s84)) | node3(c_bit1, s83, s84))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7825,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s83, s84)) | node3(c_bit1, s83, s84))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7826,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s83, s84)) | node3(c_bit1, s83, s84)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7825, 7824])).
% 36.00/23.82 tff(7827,plain,
% 36.00/23.82 (node3(c_bit1, s83, s84)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7826, 81, 2565])).
% 36.00/23.82 tff(7828,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7829,plain,
% 36.00/23.82 ((node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)) | (~m_counter_cell_v_value(c_bit1, s84))) <=> ((~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7830,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)) | (~m_counter_cell_v_value(c_bit1, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84))))),
% 36.00/23.82 inference(monotonicity,[status(thm)],[7829])).
% 36.00/23.82 tff(7831,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)) | (~m_counter_cell_v_value(c_bit1, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)))),
% 36.00/23.82 inference(transitivity,[status(thm)],[7830, 7828])).
% 36.00/23.82 tff(7832,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s83) | (~node3(c_bit1, s83, s84)) | (~m_counter_cell_v_value(c_bit1, s84)))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7833,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83) | (~node3(c_bit1, s83, s84))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7832, 7831])).
% 36.00/23.82 tff(7834,plain,
% 36.00/23.82 ((~m_counter_cell_v_value(c_bit1, s84)) | node2(c_bit1, s83)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7833, 234, 7827])).
% 36.00/23.82 tff(7835,plain,
% 36.00/23.82 (~m_counter_cell_v_value(c_bit1, s84)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7834, 7823])).
% 36.00/23.82 tff(7836,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s84) | m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84)))) <=> ((~![I0: $i, X: $i] : (m_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, s84) | m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7837,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s84) | m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84)))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7838,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s84) | m_counter_cell_v_value(c_bit1, s84) | (~node2(c_bit1, s84))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7837, 7836])).
% 36.00/23.82 tff(7839,plain,
% 36.00/23.82 (~node2(c_bit1, s84)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7838, 3291, 7835, 2927])).
% 36.00/23.82 tff(7840,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s84, s85)) | node3(c_bit1, s84, s85))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s84, s85)) | node3(c_bit1, s84, s85))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7841,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s84, s85)) | node3(c_bit1, s84, s85))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7842,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s84, s85)) | node3(c_bit1, s84, s85)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7841, 7840])).
% 36.00/23.82 tff(7843,plain,
% 36.00/23.82 (node3(c_bit1, s84, s85)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7842, 81, 2596])).
% 36.00/23.82 tff(7844,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7845,plain,
% 36.00/23.82 ((node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)) | (~m_counter_cell_v_value(c_bit1, s85))) <=> ((~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7846,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)) | (~m_counter_cell_v_value(c_bit1, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85))))),
% 36.00/23.82 inference(monotonicity,[status(thm)],[7845])).
% 36.00/23.82 tff(7847,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)) | (~m_counter_cell_v_value(c_bit1, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)))),
% 36.00/23.82 inference(transitivity,[status(thm)],[7846, 7844])).
% 36.00/23.82 tff(7848,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s84) | (~node3(c_bit1, s84, s85)) | (~m_counter_cell_v_value(c_bit1, s85)))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7849,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84) | (~node3(c_bit1, s84, s85))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7848, 7847])).
% 36.00/23.82 tff(7850,plain,
% 36.00/23.82 ((~m_counter_cell_v_value(c_bit1, s85)) | node2(c_bit1, s84)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7849, 234, 7843])).
% 36.00/23.82 tff(7851,plain,
% 36.00/23.82 (~m_counter_cell_v_value(c_bit1, s85)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7850, 7839])).
% 36.00/23.82 tff(7852,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7853,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7854,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | (~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7853, 7852])).
% 36.00/23.82 tff(7855,plain,
% 36.00/23.82 ((~m_counter_cell_v_value(c_bit0, s85)) | m_counter_cell_v_carry_out(c_bit0, s85)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7854, 3031, 2612])).
% 36.00/23.82 tff(7856,plain,
% 36.00/23.82 (m_counter_cell_v_carry_out(c_bit0, s85)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7855, 2608])).
% 36.00/23.82 tff(7857,plain,
% 36.00/23.82 (((~![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, s85)) | m_counter_cell_v_carry_in(c_bit1, s85))) <=> ((~![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, s85)) | m_counter_cell_v_carry_in(c_bit1, s85))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7858,plain,
% 36.00/23.82 ((~![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, s85)) | m_counter_cell_v_carry_in(c_bit1, s85))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7859,plain,
% 36.00/23.82 ((~![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, s85)) | m_counter_cell_v_carry_in(c_bit1, s85)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7858, 7857])).
% 36.00/23.82 tff(7860,plain,
% 36.00/23.82 (m_counter_cell_v_carry_in(c_bit1, s85)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7859, 3046, 7856])).
% 36.00/23.82 tff(7861,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7862,plain,
% 36.00/23.82 (((~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7863,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85))))),
% 36.00/23.82 inference(monotonicity,[status(thm)],[7862])).
% 36.00/23.82 tff(7864,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85)))),
% 36.00/23.82 inference(transitivity,[status(thm)],[7863, 7861])).
% 36.00/23.82 tff(7865,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s85)) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7866,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s85)) | m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7865, 7864])).
% 36.00/23.82 tff(7867,plain,
% 36.00/23.82 (m_counter_cell_v_value(c_bit1, s85) | (~node1(c_bit1, s85))),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7866, 170, 7860])).
% 36.00/23.82 tff(7868,plain,
% 36.00/23.82 (~node1(c_bit1, s85)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7867, 7851])).
% 36.00/23.82 tff(7869,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s85, s86)) | node3(c_bit1, s85, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s85, s86)) | node3(c_bit1, s85, s86))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7870,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s85, s86)) | node3(c_bit1, s85, s86))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7871,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s85, s86)) | node3(c_bit1, s85, s86)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7870, 7869])).
% 36.00/23.82 tff(7872,plain,
% 36.00/23.82 (node3(c_bit1, s85, s86)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7871, 81, 2624])).
% 36.00/23.82 tff(7873,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7874,plain,
% 36.00/23.82 ((node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)) | m_counter_cell_v_value(c_bit1, s86)) <=> (m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7875,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)) | m_counter_cell_v_value(c_bit1, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86))))),
% 36.00/23.82 inference(monotonicity,[status(thm)],[7874])).
% 36.00/23.82 tff(7876,plain,
% 36.00/23.82 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)) | m_counter_cell_v_value(c_bit1, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)))),
% 36.00/23.82 inference(transitivity,[status(thm)],[7875, 7873])).
% 36.00/23.82 tff(7877,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s85) | (~node3(c_bit1, s85, s86)) | m_counter_cell_v_value(c_bit1, s86))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7878,plain,
% 36.00/23.82 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85) | (~node3(c_bit1, s85, s86))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7877, 7876])).
% 36.00/23.82 tff(7879,plain,
% 36.00/23.82 (m_counter_cell_v_value(c_bit1, s86) | node1(c_bit1, s85)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7878, 199, 7872])).
% 36.00/23.82 tff(7880,plain,
% 36.00/23.82 (m_counter_cell_v_value(c_bit1, s86)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7879, 7868])).
% 36.00/23.82 tff(7881,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s86) | (~node4(c_bit0, s86)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s86) | (~node4(c_bit0, s86)))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7882,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s86) | (~node4(c_bit0, s86)))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7883,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s86) | (~node4(c_bit0, s86))),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7882, 7881])).
% 36.00/23.82 tff(7884,plain,
% 36.00/23.82 (~node4(c_bit0, s86)),
% 36.00/23.82 inference(unit_resolution,[status(thm)],[7883, 2875, 2636])).
% 36.00/23.82 tff(7885,assumption,(~node4(c_bit0, s86)), introduced(assumption)).
% 36.00/23.82 tff(7886,assumption,(m_counter_cell_v_carry_out(c_bit0, s86)), introduced(assumption)).
% 36.00/23.82 tff(7887,plain,
% 36.00/23.82 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86))),
% 36.00/23.82 inference(rewrite,[status(thm)],[])).
% 36.00/23.82 tff(7888,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86))),
% 36.00/23.82 inference(quant_inst,[status(thm)],[])).
% 36.00/23.82 tff(7889,plain,
% 36.00/23.82 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86)),
% 36.00/23.82 inference(modus_ponens,[status(thm)],[7888, 7887])).
% 36.00/23.83 tff(7890,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7889, 2887, 7886, 7885])).
% 36.00/23.83 tff(7891,plain,((~m_counter_cell_v_carry_out(c_bit0, s86)) | node4(c_bit0, s86)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(7892,plain,
% 36.00/23.83 (~m_counter_cell_v_carry_out(c_bit0, s86)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7891, 7884])).
% 36.00/23.83 tff(7893,assumption,(m_counter_cell_v_carry_in(c_bit1, s86)), introduced(assumption)).
% 36.00/23.83 tff(7894,assumption,(~m_counter_cell_v_carry_out(c_bit0, s86)), introduced(assumption)).
% 36.00/23.83 tff(7895,plain,
% 36.00/23.83 (((~![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, s86)) | m_counter_cell_v_carry_out(c_bit0, s86))) <=> ((~![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, s86)) | m_counter_cell_v_carry_out(c_bit0, s86))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7896,plain,
% 36.00/23.83 ((~![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, s86)) | m_counter_cell_v_carry_out(c_bit0, s86))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7897,plain,
% 36.00/23.83 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s86)) | m_counter_cell_v_carry_out(c_bit0, s86)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7896, 7895])).
% 36.00/23.83 tff(7898,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7897, 2901, 7894, 7893])).
% 36.00/23.83 tff(7899,plain,((~m_counter_cell_v_carry_in(c_bit1, s86)) | m_counter_cell_v_carry_out(c_bit0, s86)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(7900,plain,
% 36.00/23.83 (~m_counter_cell_v_carry_in(c_bit1, s86)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7899, 7892])).
% 36.00/23.83 tff(7901,assumption,(~m_counter_cell_v_carry_in(c_bit1, s86)), introduced(assumption)).
% 36.00/23.83 tff(7902,assumption,(node1(c_bit1, s86)), introduced(assumption)).
% 36.00/23.83 tff(7903,assumption,(m_counter_cell_v_value(c_bit1, s86)), introduced(assumption)).
% 36.00/23.83 tff(7904,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7905,plain,
% 36.00/23.83 (((~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86))) <=> (m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7906,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86))))),
% 36.00/23.83 inference(monotonicity,[status(thm)],[7905])).
% 36.00/23.83 tff(7907,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)))),
% 36.00/23.83 inference(transitivity,[status(thm)],[7906, 7904])).
% 36.00/23.83 tff(7908,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7909,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s86) | (~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7908, 7907])).
% 36.00/23.83 tff(7910,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7909, 3359, 7903, 7902, 7901])).
% 36.00/23.83 tff(7911,plain,((~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86)) | m_counter_cell_v_carry_in(c_bit1, s86)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(7912,plain,
% 36.00/23.83 ((~m_counter_cell_v_value(c_bit1, s86)) | (~node1(c_bit1, s86))),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7911, 7900])).
% 36.00/23.83 tff(7913,plain,
% 36.00/23.83 (~node1(c_bit1, s86)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7912, 7880])).
% 36.00/23.83 tff(7914,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s86, s87)) | node3(c_bit1, s86, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s86, s87)) | node3(c_bit1, s86, s87))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7915,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s86, s87)) | node3(c_bit1, s86, s87))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7916,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s86, s87)) | node3(c_bit1, s86, s87)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7915, 7914])).
% 36.00/23.83 tff(7917,plain,
% 36.00/23.83 (node3(c_bit1, s86, s87)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7916, 81, 2655])).
% 36.00/23.83 tff(7918,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7919,plain,
% 36.00/23.83 ((node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)) | m_counter_cell_v_value(c_bit1, s87)) <=> (m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7920,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)) | m_counter_cell_v_value(c_bit1, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87))))),
% 36.00/23.83 inference(monotonicity,[status(thm)],[7919])).
% 36.00/23.83 tff(7921,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)) | m_counter_cell_v_value(c_bit1, s87))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)))),
% 36.00/23.83 inference(transitivity,[status(thm)],[7920, 7918])).
% 36.00/23.83 tff(7922,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s86) | (~node3(c_bit1, s86, s87)) | m_counter_cell_v_value(c_bit1, s87))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7923,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86) | (~node3(c_bit1, s86, s87))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7922, 7921])).
% 36.00/23.83 tff(7924,plain,
% 36.00/23.83 (m_counter_cell_v_value(c_bit1, s87) | node1(c_bit1, s86)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7923, 199, 7917])).
% 36.00/23.83 tff(7925,plain,
% 36.00/23.83 (m_counter_cell_v_value(c_bit1, s87)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7924, 7913])).
% 36.00/23.83 tff(7926,assumption,(node2(c_bit1, s87)), introduced(assumption)).
% 36.00/23.83 tff(7927,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7928,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7929,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | (~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7928, 7927])).
% 36.00/23.83 tff(7930,plain,
% 36.00/23.83 ((~m_counter_cell_v_value(c_bit0, s87)) | m_counter_cell_v_carry_out(c_bit0, s87)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7929, 3031, 2671])).
% 36.00/23.83 tff(7931,plain,
% 36.00/23.83 (m_counter_cell_v_carry_out(c_bit0, s87)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7930, 2667])).
% 36.00/23.83 tff(7932,plain,
% 36.00/23.83 (((~![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, s87)) | m_counter_cell_v_carry_in(c_bit1, s87))) <=> ((~![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, s87)) | m_counter_cell_v_carry_in(c_bit1, s87))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7933,plain,
% 36.00/23.83 ((~![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, s87)) | m_counter_cell_v_carry_in(c_bit1, s87))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7934,plain,
% 36.00/23.83 ((~![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, s87)) | m_counter_cell_v_carry_in(c_bit1, s87)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7933, 7932])).
% 36.00/23.83 tff(7935,plain,
% 36.00/23.83 (m_counter_cell_v_carry_in(c_bit1, s87)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7934, 3046, 7931])).
% 36.00/23.83 tff(7936,assumption,(m_counter_cell_v_value(c_bit1, s87)), introduced(assumption)).
% 36.00/23.83 tff(7937,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~node2(c_bit1, s87)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~node2(c_bit1, s87)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7938,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~node2(c_bit1, s87)))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7939,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87)) | (~node2(c_bit1, s87))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7938, 7937])).
% 36.00/23.83 tff(7940,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7939, 219, 7936, 7935, 7926])).
% 36.00/23.83 tff(7941,plain,((~node2(c_bit1, s87)) | (~m_counter_cell_v_value(c_bit1, s87))), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(7942,plain,
% 36.00/23.83 (~node2(c_bit1, s87)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7941, 7925])).
% 36.00/23.83 tff(7943,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s87, s88)) | node3(c_bit1, s87, s88))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s87, s88)) | node3(c_bit1, s87, s88))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7944,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s87, s88)) | node3(c_bit1, s87, s88))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7945,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s87, s88)) | node3(c_bit1, s87, s88)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7944, 7943])).
% 36.00/23.83 tff(7946,plain,
% 36.00/23.83 (node3(c_bit1, s87, s88)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7945, 81, 2683])).
% 36.00/23.83 tff(7947,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7948,plain,
% 36.00/23.83 ((node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)) | (~m_counter_cell_v_value(c_bit1, s88))) <=> ((~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7949,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)) | (~m_counter_cell_v_value(c_bit1, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88))))),
% 36.00/23.83 inference(monotonicity,[status(thm)],[7948])).
% 36.00/23.83 tff(7950,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)) | (~m_counter_cell_v_value(c_bit1, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)))),
% 36.00/23.83 inference(transitivity,[status(thm)],[7949, 7947])).
% 36.00/23.83 tff(7951,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s87) | (~node3(c_bit1, s87, s88)) | (~m_counter_cell_v_value(c_bit1, s88)))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7952,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87) | (~node3(c_bit1, s87, s88))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7951, 7950])).
% 36.00/23.83 tff(7953,plain,
% 36.00/23.83 ((~m_counter_cell_v_value(c_bit1, s88)) | node2(c_bit1, s87)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7952, 234, 7946])).
% 36.00/23.83 tff(7954,plain,
% 36.00/23.83 (~m_counter_cell_v_value(c_bit1, s88)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7953, 7942])).
% 36.00/23.83 tff(7955,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s88) | (~node4(c_bit0, s88)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s88) | (~node4(c_bit0, s88)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7956,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s88) | (~node4(c_bit0, s88)))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7957,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s88) | (~node4(c_bit0, s88))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7956, 7955])).
% 36.00/23.83 tff(7958,plain,
% 36.00/23.83 (~node4(c_bit0, s88)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7957, 2875, 2695])).
% 36.00/23.83 tff(7959,assumption,(~node4(c_bit0, s88)), introduced(assumption)).
% 36.00/23.83 tff(7960,assumption,(m_counter_cell_v_carry_out(c_bit0, s88)), introduced(assumption)).
% 36.00/23.83 tff(7961,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7962,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7963,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7962, 7961])).
% 36.00/23.83 tff(7964,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7963, 2887, 7960, 7959])).
% 36.00/23.83 tff(7965,plain,((~m_counter_cell_v_carry_out(c_bit0, s88)) | node4(c_bit0, s88)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(7966,plain,
% 36.00/23.83 (~m_counter_cell_v_carry_out(c_bit0, s88)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7965, 7958])).
% 36.00/23.83 tff(7967,assumption,(m_counter_cell_v_carry_in(c_bit1, s88)), introduced(assumption)).
% 36.00/23.83 tff(7968,assumption,(~m_counter_cell_v_carry_out(c_bit0, s88)), introduced(assumption)).
% 36.00/23.83 tff(7969,plain,
% 36.00/23.83 (((~![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, s88)) | m_counter_cell_v_carry_out(c_bit0, s88))) <=> ((~![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, s88)) | m_counter_cell_v_carry_out(c_bit0, s88))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7970,plain,
% 36.00/23.83 ((~![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, s88)) | m_counter_cell_v_carry_out(c_bit0, s88))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7971,plain,
% 36.00/23.83 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s88)) | m_counter_cell_v_carry_out(c_bit0, s88)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7970, 7969])).
% 36.00/23.83 tff(7972,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7971, 2901, 7968, 7967])).
% 36.00/23.83 tff(7973,plain,(m_counter_cell_v_carry_out(c_bit0, s88) | (~m_counter_cell_v_carry_in(c_bit1, s88))), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(7974,plain,
% 36.00/23.83 (~m_counter_cell_v_carry_in(c_bit1, s88)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7973, 7966])).
% 36.00/23.83 tff(7975,assumption,(~m_counter_cell_v_value(c_bit1, s88)), introduced(assumption)).
% 36.00/23.83 tff(7976,assumption,(node2(c_bit1, s88)), introduced(assumption)).
% 36.00/23.83 tff(7977,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s88) | m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88)))) <=> ((~![I0: $i, X: $i] : (m_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, s88) | m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7978,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s88) | m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88)))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7979,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s88) | m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7978, 7977])).
% 36.00/23.83 tff(7980,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7979, 3291, 7976, 7975, 7974])).
% 36.00/23.83 tff(7981,plain,(m_counter_cell_v_value(c_bit1, s88) | (~node2(c_bit1, s88))), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(7982,plain,
% 36.00/23.83 (~node2(c_bit1, s88)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7981, 7954])).
% 36.00/23.83 tff(7983,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s88, s89)) | node3(c_bit1, s88, s89))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s88, s89)) | node3(c_bit1, s88, s89))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7984,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s88, s89)) | node3(c_bit1, s88, s89))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7985,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s88, s89)) | node3(c_bit1, s88, s89)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7984, 7983])).
% 36.00/23.83 tff(7986,plain,
% 36.00/23.83 (node3(c_bit1, s88, s89)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7985, 81, 2714])).
% 36.00/23.83 tff(7987,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7988,plain,
% 36.00/23.83 ((node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)) | (~m_counter_cell_v_value(c_bit1, s89))) <=> ((~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7989,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)) | (~m_counter_cell_v_value(c_bit1, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89))))),
% 36.00/23.83 inference(monotonicity,[status(thm)],[7988])).
% 36.00/23.83 tff(7990,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)) | (~m_counter_cell_v_value(c_bit1, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)))),
% 36.00/23.83 inference(transitivity,[status(thm)],[7989, 7987])).
% 36.00/23.83 tff(7991,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s88) | (~node3(c_bit1, s88, s89)) | (~m_counter_cell_v_value(c_bit1, s89)))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7992,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88) | (~node3(c_bit1, s88, s89))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7991, 7990])).
% 36.00/23.83 tff(7993,plain,
% 36.00/23.83 ((~m_counter_cell_v_value(c_bit1, s89)) | node2(c_bit1, s88)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7992, 234, 7986])).
% 36.00/23.83 tff(7994,plain,
% 36.00/23.83 (~m_counter_cell_v_value(c_bit1, s89)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7993, 7982])).
% 36.00/23.83 tff(7995,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(7996,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(7997,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | (~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[7996, 7995])).
% 36.00/23.83 tff(7998,plain,
% 36.00/23.83 ((~m_counter_cell_v_value(c_bit0, s89)) | m_counter_cell_v_carry_out(c_bit0, s89)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7997, 3031, 2730])).
% 36.00/23.83 tff(7999,plain,
% 36.00/23.83 (m_counter_cell_v_carry_out(c_bit0, s89)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[7998, 2726])).
% 36.00/23.83 tff(8000,assumption,(~m_counter_cell_v_carry_in(c_bit1, s89)), introduced(assumption)).
% 36.00/23.83 tff(8001,assumption,(m_counter_cell_v_carry_out(c_bit0, s89)), introduced(assumption)).
% 36.00/23.83 tff(8002,plain,
% 36.00/23.83 (((~![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, s89)) | m_counter_cell_v_carry_in(c_bit1, s89))) <=> ((~![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, s89)) | m_counter_cell_v_carry_in(c_bit1, s89))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8003,plain,
% 36.00/23.83 ((~![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, s89)) | m_counter_cell_v_carry_in(c_bit1, s89))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(8004,plain,
% 36.00/23.83 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s89)) | m_counter_cell_v_carry_in(c_bit1, s89)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[8003, 8002])).
% 36.00/23.83 tff(8005,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8004, 3046, 8001, 8000])).
% 36.00/23.83 tff(8006,plain,((~m_counter_cell_v_carry_out(c_bit0, s89)) | m_counter_cell_v_carry_in(c_bit1, s89)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(8007,plain,
% 36.00/23.83 (m_counter_cell_v_carry_in(c_bit1, s89)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8006, 7999])).
% 36.00/23.83 tff(8008,assumption,(node1(c_bit1, s89)), introduced(assumption)).
% 36.00/23.83 tff(8009,assumption,(~m_counter_cell_v_value(c_bit1, s89)), introduced(assumption)).
% 36.00/23.83 tff(8010,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8011,plain,
% 36.00/23.83 (((~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8012,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89))))),
% 36.00/23.83 inference(monotonicity,[status(thm)],[8011])).
% 36.00/23.83 tff(8013,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89)))),
% 36.00/23.83 inference(transitivity,[status(thm)],[8012, 8010])).
% 36.00/23.83 tff(8014,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s89)) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(8015,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s89)) | m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[8014, 8013])).
% 36.00/23.83 tff(8016,plain,
% 36.00/23.83 ($false),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8015, 170, 8009, 8008, 8007])).
% 36.00/23.83 tff(8017,plain,(m_counter_cell_v_value(c_bit1, s89) | (~node1(c_bit1, s89))), inference(lemma,lemma(discharge,[]))).
% 36.00/23.83 tff(8018,plain,
% 36.00/23.83 (~node1(c_bit1, s89)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8017, 7994])).
% 36.00/23.83 tff(8019,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s89, s90)) | node3(c_bit1, s89, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s89, s90)) | node3(c_bit1, s89, s90))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8020,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s89, s90)) | node3(c_bit1, s89, s90))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(8021,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s89, s90)) | node3(c_bit1, s89, s90)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[8020, 8019])).
% 36.00/23.83 tff(8022,plain,
% 36.00/23.83 (node3(c_bit1, s89, s90)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8021, 81, 2742])).
% 36.00/23.83 tff(8023,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8024,plain,
% 36.00/23.83 ((node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)) | m_counter_cell_v_value(c_bit1, s90)) <=> (m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8025,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)) | m_counter_cell_v_value(c_bit1, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90))))),
% 36.00/23.83 inference(monotonicity,[status(thm)],[8024])).
% 36.00/23.83 tff(8026,plain,
% 36.00/23.83 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)) | m_counter_cell_v_value(c_bit1, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)))),
% 36.00/23.83 inference(transitivity,[status(thm)],[8025, 8023])).
% 36.00/23.83 tff(8027,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s89) | (~node3(c_bit1, s89, s90)) | m_counter_cell_v_value(c_bit1, s90))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(8028,plain,
% 36.00/23.83 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89) | (~node3(c_bit1, s89, s90))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[8027, 8026])).
% 36.00/23.83 tff(8029,plain,
% 36.00/23.83 (m_counter_cell_v_value(c_bit1, s90) | node1(c_bit1, s89)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8028, 199, 8022])).
% 36.00/23.83 tff(8030,plain,
% 36.00/23.83 (m_counter_cell_v_value(c_bit1, s90)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8029, 8018])).
% 36.00/23.83 tff(8031,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s90) | (~node4(c_bit0, s90)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s90) | (~node4(c_bit0, s90)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8032,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s90) | (~node4(c_bit0, s90)))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(8033,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s90) | (~node4(c_bit0, s90))),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[8032, 8031])).
% 36.00/23.83 tff(8034,plain,
% 36.00/23.83 (~node4(c_bit0, s90)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8033, 2875, 2754])).
% 36.00/23.83 tff(8035,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s90)) | node4(c_bit0, s90))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s90)) | node4(c_bit0, s90))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8036,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s90)) | node4(c_bit0, s90))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(8037,plain,
% 36.00/23.83 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s90)) | node4(c_bit0, s90)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[8036, 8035])).
% 36.00/23.83 tff(8038,plain,
% 36.00/23.83 (~m_counter_cell_v_carry_out(c_bit0, s90)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8037, 2887, 8034])).
% 36.00/23.83 tff(8039,plain,
% 36.00/23.83 (((~![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, s90)) | m_counter_cell_v_carry_out(c_bit0, s90))) <=> ((~![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, s90)) | m_counter_cell_v_carry_out(c_bit0, s90))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8040,plain,
% 36.00/23.83 ((~![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, s90)) | m_counter_cell_v_carry_out(c_bit0, s90))),
% 36.00/23.83 inference(quant_inst,[status(thm)],[])).
% 36.00/23.83 tff(8041,plain,
% 36.00/23.83 ((~![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, s90)) | m_counter_cell_v_carry_out(c_bit0, s90)),
% 36.00/23.83 inference(modus_ponens,[status(thm)],[8040, 8039])).
% 36.00/23.83 tff(8042,plain,
% 36.00/23.83 (~m_counter_cell_v_carry_in(c_bit1, s90)),
% 36.00/23.83 inference(unit_resolution,[status(thm)],[8041, 2901, 8038])).
% 36.00/23.83 tff(8043,plain,
% 36.00/23.83 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.83 tff(8044,plain,
% 36.00/23.83 (((~node1(c_bit1, s90)) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90))) <=> (m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90)))),
% 36.00/23.83 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8045,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s90)) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90))))),
% 36.00/23.84 inference(monotonicity,[status(thm)],[8044])).
% 36.00/23.84 tff(8046,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s90)) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90)))),
% 36.00/23.84 inference(transitivity,[status(thm)],[8045, 8043])).
% 36.00/23.84 tff(8047,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s90)) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8048,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s90) | (~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90))),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8047, 8046])).
% 36.00/23.84 tff(8049,plain,
% 36.00/23.84 ((~m_counter_cell_v_value(c_bit1, s90)) | (~node1(c_bit1, s90))),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8048, 3359, 8042])).
% 36.00/23.84 tff(8050,plain,
% 36.00/23.84 (~node1(c_bit1, s90)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8049, 8030])).
% 36.00/23.84 tff(8051,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s90, s91)) | node3(c_bit1, s90, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s90, s91)) | node3(c_bit1, s90, s91))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8052,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s90, s91)) | node3(c_bit1, s90, s91))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8053,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s90, s91)) | node3(c_bit1, s90, s91)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8052, 8051])).
% 36.00/23.84 tff(8054,plain,
% 36.00/23.84 (node3(c_bit1, s90, s91)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8053, 81, 2771])).
% 36.00/23.84 tff(8055,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8056,plain,
% 36.00/23.84 ((node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)) | m_counter_cell_v_value(c_bit1, s91)) <=> (m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8057,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)) | m_counter_cell_v_value(c_bit1, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91))))),
% 36.00/23.84 inference(monotonicity,[status(thm)],[8056])).
% 36.00/23.84 tff(8058,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)) | m_counter_cell_v_value(c_bit1, s91))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)))),
% 36.00/23.84 inference(transitivity,[status(thm)],[8057, 8055])).
% 36.00/23.84 tff(8059,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s90) | (~node3(c_bit1, s90, s91)) | m_counter_cell_v_value(c_bit1, s91))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8060,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90) | (~node3(c_bit1, s90, s91))),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8059, 8058])).
% 36.00/23.84 tff(8061,plain,
% 36.00/23.84 (m_counter_cell_v_value(c_bit1, s91) | node1(c_bit1, s90)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8060, 199, 8054])).
% 36.00/23.84 tff(8062,plain,
% 36.00/23.84 (m_counter_cell_v_value(c_bit1, s91)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8061, 8050])).
% 36.00/23.84 tff(8063,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8064,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8065,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | (~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8064, 8063])).
% 36.00/23.84 tff(8066,plain,
% 36.00/23.84 ((~m_counter_cell_v_value(c_bit0, s91)) | m_counter_cell_v_carry_out(c_bit0, s91)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8065, 3031, 2785])).
% 36.00/23.84 tff(8067,plain,
% 36.00/23.84 (m_counter_cell_v_carry_out(c_bit0, s91)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8066, 2783])).
% 36.00/23.84 tff(8068,plain,
% 36.00/23.84 (((~![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, s91)) | m_counter_cell_v_carry_in(c_bit1, s91))) <=> ((~![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, s91)) | m_counter_cell_v_carry_in(c_bit1, s91))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8069,plain,
% 36.00/23.84 ((~![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, s91)) | m_counter_cell_v_carry_in(c_bit1, s91))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8070,plain,
% 36.00/23.84 ((~![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, s91)) | m_counter_cell_v_carry_in(c_bit1, s91)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8069, 8068])).
% 36.00/23.84 tff(8071,plain,
% 36.00/23.84 (m_counter_cell_v_carry_in(c_bit1, s91)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8070, 3046, 8067])).
% 36.00/23.84 tff(8072,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s91)) | (~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s91)) | (~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8073,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s91)) | (~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91)))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8074,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s91)) | (~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91))),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8073, 8072])).
% 36.00/23.84 tff(8075,plain,
% 36.00/23.84 ((~m_counter_cell_v_value(c_bit1, s91)) | (~node2(c_bit1, s91))),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8074, 219, 8071])).
% 36.00/23.84 tff(8076,plain,
% 36.00/23.84 (~node2(c_bit1, s91)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8075, 8062])).
% 36.00/23.84 tff(8077,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s91, s92)) | node3(c_bit1, s91, s92))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s91, s92)) | node3(c_bit1, s91, s92))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8078,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s91, s92)) | node3(c_bit1, s91, s92))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8079,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s91, s92)) | node3(c_bit1, s91, s92)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8078, 8077])).
% 36.00/23.84 tff(8080,plain,
% 36.00/23.84 (node3(c_bit1, s91, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8079, 81, 2797])).
% 36.00/23.84 tff(8081,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8082,plain,
% 36.00/23.84 ((node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)) | (~m_counter_cell_v_value(c_bit1, s92))) <=> ((~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8083,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)) | (~m_counter_cell_v_value(c_bit1, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92))))),
% 36.00/23.84 inference(monotonicity,[status(thm)],[8082])).
% 36.00/23.84 tff(8084,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)) | (~m_counter_cell_v_value(c_bit1, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)))),
% 36.00/23.84 inference(transitivity,[status(thm)],[8083, 8081])).
% 36.00/23.84 tff(8085,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s91) | (~node3(c_bit1, s91, s92)) | (~m_counter_cell_v_value(c_bit1, s92)))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8086,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91) | (~node3(c_bit1, s91, s92))),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8085, 8084])).
% 36.00/23.84 tff(8087,plain,
% 36.00/23.84 ((~m_counter_cell_v_value(c_bit1, s92)) | node2(c_bit1, s91)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8086, 234, 8080])).
% 36.00/23.84 tff(8088,plain,
% 36.00/23.84 (~m_counter_cell_v_value(c_bit1, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8087, 8076])).
% 36.00/23.84 tff(8089,assumption,(~m_counter_cell_v_value(c_bit1, s92)), introduced(assumption)).
% 36.00/23.84 tff(8090,assumption,(node1(c_bit1, s93)), introduced(assumption)).
% 36.00/23.84 tff(8091,assumption,(~m_counter_cell_v_carry_in(c_bit1, s92)), introduced(assumption)).
% 36.00/23.84 tff(8092,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s92) | m_counter_cell_v_value(c_bit1, s92) | (~node2(c_bit1, s92)))) <=> ((~![I0: $i, X: $i] : (m_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, s92) | m_counter_cell_v_value(c_bit1, s92) | (~node2(c_bit1, s92)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8093,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s92) | m_counter_cell_v_value(c_bit1, s92) | (~node2(c_bit1, s92)))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8094,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s92) | m_counter_cell_v_value(c_bit1, s92) | (~node2(c_bit1, s92))),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8093, 8092])).
% 36.00/23.84 tff(8095,plain,
% 36.00/23.84 (m_counter_cell_v_carry_in(c_bit1, s92) | (~node2(c_bit1, s92))),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8094, 3291, 8089])).
% 36.00/23.84 tff(8096,plain,
% 36.00/23.84 (~node2(c_bit1, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8095, 8091])).
% 36.00/23.84 tff(8097,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s92, s93)) | node3(c_bit1, s92, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s92, s93)) | node3(c_bit1, s92, s93))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8098,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s92, s93)) | node3(c_bit1, s92, s93))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8099,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s92, s93)) | node3(c_bit1, s92, s93)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8098, 8097])).
% 36.00/23.84 tff(8100,plain,
% 36.00/23.84 (node3(c_bit1, s92, s93)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8099, 81, 2828])).
% 36.00/23.84 tff(8101,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8102,plain,
% 36.00/23.84 ((node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | (~m_counter_cell_v_value(c_bit1, s93))) <=> ((~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8103,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | (~m_counter_cell_v_value(c_bit1, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93))))),
% 36.00/23.84 inference(monotonicity,[status(thm)],[8102])).
% 36.00/23.84 tff(8104,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | (~m_counter_cell_v_value(c_bit1, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 36.00/23.84 inference(transitivity,[status(thm)],[8103, 8101])).
% 36.00/23.84 tff(8105,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | (~m_counter_cell_v_value(c_bit1, s93)))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8106,plain,
% 36.00/23.84 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92) | (~node3(c_bit1, s92, s93))),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8105, 8104])).
% 36.00/23.84 tff(8107,plain,
% 36.00/23.84 ((~m_counter_cell_v_value(c_bit1, s93)) | node2(c_bit1, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8106, 234, 8100])).
% 36.00/23.84 tff(8108,plain,
% 36.00/23.84 (~m_counter_cell_v_value(c_bit1, s93)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8107, 8096])).
% 36.00/23.84 tff(8109,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8110,plain,
% 36.00/23.84 (((~node1(c_bit1, s93)) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8111,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s93)) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93))))),
% 36.00/23.84 inference(monotonicity,[status(thm)],[8110])).
% 36.00/23.84 tff(8112,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s93)) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93)))),
% 36.00/23.84 inference(transitivity,[status(thm)],[8111, 8109])).
% 36.00/23.84 tff(8113,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s93)) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8114,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93) | (~node1(c_bit1, s93))),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8113, 8112])).
% 36.00/23.84 tff(8115,plain,
% 36.00/23.84 ((~m_counter_cell_v_carry_in(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s93)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8114, 170, 8090])).
% 36.00/23.84 tff(8116,plain,
% 36.00/23.84 (~m_counter_cell_v_carry_in(c_bit1, s93)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8115, 8108])).
% 36.00/23.84 tff(8117,plain,
% 36.00/23.84 (((~![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, s93)) | m_counter_cell_v_carry_in(c_bit1, s93))) <=> ((~![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, s93)) | m_counter_cell_v_carry_in(c_bit1, s93))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8118,plain,
% 36.00/23.84 ((~![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, s93)) | m_counter_cell_v_carry_in(c_bit1, s93))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8119,plain,
% 36.00/23.84 ((~![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, s93)) | m_counter_cell_v_carry_in(c_bit1, s93)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8118, 8117])).
% 36.00/23.84 tff(8120,plain,
% 36.00/23.84 (~m_counter_cell_v_carry_out(c_bit0, s93)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8119, 3046, 8116])).
% 36.00/23.84 tff(8121,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8122,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8123,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | (~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8122, 8121])).
% 36.00/23.84 tff(8124,plain,
% 36.00/23.84 ((~m_counter_cell_v_value(c_bit0, s93)) | m_counter_cell_v_carry_out(c_bit0, s93)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8123, 3031, 2844])).
% 36.00/23.84 tff(8125,plain,
% 36.00/23.84 (~m_counter_cell_v_value(c_bit0, s93)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8124, 8120])).
% 36.00/23.84 tff(8126,plain,
% 36.00/23.84 (node1(c_bit0, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[2839, 8125])).
% 36.00/23.84 tff(8127,plain,
% 36.00/23.84 (m_counter_cell_v_value(c_bit0, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[2820, 8126])).
% 36.00/23.84 tff(8128,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s92)) | (~m_counter_cell_v_value(c_bit0, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s92)) | (~m_counter_cell_v_value(c_bit0, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8129,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s92)) | (~m_counter_cell_v_value(c_bit0, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8130,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | (~m_counter_cell_v_value(c_bit0, s92)) | m_counter_cell_v_carry_out(c_bit0, s92)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8129, 8128])).
% 36.00/23.84 tff(8131,plain,
% 36.00/23.84 ((~m_counter_cell_v_value(c_bit0, s92)) | m_counter_cell_v_carry_out(c_bit0, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8130, 3031, 2813])).
% 36.00/23.84 tff(8132,plain,
% 36.00/23.84 (m_counter_cell_v_carry_out(c_bit0, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8131, 8127])).
% 36.00/23.84 tff(8133,plain,
% 36.00/23.84 (((~![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, s92)) | m_counter_cell_v_carry_in(c_bit1, s92))) <=> ((~![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, s92)) | m_counter_cell_v_carry_in(c_bit1, s92))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8134,plain,
% 36.00/23.84 ((~![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, s92)) | m_counter_cell_v_carry_in(c_bit1, s92))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8135,plain,
% 36.00/23.84 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s92)) | m_counter_cell_v_carry_in(c_bit1, s92)),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8134, 8133])).
% 36.00/23.84 tff(8136,plain,
% 36.00/23.84 ($false),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8135, 3046, 8132, 8091])).
% 36.00/23.84 tff(8137,plain,(m_counter_cell_v_carry_in(c_bit1, s92) | (~node1(c_bit1, s93)) | m_counter_cell_v_value(c_bit1, s92)), inference(lemma,lemma(discharge,[]))).
% 36.00/23.84 tff(8138,plain,
% 36.00/23.84 (m_counter_cell_v_carry_in(c_bit1, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8137, 8089, 8090])).
% 36.00/23.84 tff(8139,assumption,(node1(c_bit1, s92)), introduced(assumption)).
% 36.00/23.84 tff(8140,assumption,(m_counter_cell_v_carry_in(c_bit1, s92)), introduced(assumption)).
% 36.00/23.84 tff(8141,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92) | (~node1(c_bit1, s92)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92) | (~node1(c_bit1, s92)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8142,plain,
% 36.00/23.84 (((~node1(c_bit1, s92)) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92) | (~node1(c_bit1, s92)))),
% 36.00/23.84 inference(rewrite,[status(thm)],[])).
% 36.00/23.84 tff(8143,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s92)) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92) | (~node1(c_bit1, s92))))),
% 36.00/23.84 inference(monotonicity,[status(thm)],[8142])).
% 36.00/23.84 tff(8144,plain,
% 36.00/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s92)) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92) | (~node1(c_bit1, s92)))),
% 36.00/23.84 inference(transitivity,[status(thm)],[8143, 8141])).
% 36.00/23.84 tff(8145,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s92)) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92))),
% 36.00/23.84 inference(quant_inst,[status(thm)],[])).
% 36.00/23.84 tff(8146,plain,
% 36.00/23.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92) | (~node1(c_bit1, s92))),
% 36.00/23.84 inference(modus_ponens,[status(thm)],[8145, 8144])).
% 36.00/23.84 tff(8147,plain,
% 36.00/23.84 ($false),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8146, 170, 8089, 8140, 8139])).
% 36.00/23.84 tff(8148,plain,((~node1(c_bit1, s92)) | m_counter_cell_v_value(c_bit1, s92) | (~m_counter_cell_v_carry_in(c_bit1, s92))), inference(lemma,lemma(discharge,[]))).
% 36.00/23.84 tff(8149,plain,
% 36.00/23.84 (~node1(c_bit1, s92)),
% 36.00/23.84 inference(unit_resolution,[status(thm)],[8148, 8138, 8089])).
% 36.00/23.84 tff(8150,plain,
% 36.00/23.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s93) | node1(c_bit1, s92) | (~node3(c_bit1, s92, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s93) | node1(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 36.04/23.84 inference(rewrite,[status(thm)],[])).
% 36.04/23.84 tff(8151,plain,
% 36.04/23.84 ((node1(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | m_counter_cell_v_value(c_bit1, s93)) <=> (m_counter_cell_v_value(c_bit1, s93) | node1(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 36.04/23.84 inference(rewrite,[status(thm)],[])).
% 36.04/23.84 tff(8152,plain,
% 36.04/23.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | m_counter_cell_v_value(c_bit1, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s93) | node1(c_bit1, s92) | (~node3(c_bit1, s92, s93))))),
% 36.04/23.84 inference(monotonicity,[status(thm)],[8151])).
% 36.04/23.84 tff(8153,plain,
% 36.04/23.84 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | m_counter_cell_v_value(c_bit1, s93))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s93) | node1(c_bit1, s92) | (~node3(c_bit1, s92, s93)))),
% 36.04/23.84 inference(transitivity,[status(thm)],[8152, 8150])).
% 36.04/23.84 tff(8154,plain,
% 36.04/23.84 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s92) | (~node3(c_bit1, s92, s93)) | m_counter_cell_v_value(c_bit1, s93))),
% 36.04/23.84 inference(quant_inst,[status(thm)],[])).
% 36.04/23.84 tff(8155,plain,
% 36.04/23.84 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s93) | node1(c_bit1, s92) | (~node3(c_bit1, s92, s93))),
% 36.04/23.84 inference(modus_ponens,[status(thm)],[8154, 8153])).
% 36.04/23.84 tff(8156,plain,
% 36.04/23.84 (m_counter_cell_v_value(c_bit1, s93) | node1(c_bit1, s92)),
% 36.04/23.84 inference(unit_resolution,[status(thm)],[8155, 199, 8100])).
% 36.04/23.84 tff(8157,plain,
% 36.04/23.84 (m_counter_cell_v_value(c_bit1, s93)),
% 36.04/23.84 inference(unit_resolution,[status(thm)],[8156, 8149])).
% 36.04/23.84 tff(8158,plain,
% 36.04/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)) | (~node1(c_bit1, s93)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)) | (~node1(c_bit1, s93)))),
% 36.04/23.84 inference(rewrite,[status(thm)],[])).
% 36.04/23.84 tff(8159,plain,
% 36.04/23.84 (((~node1(c_bit1, s93)) | m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93))) <=> (m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)) | (~node1(c_bit1, s93)))),
% 36.04/23.84 inference(rewrite,[status(thm)],[])).
% 36.04/23.84 tff(8160,plain,
% 36.04/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s93)) | m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)) | (~node1(c_bit1, s93))))),
% 36.04/23.84 inference(monotonicity,[status(thm)],[8159])).
% 36.04/23.84 tff(8161,plain,
% 36.04/23.84 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s93)) | m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)) | (~node1(c_bit1, s93)))),
% 36.04/23.84 inference(transitivity,[status(thm)],[8160, 8158])).
% 36.04/23.84 tff(8162,plain,
% 36.04/23.84 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s93)) | m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8163,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93)) | (~node1(c_bit1, s93))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8162, 8161])).
% 36.04/23.85 tff(8164,plain,
% 36.04/23.85 (m_counter_cell_v_carry_in(c_bit1, s93) | (~m_counter_cell_v_value(c_bit1, s93))),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8163, 3359, 8090])).
% 36.04/23.85 tff(8165,plain,
% 36.04/23.85 (m_counter_cell_v_carry_in(c_bit1, s93)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8164, 8157])).
% 36.04/23.85 tff(8166,plain,
% 36.04/23.85 (((~![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, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))) <=> ((~![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, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8167,plain,
% 36.04/23.85 ((~![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, s93)) | m_counter_cell_v_carry_out(c_bit0, s93))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8168,plain,
% 36.04/23.85 ((~![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, s93)) | m_counter_cell_v_carry_out(c_bit0, s93)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8167, 8166])).
% 36.04/23.85 tff(8169,plain,
% 36.04/23.85 (m_counter_cell_v_carry_out(c_bit0, s93)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8168, 2901, 8165])).
% 36.04/23.85 tff(8170,assumption,(~node4(c_bit0, s93)), introduced(assumption)).
% 36.04/23.85 tff(8171,assumption,(m_counter_cell_v_carry_out(c_bit0, s93)), introduced(assumption)).
% 36.04/23.85 tff(8172,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s93)) | node4(c_bit0, s93))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s93)) | node4(c_bit0, s93))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8173,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s93)) | node4(c_bit0, s93))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8174,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s93)) | node4(c_bit0, s93)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8173, 8172])).
% 36.04/23.85 tff(8175,plain,
% 36.04/23.85 ($false),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8174, 2887, 8171, 8170])).
% 36.04/23.85 tff(8176,plain,((~m_counter_cell_v_carry_out(c_bit0, s93)) | node4(c_bit0, s93)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.85 tff(8177,plain,
% 36.04/23.85 (node4(c_bit0, s93)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8176, 8169])).
% 36.04/23.85 tff(8178,assumption,(~m_counter_cell_v_carry_out(c_bit0, s92)), introduced(assumption)).
% 36.04/23.85 tff(8179,plain,
% 36.04/23.85 (((~![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, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))) <=> ((~![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, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8180,plain,
% 36.04/23.85 ((~![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, s92)) | m_counter_cell_v_carry_out(c_bit0, s92))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8181,plain,
% 36.04/23.85 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s92)) | m_counter_cell_v_carry_out(c_bit0, s92)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8180, 8179])).
% 36.04/23.85 tff(8182,plain,
% 36.04/23.85 ($false),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8181, 2901, 8178, 8140])).
% 36.04/23.85 tff(8183,plain,(m_counter_cell_v_carry_out(c_bit0, s92) | (~m_counter_cell_v_carry_in(c_bit1, s92))), inference(lemma,lemma(discharge,[]))).
% 36.04/23.85 tff(8184,plain,
% 36.04/23.85 (m_counter_cell_v_carry_out(c_bit0, s92)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8183, 8138])).
% 36.04/23.85 tff(8185,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s92)) | node4(c_bit0, s92))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s92)) | node4(c_bit0, s92))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8186,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s92)) | node4(c_bit0, s92))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8187,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s92)) | node4(c_bit0, s92)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8186, 8185])).
% 36.04/23.85 tff(8188,plain,
% 36.04/23.85 (node4(c_bit0, s92)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8187, 2887, 8184])).
% 36.04/23.85 tff(8189,assumption,(node4(c_bit0, s92)), introduced(assumption)).
% 36.04/23.85 tff(8190,assumption,(~m_counter_cell_v_value(c_bit0, s92)), introduced(assumption)).
% 36.04/23.85 tff(8191,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8192,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92)))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8193,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8192, 8191])).
% 36.04/23.85 tff(8194,plain,
% 36.04/23.85 ($false),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8193, 2875, 8190, 8189])).
% 36.04/23.85 tff(8195,plain,(m_counter_cell_v_value(c_bit0, s92) | (~node4(c_bit0, s92))), inference(lemma,lemma(discharge,[]))).
% 36.04/23.85 tff(8196,plain,
% 36.04/23.85 (m_counter_cell_v_value(c_bit0, s92)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8195, 8188])).
% 36.04/23.85 tff(8197,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s92)) | (~m_counter_cell_v_value(c_bit0, s92)) | (~node2(c_bit0, s92)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s92)) | (~m_counter_cell_v_value(c_bit0, s92)) | (~node2(c_bit0, s92)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8198,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s92)) | (~m_counter_cell_v_value(c_bit0, s92)) | (~node2(c_bit0, s92)))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8199,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s92)) | (~m_counter_cell_v_value(c_bit0, s92)) | (~node2(c_bit0, s92))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8198, 8197])).
% 36.04/23.85 tff(8200,plain,
% 36.04/23.85 ((~m_counter_cell_v_value(c_bit0, s92)) | (~node2(c_bit0, s92))),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8199, 219, 2813])).
% 36.04/23.85 tff(8201,plain,
% 36.04/23.85 (~node2(c_bit0, s92)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8200, 8196])).
% 36.04/23.85 tff(8202,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s93)) | node2(c_bit0, s92) | (~node3(c_bit0, s92, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s93)) | node2(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8203,plain,
% 36.04/23.85 ((node2(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | (~m_counter_cell_v_value(c_bit0, s93))) <=> ((~m_counter_cell_v_value(c_bit0, s93)) | node2(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8204,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | (~m_counter_cell_v_value(c_bit0, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s93)) | node2(c_bit0, s92) | (~node3(c_bit0, s92, s93))))),
% 36.04/23.85 inference(monotonicity,[status(thm)],[8203])).
% 36.04/23.85 tff(8205,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | (~m_counter_cell_v_value(c_bit0, s93)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s93)) | node2(c_bit0, s92) | (~node3(c_bit0, s92, s93)))),
% 36.04/23.85 inference(transitivity,[status(thm)],[8204, 8202])).
% 36.04/23.85 tff(8206,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s92) | (~node3(c_bit0, s92, s93)) | (~m_counter_cell_v_value(c_bit0, s93)))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8207,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s93)) | node2(c_bit0, s92) | (~node3(c_bit0, s92, s93))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8206, 8205])).
% 36.04/23.85 tff(8208,plain,
% 36.04/23.85 ((~m_counter_cell_v_value(c_bit0, s93)) | node2(c_bit0, s92)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8207, 234, 2832])).
% 36.04/23.85 tff(8209,plain,
% 36.04/23.85 (~m_counter_cell_v_value(c_bit0, s93)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8208, 8201])).
% 36.04/23.85 tff(8210,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s93) | (~node4(c_bit0, s93)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s93) | (~node4(c_bit0, s93)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8211,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s93) | (~node4(c_bit0, s93)))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8212,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s93) | (~node4(c_bit0, s93))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8211, 8210])).
% 36.04/23.85 tff(8213,plain,
% 36.04/23.85 ($false),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8212, 2875, 8209, 8177])).
% 36.04/23.85 tff(8214,plain,(m_counter_cell_v_value(c_bit1, s92) | (~node1(c_bit1, s93))), inference(lemma,lemma(discharge,[]))).
% 36.04/23.85 tff(8215,plain,
% 36.04/23.85 (~node1(c_bit1, s93)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8214, 8088])).
% 36.04/23.85 tff(8216,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s93, s94)) | node3(c_bit1, s93, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s93, s94)) | node3(c_bit1, s93, s94))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8217,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s93, s94)) | node3(c_bit1, s93, s94))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8218,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s93, s94)) | node3(c_bit1, s93, s94)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8217, 8216])).
% 36.04/23.85 tff(8219,plain,
% 36.04/23.85 (node3(c_bit1, s93, s94)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8218, 81, 2856])).
% 36.04/23.85 tff(8220,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8221,plain,
% 36.04/23.85 ((node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)) | m_counter_cell_v_value(c_bit1, s94)) <=> (m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8222,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)) | m_counter_cell_v_value(c_bit1, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94))))),
% 36.04/23.85 inference(monotonicity,[status(thm)],[8221])).
% 36.04/23.85 tff(8223,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)) | m_counter_cell_v_value(c_bit1, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)))),
% 36.04/23.85 inference(transitivity,[status(thm)],[8222, 8220])).
% 36.04/23.85 tff(8224,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s93) | (~node3(c_bit1, s93, s94)) | m_counter_cell_v_value(c_bit1, s94))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8225,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93) | (~node3(c_bit1, s93, s94))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8224, 8223])).
% 36.04/23.85 tff(8226,plain,
% 36.04/23.85 (m_counter_cell_v_value(c_bit1, s94) | node1(c_bit1, s93)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8225, 199, 8219])).
% 36.04/23.85 tff(8227,plain,
% 36.04/23.85 (m_counter_cell_v_value(c_bit1, s94)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8226, 8215])).
% 36.04/23.85 tff(8228,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8229,plain,
% 36.04/23.85 (((~node1(c_bit1, s94)) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94))) <=> (m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8230,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s94)) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94))))),
% 36.04/23.85 inference(monotonicity,[status(thm)],[8229])).
% 36.04/23.85 tff(8231,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s94)) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94)))),
% 36.04/23.85 inference(transitivity,[status(thm)],[8230, 8228])).
% 36.04/23.85 tff(8232,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s94)) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8233,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s94) | (~m_counter_cell_v_value(c_bit1, s94)) | (~node1(c_bit1, s94))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8232, 8231])).
% 36.04/23.85 tff(8234,plain,
% 36.04/23.85 ($false),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8233, 3359, 8227, 2907, 67])).
% 36.04/23.85 tff(8235,plain,(~node1(c_bit1, s94)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.85 tff(8236,plain,
% 36.04/23.85 (succ(s94, s95) <=> succ(s94, s95)),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8237,axiom,(succ(s94, s95)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound95')).
% 36.04/23.85 tff(8238,plain,
% 36.04/23.85 (succ(s94, s95)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8237, 8236])).
% 36.04/23.85 tff(8239,plain,
% 36.04/23.85 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s94, s95)) | trans(s94, s95))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s94, s95)) | trans(s94, s95))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8240,plain,
% 36.04/23.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s94, s95)) | trans(s94, s95))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8241,plain,
% 36.04/23.85 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s94, s95)) | trans(s94, s95)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8240, 8239])).
% 36.04/23.85 tff(8242,plain,
% 36.04/23.85 (trans(s94, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8241, 8238, 8])).
% 36.04/23.85 tff(8243,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit1, s94, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit1, s94, s95))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8244,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit1, s94, s95))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8245,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit1, s94, s95)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8244, 8243])).
% 36.04/23.85 tff(8246,plain,
% 36.04/23.85 (node3(c_bit1, s94, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8245, 81, 8242])).
% 36.04/23.85 tff(8247,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8248,plain,
% 36.04/23.85 ((node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | m_counter_cell_v_value(c_bit1, s95)) <=> (m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8249,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | m_counter_cell_v_value(c_bit1, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95))))),
% 36.04/23.85 inference(monotonicity,[status(thm)],[8248])).
% 36.04/23.85 tff(8250,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | m_counter_cell_v_value(c_bit1, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 36.04/23.85 inference(transitivity,[status(thm)],[8249, 8247])).
% 36.04/23.85 tff(8251,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | m_counter_cell_v_value(c_bit1, s95))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8252,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94) | (~node3(c_bit1, s94, s95))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8251, 8250])).
% 36.04/23.85 tff(8253,plain,
% 36.04/23.85 (m_counter_cell_v_value(c_bit1, s95) | node1(c_bit1, s94)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8252, 199, 8246])).
% 36.04/23.85 tff(8254,plain,
% 36.04/23.85 (m_counter_cell_v_value(c_bit1, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8253, 8235])).
% 36.04/23.85 tff(8255,assumption,(~m_counter_cell_v_carry_in(c_bit0, s94)), introduced(assumption)).
% 36.04/23.85 tff(8256,plain,
% 36.04/23.85 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s94)),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8257,plain,
% 36.04/23.85 ($false),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8256, 158, 8255])).
% 36.04/23.85 tff(8258,plain,(m_counter_cell_v_carry_in(c_bit0, s94)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.85 tff(8259,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8260,plain,
% 36.04/23.85 (((~node1(c_bit0, s94)) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8261,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s94)) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94))))),
% 36.04/23.85 inference(monotonicity,[status(thm)],[8260])).
% 36.04/23.85 tff(8262,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s94)) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94)))),
% 36.04/23.85 inference(transitivity,[status(thm)],[8261, 8259])).
% 36.04/23.85 tff(8263,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s94)) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8264,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s94)) | m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8263, 8262])).
% 36.04/23.85 tff(8265,plain,
% 36.04/23.85 (m_counter_cell_v_value(c_bit0, s94) | (~node1(c_bit0, s94))),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8264, 170, 8258])).
% 36.04/23.85 tff(8266,plain,
% 36.04/23.85 (~node1(c_bit0, s94)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8265, 2868])).
% 36.04/23.85 tff(8267,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit0, s94, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit0, s94, s95))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8268,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit0, s94, s95))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8269,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit0, s94, s95)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8268, 8267])).
% 36.04/23.85 tff(8270,plain,
% 36.04/23.85 (node3(c_bit0, s94, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8269, 81, 8242])).
% 36.04/23.85 tff(8271,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8272,plain,
% 36.04/23.85 ((node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | m_counter_cell_v_value(c_bit0, s95)) <=> (m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8273,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | m_counter_cell_v_value(c_bit0, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95))))),
% 36.04/23.85 inference(monotonicity,[status(thm)],[8272])).
% 36.04/23.85 tff(8274,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | m_counter_cell_v_value(c_bit0, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 36.04/23.85 inference(transitivity,[status(thm)],[8273, 8271])).
% 36.04/23.85 tff(8275,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | m_counter_cell_v_value(c_bit0, s95))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8276,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94) | (~node3(c_bit0, s94, s95))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8275, 8274])).
% 36.04/23.85 tff(8277,plain,
% 36.04/23.85 (m_counter_cell_v_value(c_bit0, s95) | node1(c_bit0, s94)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8276, 199, 8270])).
% 36.04/23.85 tff(8278,plain,
% 36.04/23.85 (m_counter_cell_v_value(c_bit0, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8277, 8266])).
% 36.04/23.85 tff(8279,assumption,(~m_counter_cell_v_carry_in(c_bit0, s95)), introduced(assumption)).
% 36.04/23.85 tff(8280,plain,
% 36.04/23.85 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s95)),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8281,plain,
% 36.04/23.85 ($false),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8280, 158, 8279])).
% 36.04/23.85 tff(8282,plain,(m_counter_cell_v_carry_in(c_bit0, s95)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.85 tff(8283,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8284,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8285,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8284, 8283])).
% 36.04/23.85 tff(8286,plain,
% 36.04/23.85 ((~m_counter_cell_v_value(c_bit0, s95)) | m_counter_cell_v_carry_out(c_bit0, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8285, 3031, 8282])).
% 36.04/23.85 tff(8287,plain,
% 36.04/23.85 (m_counter_cell_v_carry_out(c_bit0, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8286, 8278])).
% 36.04/23.85 tff(8288,plain,
% 36.04/23.85 (((~![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, s95)) | m_counter_cell_v_carry_in(c_bit1, s95))) <=> ((~![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, s95)) | m_counter_cell_v_carry_in(c_bit1, s95))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8289,plain,
% 36.04/23.85 ((~![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, s95)) | m_counter_cell_v_carry_in(c_bit1, s95))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8290,plain,
% 36.04/23.85 ((~![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, s95)) | m_counter_cell_v_carry_in(c_bit1, s95)),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8289, 8288])).
% 36.04/23.85 tff(8291,plain,
% 36.04/23.85 (m_counter_cell_v_carry_in(c_bit1, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8290, 3046, 8287])).
% 36.04/23.85 tff(8292,plain,
% 36.04/23.85 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95)))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8293,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95)))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8294,plain,
% 36.04/23.85 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95))),
% 36.04/23.85 inference(modus_ponens,[status(thm)],[8293, 8292])).
% 36.04/23.85 tff(8295,plain,
% 36.04/23.85 ((~m_counter_cell_v_value(c_bit1, s95)) | (~node2(c_bit1, s95))),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8294, 219, 8291])).
% 36.04/23.85 tff(8296,plain,
% 36.04/23.85 (~node2(c_bit1, s95)),
% 36.04/23.85 inference(unit_resolution,[status(thm)],[8295, 8254])).
% 36.04/23.85 tff(8297,plain,
% 36.04/23.85 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit1, s95, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit1, s95, s96))),
% 36.04/23.85 inference(rewrite,[status(thm)],[])).
% 36.04/23.85 tff(8298,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit1, s95, s96))),
% 36.04/23.85 inference(quant_inst,[status(thm)],[])).
% 36.04/23.85 tff(8299,plain,
% 36.04/23.85 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit1, s95, s96)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8298, 8297])).
% 36.04/23.86 tff(8300,plain,
% 36.04/23.86 (node3(c_bit1, s95, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8299, 81, 15])).
% 36.04/23.86 tff(8301,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8302,plain,
% 36.04/23.86 ((node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | (~m_counter_cell_v_value(c_bit1, s96))) <=> ((~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8303,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | (~m_counter_cell_v_value(c_bit1, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96))))),
% 36.04/23.86 inference(monotonicity,[status(thm)],[8302])).
% 36.04/23.86 tff(8304,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | (~m_counter_cell_v_value(c_bit1, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 36.04/23.86 inference(transitivity,[status(thm)],[8303, 8301])).
% 36.04/23.86 tff(8305,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | (~m_counter_cell_v_value(c_bit1, s96)))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8306,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95) | (~node3(c_bit1, s95, s96))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8305, 8304])).
% 36.04/23.86 tff(8307,plain,
% 36.04/23.86 ((~m_counter_cell_v_value(c_bit1, s96)) | node2(c_bit1, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8306, 234, 8300])).
% 36.04/23.86 tff(8308,plain,
% 36.04/23.86 (~m_counter_cell_v_value(c_bit1, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8307, 8296])).
% 36.04/23.86 tff(8309,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s96) | (~node4(c_bit1, s96)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s96) | (~node4(c_bit1, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8310,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s96) | (~node4(c_bit1, s96)))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8311,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s96) | (~node4(c_bit1, s96))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8310, 8309])).
% 36.04/23.86 tff(8312,plain,
% 36.04/23.86 (~node4(c_bit1, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8311, 2875, 8308])).
% 36.04/23.86 tff(8313,assumption,(~node4(c_bit1, s96)), introduced(assumption)).
% 36.04/23.86 tff(8314,assumption,(m_counter_cell_v_carry_out(c_bit1, s96)), introduced(assumption)).
% 36.04/23.86 tff(8315,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8316,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8317,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8316, 8315])).
% 36.04/23.86 tff(8318,plain,
% 36.04/23.86 ($false),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8317, 2887, 8314, 8313])).
% 36.04/23.86 tff(8319,plain,((~m_counter_cell_v_carry_out(c_bit1, s96)) | node4(c_bit1, s96)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.86 tff(8320,plain,
% 36.04/23.86 (~m_counter_cell_v_carry_out(c_bit1, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8319, 8312])).
% 36.04/23.86 tff(8321,assumption,(m_counter_cell_v_carry_in(c_bit2, s96)), introduced(assumption)).
% 36.04/23.86 tff(8322,assumption,(~m_counter_cell_v_carry_out(c_bit1, s96)), introduced(assumption)).
% 36.04/23.86 tff(8323,plain,
% 36.04/23.86 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))) <=> ((~![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, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8324,plain,
% 36.04/23.86 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8325,plain,
% 36.04/23.86 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit1, s96)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8324, 8323])).
% 36.04/23.86 tff(8326,plain,
% 36.04/23.86 ($false),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8325, 3167, 8322, 8321])).
% 36.04/23.86 tff(8327,plain,((~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit1, s96)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.86 tff(8328,plain,
% 36.04/23.86 (~m_counter_cell_v_carry_in(c_bit2, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8327, 8320])).
% 36.04/23.86 tff(8329,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s96) | (~node4(c_bit2, s96)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s96) | (~node4(c_bit2, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8330,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s96) | (~node4(c_bit2, s96)))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8331,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s96) | (~node4(c_bit2, s96))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8330, 8329])).
% 36.04/23.86 tff(8332,plain,
% 36.04/23.86 (~node4(c_bit2, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8331, 3076, 8328])).
% 36.04/23.86 tff(8333,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit2, s96)) | node4(c_bit2, s96))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit2, s96)) | node4(c_bit2, s96))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8334,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit2, s96)) | node4(c_bit2, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8335,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit2, s96)) | node4(c_bit2, s96)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8334, 8333])).
% 36.04/23.86 tff(8336,plain,
% 36.04/23.86 (~m_counter_cell_v_carry_out(c_bit2, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8335, 2887, 8332])).
% 36.04/23.86 tff(8337,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8338,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | ((~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95)))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8339,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | (~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8338, 8337])).
% 36.04/23.86 tff(8340,plain,
% 36.04/23.86 ((~m_counter_cell_v_value(c_bit0, s95)) | (~node2(c_bit0, s95))),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8339, 219, 8282])).
% 36.04/23.86 tff(8341,plain,
% 36.04/23.86 (~node2(c_bit0, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8340, 8278])).
% 36.04/23.86 tff(8342,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit0, s95, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit0, s95, s96))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8343,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit0, s95, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8344,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit0, s95, s96)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8343, 8342])).
% 36.04/23.86 tff(8345,plain,
% 36.04/23.86 (node3(c_bit0, s95, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8344, 81, 15])).
% 36.04/23.86 tff(8346,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8347,plain,
% 36.04/23.86 ((node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | (~m_counter_cell_v_value(c_bit0, s96))) <=> ((~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8348,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | (~m_counter_cell_v_value(c_bit0, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96))))),
% 36.04/23.86 inference(monotonicity,[status(thm)],[8347])).
% 36.04/23.86 tff(8349,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | (~m_counter_cell_v_value(c_bit0, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 36.04/23.86 inference(transitivity,[status(thm)],[8348, 8346])).
% 36.04/23.86 tff(8350,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | (~m_counter_cell_v_value(c_bit0, s96)))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8351,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95) | (~node3(c_bit0, s95, s96))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8350, 8349])).
% 36.04/23.86 tff(8352,plain,
% 36.04/23.86 ((~m_counter_cell_v_value(c_bit0, s96)) | node2(c_bit0, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8351, 234, 8345])).
% 36.04/23.86 tff(8353,plain,
% 36.04/23.86 (~m_counter_cell_v_value(c_bit0, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8352, 8341])).
% 36.04/23.86 tff(8354,assumption,(~m_counter_cell_v_carry_in(c_bit0, s96)), introduced(assumption)).
% 36.04/23.86 tff(8355,plain,
% 36.04/23.86 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s96)),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8356,plain,
% 36.04/23.86 ($false),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8355, 158, 8354])).
% 36.04/23.86 tff(8357,plain,(m_counter_cell_v_carry_in(c_bit0, s96)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.86 tff(8358,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8359,plain,
% 36.04/23.86 (((~node1(c_bit0, s96)) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8360,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s96)) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96))))),
% 36.04/23.86 inference(monotonicity,[status(thm)],[8359])).
% 36.04/23.86 tff(8361,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s96)) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96)))),
% 36.04/23.86 inference(transitivity,[status(thm)],[8360, 8358])).
% 36.04/23.86 tff(8362,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s96)) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8363,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s96)) | m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8362, 8361])).
% 36.04/23.86 tff(8364,plain,
% 36.04/23.86 (m_counter_cell_v_value(c_bit0, s96) | (~node1(c_bit0, s96))),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8363, 170, 8357])).
% 36.04/23.86 tff(8365,plain,
% 36.04/23.86 (~node1(c_bit0, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8364, 8353])).
% 36.04/23.86 tff(8366,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit0, s96, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit0, s96, s97))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8367,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit0, s96, s97))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8368,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit0, s96, s97)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8367, 8366])).
% 36.04/23.86 tff(8369,plain,
% 36.04/23.86 (node3(c_bit0, s96, s97)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8368, 81, 40])).
% 36.04/23.86 tff(8370,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8371,plain,
% 36.04/23.86 ((node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | m_counter_cell_v_value(c_bit0, s97)) <=> (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8372,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | m_counter_cell_v_value(c_bit0, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97))))),
% 36.04/23.86 inference(monotonicity,[status(thm)],[8371])).
% 36.04/23.86 tff(8373,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | m_counter_cell_v_value(c_bit0, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 36.04/23.86 inference(transitivity,[status(thm)],[8372, 8370])).
% 36.04/23.86 tff(8374,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | m_counter_cell_v_value(c_bit0, s97))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8375,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96) | (~node3(c_bit0, s96, s97))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8374, 8373])).
% 36.04/23.86 tff(8376,plain,
% 36.04/23.86 (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8375, 199, 8369])).
% 36.04/23.86 tff(8377,plain,
% 36.04/23.86 (m_counter_cell_v_value(c_bit0, s97)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8376, 8365])).
% 36.04/23.86 tff(8378,assumption,(~m_counter_cell_v_carry_in(c_bit0, s97)), introduced(assumption)).
% 36.04/23.86 tff(8379,plain,
% 36.04/23.86 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s97)),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8380,plain,
% 36.04/23.86 ($false),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8379, 158, 8378])).
% 36.04/23.86 tff(8381,plain,(m_counter_cell_v_carry_in(c_bit0, s97)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.86 tff(8382,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8383,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8384,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8383, 8382])).
% 36.04/23.86 tff(8385,plain,
% 36.04/23.86 ((~m_counter_cell_v_value(c_bit0, s97)) | m_counter_cell_v_carry_out(c_bit0, s97)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8384, 3031, 8381])).
% 36.04/23.86 tff(8386,plain,
% 36.04/23.86 (m_counter_cell_v_carry_out(c_bit0, s97)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8385, 8377])).
% 36.04/23.86 tff(8387,plain,
% 36.04/23.86 (((~![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, s97)) | m_counter_cell_v_carry_in(c_bit1, s97))) <=> ((~![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, s97)) | m_counter_cell_v_carry_in(c_bit1, s97))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8388,plain,
% 36.04/23.86 ((~![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, s97)) | m_counter_cell_v_carry_in(c_bit1, s97))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8389,plain,
% 36.04/23.86 ((~![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, s97)) | m_counter_cell_v_carry_in(c_bit1, s97)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8388, 8387])).
% 36.04/23.86 tff(8390,plain,
% 36.04/23.86 (m_counter_cell_v_carry_in(c_bit1, s97)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8389, 3046, 8386])).
% 36.04/23.86 tff(8391,assumption,(~m_counter_cell_v_carry_out(c_bit2, s95)), introduced(assumption)).
% 36.04/23.86 tff(8392,assumption,(m_counter_cell_v_value(c_bit2, s95)), introduced(assumption)).
% 36.04/23.86 tff(8393,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s95)) | (~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s95)) | (~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8394,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s95)) | (~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8395,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | (~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8394, 8393])).
% 36.04/23.86 tff(8396,plain,
% 36.04/23.86 ((~m_counter_cell_v_carry_in(c_bit2, s95)) | (~m_counter_cell_v_value(c_bit2, s95))),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8395, 3031, 8391])).
% 36.04/23.86 tff(8397,plain,
% 36.04/23.86 (~m_counter_cell_v_carry_in(c_bit2, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8396, 8392])).
% 36.04/23.86 tff(8398,assumption,(node1(c_bit2, s95)), introduced(assumption)).
% 36.04/23.86 tff(8399,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_value(c_bit2, s95)) | (~node1(c_bit2, s95)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s95) | (~m_counter_cell_v_value(c_bit2, s95)) | (~node1(c_bit2, s95)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8400,plain,
% 36.04/23.86 (((~node1(c_bit2, s95)) | m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_value(c_bit2, s95))) <=> (m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_value(c_bit2, s95)) | (~node1(c_bit2, s95)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8401,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s95)) | m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_value(c_bit2, s95)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s95) | (~m_counter_cell_v_value(c_bit2, s95)) | (~node1(c_bit2, s95))))),
% 36.04/23.86 inference(monotonicity,[status(thm)],[8400])).
% 36.04/23.86 tff(8402,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s95)) | m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_value(c_bit2, s95)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s95) | (~m_counter_cell_v_value(c_bit2, s95)) | (~node1(c_bit2, s95)))),
% 36.04/23.86 inference(transitivity,[status(thm)],[8401, 8399])).
% 36.04/23.86 tff(8403,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s95)) | m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_value(c_bit2, s95)))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8404,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_value(c_bit2, s95)) | (~node1(c_bit2, s95))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8403, 8402])).
% 36.04/23.86 tff(8405,plain,
% 36.04/23.86 (m_counter_cell_v_carry_in(c_bit2, s95) | (~m_counter_cell_v_value(c_bit2, s95))),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8404, 3359, 8398])).
% 36.04/23.86 tff(8406,plain,
% 36.04/23.86 ($false),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8405, 8397, 8392])).
% 36.04/23.86 tff(8407,plain,((~m_counter_cell_v_value(c_bit2, s95)) | (~node1(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s95)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.86 tff(8408,plain,
% 36.04/23.86 (~node1(c_bit2, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8407, 8392, 8391])).
% 36.04/23.86 tff(8409,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit2, s95, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit2, s95, s96))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8410,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s95, s96)) | node3(c_bit2, s95, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8411,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s95, s96)) | node3(c_bit2, s95, s96)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8410, 8409])).
% 36.04/23.86 tff(8412,plain,
% 36.04/23.86 (node3(c_bit2, s95, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8411, 81, 15])).
% 36.04/23.86 tff(8413,plain,
% 36.04/23.86 (((~![Y: $i, 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, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)))) <=> ((~![Y: $i, 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, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8414,plain,
% 36.04/23.86 ((node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)) | m_counter_cell_v_value(c_bit2, s96)) <=> (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8415,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![Y: $i, 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, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96))))),
% 36.04/23.86 inference(monotonicity,[status(thm)],[8414])).
% 36.04/23.86 tff(8416,plain,
% 36.04/23.86 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![Y: $i, 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, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)))),
% 36.04/23.86 inference(transitivity,[status(thm)],[8415, 8413])).
% 36.04/23.86 tff(8417,plain,
% 36.04/23.86 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s95) | (~node3(c_bit2, s95, s96)) | m_counter_cell_v_value(c_bit2, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8418,plain,
% 36.04/23.86 ((~![Y: $i, 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, s96) | node1(c_bit2, s95) | (~node3(c_bit2, s95, s96))),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8417, 8416])).
% 36.04/23.86 tff(8419,plain,
% 36.04/23.86 (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8418, 199, 8412])).
% 36.04/23.86 tff(8420,plain,
% 36.04/23.86 (m_counter_cell_v_value(c_bit2, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8419, 8408])).
% 36.04/23.86 tff(8421,assumption,(~m_counter_cell_v_carry_out(c_bit2, s96)), introduced(assumption)).
% 36.04/23.86 tff(8422,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s96)) | (~m_counter_cell_v_value(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit2, s96))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s96)) | (~m_counter_cell_v_value(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit2, s96))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8423,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s96)) | (~m_counter_cell_v_value(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit2, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8424,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s96)) | (~m_counter_cell_v_value(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit2, s96)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8423, 8422])).
% 36.04/23.86 tff(8425,plain,
% 36.04/23.86 ((~m_counter_cell_v_carry_in(c_bit2, s96)) | (~m_counter_cell_v_value(c_bit2, s96))),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8424, 3031, 8421])).
% 36.04/23.86 tff(8426,plain,
% 36.04/23.86 (~m_counter_cell_v_carry_in(c_bit2, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8425, 8420])).
% 36.04/23.86 tff(8427,assumption,(~m_counter_cell_v_carry_in(c_bit2, s96)), introduced(assumption)).
% 36.04/23.86 tff(8428,plain,
% 36.04/23.86 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s96)) | m_counter_cell_v_carry_in(c_bit2, s96))) <=> ((~![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, s96)) | m_counter_cell_v_carry_in(c_bit2, s96))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8429,plain,
% 36.04/23.86 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s96)) | m_counter_cell_v_carry_in(c_bit2, s96))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8430,plain,
% 36.04/23.86 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s96)) | m_counter_cell_v_carry_in(c_bit2, s96)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8429, 8428])).
% 36.04/23.86 tff(8431,plain,
% 36.04/23.86 ($false),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8430, 4417, 8427, 8314])).
% 36.04/23.86 tff(8432,plain,(m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_carry_out(c_bit1, s96))), inference(lemma,lemma(discharge,[]))).
% 36.04/23.86 tff(8433,plain,
% 36.04/23.86 (~m_counter_cell_v_carry_out(c_bit1, s96)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8432, 8426])).
% 36.04/23.86 tff(8434,plain,
% 36.04/23.86 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s95)) | m_counter_cell_v_carry_in(c_bit2, s95))) <=> ((~![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, s95)) | m_counter_cell_v_carry_in(c_bit2, s95))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8435,plain,
% 36.04/23.86 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s95)) | m_counter_cell_v_carry_in(c_bit2, s95))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8436,plain,
% 36.04/23.86 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s95)) | m_counter_cell_v_carry_in(c_bit2, s95)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8435, 8434])).
% 36.04/23.86 tff(8437,plain,
% 36.04/23.86 (~m_counter_cell_v_carry_out(c_bit1, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8436, 4417, 8397])).
% 36.04/23.86 tff(8438,assumption,(m_counter_cell_v_carry_in(c_bit1, s95)), introduced(assumption)).
% 36.04/23.86 tff(8439,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8440,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95))),
% 36.04/23.86 inference(quant_inst,[status(thm)],[])).
% 36.04/23.86 tff(8441,plain,
% 36.04/23.86 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | (~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95)),
% 36.04/23.86 inference(modus_ponens,[status(thm)],[8440, 8439])).
% 36.04/23.86 tff(8442,plain,
% 36.04/23.86 ((~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8441, 3031, 8438])).
% 36.04/23.86 tff(8443,plain,
% 36.04/23.86 (~m_counter_cell_v_value(c_bit1, s95)),
% 36.04/23.86 inference(unit_resolution,[status(thm)],[8442, 8437])).
% 36.04/23.86 tff(8444,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95) | (~node1(c_bit1, s95)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95) | (~node1(c_bit1, s95)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8445,plain,
% 36.04/23.86 (((~node1(c_bit1, s95)) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95) | (~node1(c_bit1, s95)))),
% 36.04/23.86 inference(rewrite,[status(thm)],[])).
% 36.04/23.86 tff(8446,plain,
% 36.04/23.86 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s95)) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95) | (~node1(c_bit1, s95))))),
% 36.04/23.87 inference(monotonicity,[status(thm)],[8445])).
% 36.04/23.87 tff(8447,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s95)) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95) | (~node1(c_bit1, s95)))),
% 36.04/23.87 inference(transitivity,[status(thm)],[8446, 8444])).
% 36.04/23.87 tff(8448,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit1, s95)) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8449,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_value(c_bit1, s95) | (~node1(c_bit1, s95))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8448, 8447])).
% 36.04/23.87 tff(8450,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit1, s95) | (~node1(c_bit1, s95))),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8449, 170, 8438])).
% 36.04/23.87 tff(8451,plain,
% 36.04/23.87 (~node1(c_bit1, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8450, 8443])).
% 36.04/23.87 tff(8452,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s95) | (~node3(c_bit1, s95, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8453,plain,
% 36.04/23.87 ((node1(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | m_counter_cell_v_value(c_bit1, s96)) <=> (m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8454,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | m_counter_cell_v_value(c_bit1, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s95) | (~node3(c_bit1, s95, s96))))),
% 36.04/23.87 inference(monotonicity,[status(thm)],[8453])).
% 36.04/23.87 tff(8455,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | m_counter_cell_v_value(c_bit1, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s95) | (~node3(c_bit1, s95, s96)))),
% 36.04/23.87 inference(transitivity,[status(thm)],[8454, 8452])).
% 36.04/23.87 tff(8456,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s95) | (~node3(c_bit1, s95, s96)) | m_counter_cell_v_value(c_bit1, s96))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8457,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s95) | (~node3(c_bit1, s95, s96))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8456, 8455])).
% 36.04/23.87 tff(8458,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8457, 199, 8300])).
% 36.04/23.87 tff(8459,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit1, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8458, 8451])).
% 36.04/23.87 tff(8460,assumption,(m_counter_cell_v_carry_in(c_bit1, s96)), introduced(assumption)).
% 36.04/23.87 tff(8461,assumption,(m_counter_cell_v_value(c_bit1, s96)), introduced(assumption)).
% 36.04/23.87 tff(8462,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s96)) | (~m_counter_cell_v_value(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s96)) | (~m_counter_cell_v_value(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8463,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s96)) | (~m_counter_cell_v_value(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit1, s96))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8464,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s96)) | (~m_counter_cell_v_value(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit1, s96)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8463, 8462])).
% 36.04/23.87 tff(8465,plain,
% 36.04/23.87 ($false),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8464, 3031, 8461, 8460, 8322])).
% 36.04/23.87 tff(8466,plain,((~m_counter_cell_v_value(c_bit1, s96)) | (~m_counter_cell_v_carry_in(c_bit1, s96)) | m_counter_cell_v_carry_out(c_bit1, s96)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.87 tff(8467,plain,
% 36.04/23.87 (~m_counter_cell_v_carry_in(c_bit1, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8466, 8459, 8433])).
% 36.04/23.87 tff(8468,assumption,(m_counter_cell_v_carry_in(c_bit1, s97)), introduced(assumption)).
% 36.04/23.87 tff(8469,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8470,plain,
% 36.04/23.87 (((~node1(c_bit2, s96)) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96))) <=> (m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8471,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s96)) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96))))),
% 36.04/23.87 inference(monotonicity,[status(thm)],[8470])).
% 36.04/23.87 tff(8472,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s96)) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)))),
% 36.04/23.87 inference(transitivity,[status(thm)],[8471, 8469])).
% 36.04/23.87 tff(8473,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s96)) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8474,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8473, 8472])).
% 36.04/23.87 tff(8475,plain,
% 36.04/23.87 (~node1(c_bit2, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8474, 3359, 8420, 8426])).
% 36.04/23.87 tff(8476,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit2, s96, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit2, s96, s97))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8477,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit2, s96, s97))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8478,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit2, s96, s97)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8477, 8476])).
% 36.04/23.87 tff(8479,plain,
% 36.04/23.87 (node3(c_bit2, s96, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8478, 81, 40])).
% 36.04/23.87 tff(8480,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)))) <=> ((~![Y: $i, 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, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8481,plain,
% 36.04/23.87 ((node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)) | m_counter_cell_v_value(c_bit2, s97)) <=> (m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8482,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)) | m_counter_cell_v_value(c_bit2, s97))) <=> ((~![Y: $i, 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, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97))))),
% 36.04/23.87 inference(monotonicity,[status(thm)],[8481])).
% 36.04/23.87 tff(8483,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)) | m_counter_cell_v_value(c_bit2, s97))) <=> ((~![Y: $i, 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, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)))),
% 36.04/23.87 inference(transitivity,[status(thm)],[8482, 8480])).
% 36.04/23.87 tff(8484,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s96) | (~node3(c_bit2, s96, s97)) | m_counter_cell_v_value(c_bit2, s97))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8485,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96) | (~node3(c_bit2, s96, s97))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8484, 8483])).
% 36.04/23.87 tff(8486,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit2, s97) | node1(c_bit2, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8485, 199, 8479])).
% 36.04/23.87 tff(8487,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit2, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8486, 8475])).
% 36.04/23.87 tff(8488,assumption,(~m_counter_cell_v_carry_out(c_bit2, s97)), introduced(assumption)).
% 36.04/23.87 tff(8489,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s97))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s97)) | (~m_counter_cell_v_value(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s97))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8490,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s97))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8491,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s97)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8490, 8489])).
% 36.04/23.87 tff(8492,plain,
% 36.04/23.87 ((~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97))),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8491, 3031, 8488])).
% 36.04/23.87 tff(8493,plain,
% 36.04/23.87 (~m_counter_cell_v_carry_in(c_bit2, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8492, 8487])).
% 36.04/23.87 tff(8494,assumption,(~m_counter_cell_v_carry_in(c_bit2, s97)), introduced(assumption)).
% 36.04/23.87 tff(8495,assumption,(m_counter_cell_v_carry_out(c_bit1, s97)), introduced(assumption)).
% 36.04/23.87 tff(8496,plain,
% 36.04/23.87 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s97)) | m_counter_cell_v_carry_in(c_bit2, s97))) <=> ((~![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, s97)) | m_counter_cell_v_carry_in(c_bit2, s97))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8497,plain,
% 36.04/23.87 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s97)) | m_counter_cell_v_carry_in(c_bit2, s97))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8498,plain,
% 36.04/23.87 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s97)) | m_counter_cell_v_carry_in(c_bit2, s97)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8497, 8496])).
% 36.04/23.87 tff(8499,plain,
% 36.04/23.87 ($false),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8498, 4417, 8495, 8494])).
% 36.04/23.87 tff(8500,plain,(m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_carry_out(c_bit1, s97))), inference(lemma,lemma(discharge,[]))).
% 36.04/23.87 tff(8501,plain,
% 36.04/23.87 (~m_counter_cell_v_carry_out(c_bit1, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8500, 8493])).
% 36.04/23.87 tff(8502,assumption,(~m_counter_cell_v_carry_out(c_bit1, s97)), introduced(assumption)).
% 36.04/23.87 tff(8503,assumption,(m_counter_cell_v_value(c_bit1, s97)), introduced(assumption)).
% 36.04/23.87 tff(8504,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s97)) | (~m_counter_cell_v_value(c_bit1, s97)) | m_counter_cell_v_carry_out(c_bit1, s97))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s97)) | (~m_counter_cell_v_value(c_bit1, s97)) | m_counter_cell_v_carry_out(c_bit1, s97))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8505,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s97)) | (~m_counter_cell_v_value(c_bit1, s97)) | m_counter_cell_v_carry_out(c_bit1, s97))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8506,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | (~m_counter_cell_v_value(c_bit1, s97)) | m_counter_cell_v_carry_out(c_bit1, s97)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8505, 8504])).
% 36.04/23.87 tff(8507,plain,
% 36.04/23.87 ($false),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8506, 3031, 8468, 8503, 8502])).
% 36.04/23.87 tff(8508,plain,(m_counter_cell_v_carry_out(c_bit1, s97) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | (~m_counter_cell_v_value(c_bit1, s97))), inference(lemma,lemma(discharge,[]))).
% 36.04/23.87 tff(8509,plain,
% 36.04/23.87 (~m_counter_cell_v_value(c_bit1, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8508, 8501, 8468])).
% 36.04/23.87 tff(8510,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit1, s96, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit1, s96, s97))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8511,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s96, s97)) | node3(c_bit1, s96, s97))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8512,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s96, s97)) | node3(c_bit1, s96, s97)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8511, 8510])).
% 36.04/23.87 tff(8513,plain,
% 36.04/23.87 (node3(c_bit1, s96, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8512, 81, 40])).
% 36.04/23.87 tff(8514,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s97) | node1(c_bit1, s96) | (~node3(c_bit1, s96, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s97) | node1(c_bit1, s96) | (~node3(c_bit1, s96, s97)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8515,plain,
% 36.04/23.87 ((node1(c_bit1, s96) | (~node3(c_bit1, s96, s97)) | m_counter_cell_v_value(c_bit1, s97)) <=> (m_counter_cell_v_value(c_bit1, s97) | node1(c_bit1, s96) | (~node3(c_bit1, s96, s97)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8516,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s96) | (~node3(c_bit1, s96, s97)) | m_counter_cell_v_value(c_bit1, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s97) | node1(c_bit1, s96) | (~node3(c_bit1, s96, s97))))),
% 36.04/23.87 inference(monotonicity,[status(thm)],[8515])).
% 36.04/23.87 tff(8517,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s96) | (~node3(c_bit1, s96, s97)) | m_counter_cell_v_value(c_bit1, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s97) | node1(c_bit1, s96) | (~node3(c_bit1, s96, s97)))),
% 36.04/23.87 inference(transitivity,[status(thm)],[8516, 8514])).
% 36.04/23.87 tff(8518,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s96) | (~node3(c_bit1, s96, s97)) | m_counter_cell_v_value(c_bit1, s97))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8519,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s97) | node1(c_bit1, s96) | (~node3(c_bit1, s96, s97))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8518, 8517])).
% 36.04/23.87 tff(8520,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit1, s97) | node1(c_bit1, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8519, 199, 8513])).
% 36.04/23.87 tff(8521,plain,
% 36.04/23.87 (node1(c_bit1, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8520, 8509])).
% 36.04/23.87 tff(8522,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)) | (~node1(c_bit1, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)) | (~node1(c_bit1, s96)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8523,plain,
% 36.04/23.87 (((~node1(c_bit1, s96)) | m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96))) <=> (m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)) | (~node1(c_bit1, s96)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8524,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s96)) | m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)) | (~node1(c_bit1, s96))))),
% 36.04/23.87 inference(monotonicity,[status(thm)],[8523])).
% 36.04/23.87 tff(8525,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s96)) | m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)) | (~node1(c_bit1, s96)))),
% 36.04/23.87 inference(transitivity,[status(thm)],[8524, 8522])).
% 36.04/23.87 tff(8526,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit1, s96)) | m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8527,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s96) | (~m_counter_cell_v_value(c_bit1, s96)) | (~node1(c_bit1, s96))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8526, 8525])).
% 36.04/23.87 tff(8528,plain,
% 36.04/23.87 ($false),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8527, 3359, 8459, 8521, 8467])).
% 36.04/23.87 tff(8529,plain,((~m_counter_cell_v_value(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit2, s97) | m_counter_cell_v_carry_out(c_bit2, s96) | m_counter_cell_v_carry_out(c_bit2, s95)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.87 tff(8530,plain,
% 36.04/23.87 ((~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s97) | m_counter_cell_v_carry_out(c_bit2, s96) | m_counter_cell_v_carry_out(c_bit2, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8529, 8291, 8390])).
% 36.04/23.87 tff(8531,plain,
% 36.04/23.87 ((~m_counter_cell_v_value(c_bit2, s95)) | m_counter_cell_v_carry_out(c_bit2, s97) | m_counter_cell_v_carry_out(c_bit2, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8530, 8336])).
% 36.04/23.87 tff(8532,plain,
% 36.04/23.87 (~m_counter_cell_v_value(c_bit2, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8531, 66, 62])).
% 36.04/23.87 tff(8533,plain,
% 36.04/23.87 ((~m_counter_cell_v_value(c_bit1, s95)) | m_counter_cell_v_carry_out(c_bit1, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8441, 3031, 8291])).
% 36.04/23.87 tff(8534,plain,
% 36.04/23.87 (m_counter_cell_v_carry_out(c_bit1, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8533, 8254])).
% 36.04/23.87 tff(8535,plain,
% 36.04/23.87 (m_counter_cell_v_carry_in(c_bit2, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8436, 4417, 8534])).
% 36.04/23.87 tff(8536,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8537,plain,
% 36.04/23.87 (((~node1(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8538,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95))))),
% 36.04/23.87 inference(monotonicity,[status(thm)],[8537])).
% 36.04/23.87 tff(8539,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95)))),
% 36.04/23.87 inference(transitivity,[status(thm)],[8538, 8536])).
% 36.04/23.87 tff(8540,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit2, s95)) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8541,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s95)) | m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8540, 8539])).
% 36.04/23.87 tff(8542,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit2, s95) | (~node1(c_bit2, s95))),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8541, 170, 8535])).
% 36.04/23.87 tff(8543,plain,
% 36.04/23.87 (~node1(c_bit2, s95)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8542, 8532])).
% 36.04/23.87 tff(8544,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit2, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8419, 8543])).
% 36.04/23.87 tff(8545,assumption,(m_counter_cell_v_value(c_bit2, s96)), introduced(assumption)).
% 36.04/23.87 tff(8546,plain,
% 36.04/23.87 (~m_counter_cell_v_carry_in(c_bit2, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8425, 8545])).
% 36.04/23.87 tff(8547,assumption,(node1(c_bit2, s96)), introduced(assumption)).
% 36.04/23.87 tff(8548,plain,
% 36.04/23.87 (m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96))),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8474, 3359, 8547])).
% 36.04/23.87 tff(8549,plain,
% 36.04/23.87 ($false),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8548, 8546, 8545])).
% 36.04/23.87 tff(8550,plain,((~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96)) | m_counter_cell_v_carry_out(c_bit2, s96)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.87 tff(8551,plain,
% 36.04/23.87 ((~m_counter_cell_v_value(c_bit2, s96)) | (~node1(c_bit2, s96))),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8550, 8336])).
% 36.04/23.87 tff(8552,plain,
% 36.04/23.87 (~node1(c_bit2, s96)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8551, 8544])).
% 36.04/23.87 tff(8553,plain,
% 36.04/23.87 (m_counter_cell_v_value(c_bit2, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8486, 8552])).
% 36.04/23.87 tff(8554,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~m_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, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8555,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_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, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97)))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8556,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_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, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8555, 8554])).
% 36.04/23.87 tff(8557,plain,
% 36.04/23.87 ((~m_counter_cell_v_value(c_bit0, s97)) | (~node2(c_bit0, s97))),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8556, 219, 8381])).
% 36.04/23.87 tff(8558,plain,
% 36.04/23.87 (~node2(c_bit0, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8557, 8377])).
% 36.04/23.87 tff(8559,plain,
% 36.04/23.87 (succ(s97, s98) <=> succ(s97, s98)),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8560,axiom,(succ(s97, s98)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound98')).
% 36.04/23.87 tff(8561,plain,
% 36.04/23.87 (succ(s97, s98)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8560, 8559])).
% 36.04/23.87 tff(8562,plain,
% 36.04/23.87 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s97, s98)) | trans(s97, s98))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s97, s98)) | trans(s97, s98))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8563,plain,
% 36.04/23.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s97, s98)) | trans(s97, s98))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8564,plain,
% 36.04/23.87 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s97, s98)) | trans(s97, s98)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8563, 8562])).
% 36.04/23.87 tff(8565,plain,
% 36.04/23.87 (trans(s97, s98)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8564, 8561, 8])).
% 36.04/23.87 tff(8566,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit0, s97, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit0, s97, s98))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8567,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit0, s97, s98))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8568,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit0, s97, s98)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8567, 8566])).
% 36.04/23.87 tff(8569,plain,
% 36.04/23.87 (node3(c_bit0, s97, s98)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8568, 81, 8565])).
% 36.04/23.87 tff(8570,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8571,plain,
% 36.04/23.87 ((node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | (~m_counter_cell_v_value(c_bit0, s98))) <=> ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8572,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98))))),
% 36.04/23.87 inference(monotonicity,[status(thm)],[8571])).
% 36.04/23.87 tff(8573,plain,
% 36.04/23.87 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 36.04/23.87 inference(transitivity,[status(thm)],[8572, 8570])).
% 36.04/23.87 tff(8574,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8575,plain,
% 36.04/23.87 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97) | (~node3(c_bit0, s97, s98))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8574, 8573])).
% 36.04/23.87 tff(8576,plain,
% 36.04/23.87 ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s97)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8575, 234, 8569])).
% 36.04/23.87 tff(8577,plain,
% 36.04/23.87 (~m_counter_cell_v_value(c_bit0, s98)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8576, 8558])).
% 36.04/23.87 tff(8578,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s98) | (~node4(c_bit0, s98)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s98) | (~node4(c_bit0, s98)))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8579,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s98) | (~node4(c_bit0, s98)))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8580,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s98) | (~node4(c_bit0, s98))),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8579, 8578])).
% 36.04/23.87 tff(8581,plain,
% 36.04/23.87 (~node4(c_bit0, s98)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8580, 2875, 8577])).
% 36.04/23.87 tff(8582,assumption,(~node4(c_bit0, s98)), introduced(assumption)).
% 36.04/23.87 tff(8583,assumption,(m_counter_cell_v_carry_out(c_bit0, s98)), introduced(assumption)).
% 36.04/23.87 tff(8584,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8585,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8586,plain,
% 36.04/23.87 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8585, 8584])).
% 36.04/23.87 tff(8587,plain,
% 36.04/23.87 ($false),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8586, 2887, 8583, 8582])).
% 36.04/23.87 tff(8588,plain,((~m_counter_cell_v_carry_out(c_bit0, s98)) | node4(c_bit0, s98)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.87 tff(8589,plain,
% 36.04/23.87 (~m_counter_cell_v_carry_out(c_bit0, s98)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8588, 8581])).
% 36.04/23.87 tff(8590,assumption,(m_counter_cell_v_carry_in(c_bit1, s98)), introduced(assumption)).
% 36.04/23.87 tff(8591,assumption,(~m_counter_cell_v_carry_out(c_bit0, s98)), introduced(assumption)).
% 36.04/23.87 tff(8592,plain,
% 36.04/23.87 (((~![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, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))) <=> ((~![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, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))),
% 36.04/23.87 inference(rewrite,[status(thm)],[])).
% 36.04/23.87 tff(8593,plain,
% 36.04/23.87 ((~![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, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))),
% 36.04/23.87 inference(quant_inst,[status(thm)],[])).
% 36.04/23.87 tff(8594,plain,
% 36.04/23.87 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit1, X)) | m_counter_cell_v_carry_out(c_bit0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_carry_out(c_bit0, s98)),
% 36.04/23.87 inference(modus_ponens,[status(thm)],[8593, 8592])).
% 36.04/23.87 tff(8595,plain,
% 36.04/23.87 ($false),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8594, 2901, 8591, 8590])).
% 36.04/23.87 tff(8596,plain,((~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_carry_out(c_bit0, s98)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.87 tff(8597,plain,
% 36.04/23.87 (~m_counter_cell_v_carry_in(c_bit1, s98)),
% 36.04/23.87 inference(unit_resolution,[status(thm)],[8596, 8589])).
% 36.04/23.87 tff(8598,plain,
% 36.04/23.87 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s98) | (~node4(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | (~node4(c_bit1, s98)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8599,plain,
% 36.04/23.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s98) | (~node4(c_bit1, s98)))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8600,plain,
% 36.04/23.88 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | (~node4(c_bit1, s98))),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8599, 8598])).
% 36.04/23.88 tff(8601,plain,
% 36.04/23.88 (~node4(c_bit1, s98)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8600, 3076, 8597])).
% 36.04/23.88 tff(8602,plain,
% 36.04/23.88 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s98)) | node4(c_bit1, s98))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s98)) | node4(c_bit1, s98))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8603,plain,
% 36.04/23.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s98)) | node4(c_bit1, s98))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8604,plain,
% 36.04/23.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s98)) | node4(c_bit1, s98)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8603, 8602])).
% 36.04/23.88 tff(8605,plain,
% 36.04/23.88 (~m_counter_cell_v_carry_out(c_bit1, s98)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8604, 2887, 8601])).
% 36.04/23.88 tff(8606,plain,
% 36.04/23.88 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s98)) | m_counter_cell_v_carry_out(c_bit1, s98))) <=> ((~![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, s98)) | m_counter_cell_v_carry_out(c_bit1, s98))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8607,plain,
% 36.04/23.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s98)) | m_counter_cell_v_carry_out(c_bit1, s98))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8608,plain,
% 36.04/23.88 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s98)) | m_counter_cell_v_carry_out(c_bit1, s98)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8607, 8606])).
% 36.04/23.88 tff(8609,plain,
% 36.04/23.88 (~m_counter_cell_v_carry_in(c_bit2, s98)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8608, 3167, 8605])).
% 36.04/23.88 tff(8610,assumption,(~m_counter_cell_v_value(c_bit1, s99)), introduced(assumption)).
% 36.04/23.88 tff(8611,assumption,(~m_counter_cell_v_carry_in(c_bit0, s98)), introduced(assumption)).
% 36.04/23.88 tff(8612,plain,
% 36.04/23.88 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s98)),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8613,plain,
% 36.04/23.88 ($false),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8612, 158, 8611])).
% 36.04/23.88 tff(8614,plain,(m_counter_cell_v_carry_in(c_bit0, s98)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.88 tff(8615,plain,
% 36.04/23.88 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8616,plain,
% 36.04/23.88 (((~node1(c_bit0, s98)) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8617,plain,
% 36.04/23.88 (((~![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, s98)) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98))))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8616])).
% 36.04/23.88 tff(8618,plain,
% 36.04/23.88 (((~![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, s98)) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98)))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8617, 8615])).
% 36.04/23.88 tff(8619,plain,
% 36.04/23.88 ((~![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, s98)) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8620,plain,
% 36.04/23.88 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s98)) | m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98))),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8619, 8618])).
% 36.04/23.88 tff(8621,plain,
% 36.04/23.88 (m_counter_cell_v_value(c_bit0, s98) | (~node1(c_bit0, s98))),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8620, 170, 8614])).
% 36.04/23.88 tff(8622,plain,
% 36.04/23.88 (~node1(c_bit0, s98)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8621, 8577])).
% 36.04/23.88 tff(8623,plain,
% 36.04/23.88 (succ(s98, s99) <=> succ(s98, s99)),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8624,axiom,(succ(s98, s99)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound99')).
% 36.04/23.88 tff(8625,plain,
% 36.04/23.88 (succ(s98, s99)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8624, 8623])).
% 36.04/23.88 tff(8626,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s98, s99)) | trans(s98, s99))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s98, s99)) | trans(s98, s99))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8627,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | ((~succ(s98, s99)) | trans(s98, s99))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8628,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | trans(X, Y))) | (~succ(s98, s99)) | trans(s98, s99)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8627, 8626])).
% 36.04/23.88 tff(8629,plain,
% 36.04/23.88 (trans(s98, s99)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8628, 8625, 8])).
% 36.04/23.88 tff(8630,plain,
% 36.04/23.88 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit0, s98, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit0, s98, s99))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8631,plain,
% 36.04/23.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit0, s98, s99))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8632,plain,
% 36.04/23.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit0, s98, s99)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8631, 8630])).
% 36.04/23.88 tff(8633,plain,
% 36.04/23.88 (node3(c_bit0, s98, s99)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8632, 81, 8629])).
% 36.04/23.88 tff(8634,plain,
% 36.04/23.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8635,plain,
% 36.04/23.88 ((node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | m_counter_cell_v_value(c_bit0, s99)) <=> (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8636,plain,
% 36.04/23.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99))))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8635])).
% 36.04/23.88 tff(8637,plain,
% 36.04/23.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8636, 8634])).
% 36.04/23.88 tff(8638,plain,
% 36.04/23.88 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | m_counter_cell_v_value(c_bit0, s99))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8639,plain,
% 36.04/23.88 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98) | (~node3(c_bit0, s98, s99))),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8638, 8637])).
% 36.04/23.88 tff(8640,plain,
% 36.04/23.88 (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s98)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8639, 199, 8633])).
% 36.04/23.88 tff(8641,plain,
% 36.04/23.88 (m_counter_cell_v_value(c_bit0, s99)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8640, 8622])).
% 36.04/23.88 tff(8642,assumption,(~m_counter_cell_v_carry_in(c_bit0, s99)), introduced(assumption)).
% 36.04/23.88 tff(8643,plain,
% 36.04/23.88 ((~![X: $i] : m_counter_cell_v_carry_in(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit0, s99)),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8644,plain,
% 36.04/23.88 ($false),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8643, 158, 8642])).
% 36.04/23.88 tff(8645,plain,(m_counter_cell_v_carry_in(c_bit0, s99)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.88 tff(8646,plain,
% 36.04/23.88 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8647,plain,
% 36.04/23.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8648,plain,
% 36.04/23.88 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8647, 8646])).
% 36.04/23.88 tff(8649,plain,
% 36.04/23.88 ((~m_counter_cell_v_value(c_bit0, s99)) | m_counter_cell_v_carry_out(c_bit0, s99)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8648, 3031, 8645])).
% 36.04/23.88 tff(8650,plain,
% 36.04/23.88 (m_counter_cell_v_carry_out(c_bit0, s99)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8649, 8641])).
% 36.04/23.88 tff(8651,plain,
% 36.04/23.88 (((~![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, s99)) | m_counter_cell_v_carry_in(c_bit1, s99))) <=> ((~![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, s99)) | m_counter_cell_v_carry_in(c_bit1, s99))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8652,plain,
% 36.04/23.88 ((~![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, s99)) | m_counter_cell_v_carry_in(c_bit1, s99))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8653,plain,
% 36.04/23.88 ((~![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, s99)) | m_counter_cell_v_carry_in(c_bit1, s99)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8652, 8651])).
% 36.04/23.88 tff(8654,plain,
% 36.04/23.88 (m_counter_cell_v_carry_in(c_bit1, s99)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8653, 3046, 8650])).
% 36.04/23.88 tff(8655,plain,
% 36.04/23.88 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99) | (~node1(c_bit1, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99) | (~node1(c_bit1, s99)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8656,plain,
% 36.04/23.88 (((~node1(c_bit1, s99)) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99) | (~node1(c_bit1, s99)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8657,plain,
% 36.04/23.88 (((~![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, s99)) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99) | (~node1(c_bit1, s99))))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8656])).
% 36.04/23.88 tff(8658,plain,
% 36.04/23.88 (((~![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, s99)) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99) | (~node1(c_bit1, s99)))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8657, 8655])).
% 36.04/23.88 tff(8659,plain,
% 36.04/23.88 ((~![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, s99)) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8660,plain,
% 36.04/23.88 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_value(c_bit1, s99) | (~node1(c_bit1, s99))),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8659, 8658])).
% 36.04/23.88 tff(8661,plain,
% 36.04/23.88 (m_counter_cell_v_value(c_bit1, s99) | (~node1(c_bit1, s99))),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8660, 170, 8654])).
% 36.04/23.88 tff(8662,plain,
% 36.04/23.88 (~node1(c_bit1, s99)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8661, 8610])).
% 36.04/23.88 tff(8663,assumption,(node3(c_bit1, s99, s96)), introduced(assumption)).
% 36.04/23.88 tff(8664,assumption,(~node1(c_bit1, s99)), introduced(assumption)).
% 36.04/23.88 tff(8665,plain,
% 36.04/23.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s96)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8666,plain,
% 36.04/23.88 ((node1(c_bit1, s99) | (~node3(c_bit1, s99, s96)) | m_counter_cell_v_value(c_bit1, s96)) <=> (m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s96)))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8667,plain,
% 36.04/23.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s99) | (~node3(c_bit1, s99, s96)) | m_counter_cell_v_value(c_bit1, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s96))))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8666])).
% 36.04/23.88 tff(8668,plain,
% 36.04/23.88 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s99) | (~node3(c_bit1, s99, s96)) | m_counter_cell_v_value(c_bit1, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s96)))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8667, 8665])).
% 36.04/23.88 tff(8669,plain,
% 36.04/23.88 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s99) | (~node3(c_bit1, s99, s96)) | m_counter_cell_v_value(c_bit1, s96))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8670,plain,
% 36.04/23.88 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s96) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s96))),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8669, 8668])).
% 36.04/23.88 tff(8671,plain,
% 36.04/23.88 ($false),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8670, 199, 8308, 8664, 8663])).
% 36.04/23.88 tff(8672,plain,((~node3(c_bit1, s99, s96)) | node1(c_bit1, s99)), inference(lemma,lemma(discharge,[]))).
% 36.04/23.88 tff(8673,plain,
% 36.04/23.88 (~node3(c_bit1, s99, s96)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8672, 8662])).
% 36.04/23.88 tff(8674,plain,
% 36.04/23.88 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s96)) | node3(c_bit1, s99, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s96)) | node3(c_bit1, s99, s96))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8675,plain,
% 36.04/23.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s96)) | node3(c_bit1, s99, s96))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8676,plain,
% 36.04/23.88 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s96)) | node3(c_bit1, s99, s96)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8675, 8674])).
% 36.04/23.88 tff(8677,plain,
% 36.04/23.88 ((~trans(s99, s96)) | node3(c_bit1, s99, s96)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8676, 81])).
% 36.04/23.88 tff(8678,plain,
% 36.04/23.88 (~trans(s99, s96)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8677, 8673])).
% 36.04/23.88 tff(8679,assumption,(~always5(s95)), introduced(assumption)).
% 36.04/23.88 tff(8680,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s94, s95)) | (~always5(s94)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s94, s95)) | (~always5(s94)) | always5(s95))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8681,plain,
% 36.04/23.88 (((~always5(s94)) | (~trans(s94, s95)) | always5(s95)) <=> ((~trans(s94, s95)) | (~always5(s94)) | always5(s95))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8682,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s94)) | (~trans(s94, s95)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s94, s95)) | (~always5(s94)) | always5(s95)))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8681])).
% 36.04/23.88 tff(8683,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s94)) | (~trans(s94, s95)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s94, s95)) | (~always5(s94)) | always5(s95))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8682, 8680])).
% 36.04/23.88 tff(8684,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s94)) | (~trans(s94, s95)) | always5(s95))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8685,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s94, s95)) | (~always5(s94)) | always5(s95)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8684, 8683])).
% 36.04/23.88 tff(8686,plain,
% 36.04/23.88 ((~always5(s94)) | always5(s95)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8685, 25, 8242])).
% 36.04/23.88 tff(8687,plain,
% 36.04/23.88 (~always5(s94)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8686, 8679])).
% 36.04/23.88 tff(8688,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s93, s94)) | (~always5(s93)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s93, s94)) | (~always5(s93)) | always5(s94))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8689,plain,
% 36.04/23.88 (((~always5(s93)) | (~trans(s93, s94)) | always5(s94)) <=> ((~trans(s93, s94)) | (~always5(s93)) | always5(s94))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8690,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s93)) | (~trans(s93, s94)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s93, s94)) | (~always5(s93)) | always5(s94)))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8689])).
% 36.04/23.88 tff(8691,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s93)) | (~trans(s93, s94)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s93, s94)) | (~always5(s93)) | always5(s94))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8690, 8688])).
% 36.04/23.88 tff(8692,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s93)) | (~trans(s93, s94)) | always5(s94))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8693,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s93, s94)) | (~always5(s93)) | always5(s94)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8692, 8691])).
% 36.04/23.88 tff(8694,plain,
% 36.04/23.88 ((~always5(s93)) | always5(s94)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8693, 25, 2856])).
% 36.04/23.88 tff(8695,plain,
% 36.04/23.88 (~always5(s93)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8694, 8687])).
% 36.04/23.88 tff(8696,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s92, s93)) | (~always5(s92)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s92, s93)) | (~always5(s92)) | always5(s93))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8697,plain,
% 36.04/23.88 (((~always5(s92)) | (~trans(s92, s93)) | always5(s93)) <=> ((~trans(s92, s93)) | (~always5(s92)) | always5(s93))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8698,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s92)) | (~trans(s92, s93)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s92, s93)) | (~always5(s92)) | always5(s93)))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8697])).
% 36.04/23.88 tff(8699,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s92)) | (~trans(s92, s93)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s92, s93)) | (~always5(s92)) | always5(s93))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8698, 8696])).
% 36.04/23.88 tff(8700,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s92)) | (~trans(s92, s93)) | always5(s93))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8701,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s92, s93)) | (~always5(s92)) | always5(s93)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8700, 8699])).
% 36.04/23.88 tff(8702,plain,
% 36.04/23.88 ((~always5(s92)) | always5(s93)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8701, 25, 2828])).
% 36.04/23.88 tff(8703,plain,
% 36.04/23.88 (~always5(s92)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8702, 8695])).
% 36.04/23.88 tff(8704,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s91, s92)) | (~always5(s91)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s91, s92)) | (~always5(s91)) | always5(s92))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8705,plain,
% 36.04/23.88 (((~always5(s91)) | (~trans(s91, s92)) | always5(s92)) <=> ((~trans(s91, s92)) | (~always5(s91)) | always5(s92))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8706,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s91)) | (~trans(s91, s92)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s91, s92)) | (~always5(s91)) | always5(s92)))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8705])).
% 36.04/23.88 tff(8707,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s91)) | (~trans(s91, s92)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s91, s92)) | (~always5(s91)) | always5(s92))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8706, 8704])).
% 36.04/23.88 tff(8708,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s91)) | (~trans(s91, s92)) | always5(s92))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8709,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s91, s92)) | (~always5(s91)) | always5(s92)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8708, 8707])).
% 36.04/23.88 tff(8710,plain,
% 36.04/23.88 ((~always5(s91)) | always5(s92)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8709, 25, 2797])).
% 36.04/23.88 tff(8711,plain,
% 36.04/23.88 (~always5(s91)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8710, 8703])).
% 36.04/23.88 tff(8712,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s90, s91)) | (~always5(s90)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s90, s91)) | (~always5(s90)) | always5(s91))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8713,plain,
% 36.04/23.88 (((~always5(s90)) | (~trans(s90, s91)) | always5(s91)) <=> ((~trans(s90, s91)) | (~always5(s90)) | always5(s91))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8714,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s90)) | (~trans(s90, s91)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s90, s91)) | (~always5(s90)) | always5(s91)))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8713])).
% 36.04/23.88 tff(8715,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s90)) | (~trans(s90, s91)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s90, s91)) | (~always5(s90)) | always5(s91))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8714, 8712])).
% 36.04/23.88 tff(8716,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s90)) | (~trans(s90, s91)) | always5(s91))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8717,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s90, s91)) | (~always5(s90)) | always5(s91)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8716, 8715])).
% 36.04/23.88 tff(8718,plain,
% 36.04/23.88 ((~always5(s90)) | always5(s91)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8717, 25, 2771])).
% 36.04/23.88 tff(8719,plain,
% 36.04/23.88 (~always5(s90)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8718, 8711])).
% 36.04/23.88 tff(8720,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s89, s90)) | (~always5(s89)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s89, s90)) | (~always5(s89)) | always5(s90))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8721,plain,
% 36.04/23.88 (((~always5(s89)) | (~trans(s89, s90)) | always5(s90)) <=> ((~trans(s89, s90)) | (~always5(s89)) | always5(s90))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8722,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s89)) | (~trans(s89, s90)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s89, s90)) | (~always5(s89)) | always5(s90)))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8721])).
% 36.04/23.88 tff(8723,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s89)) | (~trans(s89, s90)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s89, s90)) | (~always5(s89)) | always5(s90))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8722, 8720])).
% 36.04/23.88 tff(8724,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s89)) | (~trans(s89, s90)) | always5(s90))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8725,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s89, s90)) | (~always5(s89)) | always5(s90)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8724, 8723])).
% 36.04/23.88 tff(8726,plain,
% 36.04/23.88 ((~always5(s89)) | always5(s90)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8725, 25, 2742])).
% 36.04/23.88 tff(8727,plain,
% 36.04/23.88 (~always5(s89)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8726, 8719])).
% 36.04/23.88 tff(8728,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s88, s89)) | (~always5(s88)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s88, s89)) | (~always5(s88)) | always5(s89))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8729,plain,
% 36.04/23.88 (((~always5(s88)) | (~trans(s88, s89)) | always5(s89)) <=> ((~trans(s88, s89)) | (~always5(s88)) | always5(s89))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8730,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s88)) | (~trans(s88, s89)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s88, s89)) | (~always5(s88)) | always5(s89)))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8729])).
% 36.04/23.88 tff(8731,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s88)) | (~trans(s88, s89)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s88, s89)) | (~always5(s88)) | always5(s89))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8730, 8728])).
% 36.04/23.88 tff(8732,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s88)) | (~trans(s88, s89)) | always5(s89))),
% 36.04/23.88 inference(quant_inst,[status(thm)],[])).
% 36.04/23.88 tff(8733,plain,
% 36.04/23.88 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s88, s89)) | (~always5(s88)) | always5(s89)),
% 36.04/23.88 inference(modus_ponens,[status(thm)],[8732, 8731])).
% 36.04/23.88 tff(8734,plain,
% 36.04/23.88 ((~always5(s88)) | always5(s89)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8733, 25, 2714])).
% 36.04/23.88 tff(8735,plain,
% 36.04/23.88 (~always5(s88)),
% 36.04/23.88 inference(unit_resolution,[status(thm)],[8734, 8727])).
% 36.04/23.88 tff(8736,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s87, s88)) | (~always5(s87)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s87, s88)) | (~always5(s87)) | always5(s88))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8737,plain,
% 36.04/23.88 (((~always5(s87)) | (~trans(s87, s88)) | always5(s88)) <=> ((~trans(s87, s88)) | (~always5(s87)) | always5(s88))),
% 36.04/23.88 inference(rewrite,[status(thm)],[])).
% 36.04/23.88 tff(8738,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s87)) | (~trans(s87, s88)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s87, s88)) | (~always5(s87)) | always5(s88)))),
% 36.04/23.88 inference(monotonicity,[status(thm)],[8737])).
% 36.04/23.88 tff(8739,plain,
% 36.04/23.88 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s87)) | (~trans(s87, s88)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s87, s88)) | (~always5(s87)) | always5(s88))),
% 36.04/23.88 inference(transitivity,[status(thm)],[8738, 8736])).
% 36.04/23.88 tff(8740,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s87)) | (~trans(s87, s88)) | always5(s88))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8741,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s87, s88)) | (~always5(s87)) | always5(s88)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8740, 8739])).
% 36.04/23.89 tff(8742,plain,
% 36.04/23.89 ((~always5(s87)) | always5(s88)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8741, 25, 2683])).
% 36.04/23.89 tff(8743,plain,
% 36.04/23.89 (~always5(s87)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8742, 8735])).
% 36.04/23.89 tff(8744,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s86, s87)) | (~always5(s86)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s86, s87)) | (~always5(s86)) | always5(s87))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8745,plain,
% 36.04/23.89 (((~always5(s86)) | (~trans(s86, s87)) | always5(s87)) <=> ((~trans(s86, s87)) | (~always5(s86)) | always5(s87))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8746,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s86)) | (~trans(s86, s87)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s86, s87)) | (~always5(s86)) | always5(s87)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8745])).
% 36.04/23.89 tff(8747,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s86)) | (~trans(s86, s87)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s86, s87)) | (~always5(s86)) | always5(s87))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8746, 8744])).
% 36.04/23.89 tff(8748,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s86)) | (~trans(s86, s87)) | always5(s87))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8749,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s86, s87)) | (~always5(s86)) | always5(s87)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8748, 8747])).
% 36.04/23.89 tff(8750,plain,
% 36.04/23.89 ((~always5(s86)) | always5(s87)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8749, 25, 2655])).
% 36.04/23.89 tff(8751,plain,
% 36.04/23.89 (~always5(s86)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8750, 8743])).
% 36.04/23.89 tff(8752,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s85, s86)) | (~always5(s85)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s85, s86)) | (~always5(s85)) | always5(s86))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8753,plain,
% 36.04/23.89 (((~always5(s85)) | (~trans(s85, s86)) | always5(s86)) <=> ((~trans(s85, s86)) | (~always5(s85)) | always5(s86))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8754,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s85)) | (~trans(s85, s86)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s85, s86)) | (~always5(s85)) | always5(s86)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8753])).
% 36.04/23.89 tff(8755,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s85)) | (~trans(s85, s86)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s85, s86)) | (~always5(s85)) | always5(s86))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8754, 8752])).
% 36.04/23.89 tff(8756,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s85)) | (~trans(s85, s86)) | always5(s86))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8757,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s85, s86)) | (~always5(s85)) | always5(s86)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8756, 8755])).
% 36.04/23.89 tff(8758,plain,
% 36.04/23.89 ((~always5(s85)) | always5(s86)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8757, 25, 2624])).
% 36.04/23.89 tff(8759,plain,
% 36.04/23.89 (~always5(s85)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8758, 8751])).
% 36.04/23.89 tff(8760,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s84, s85)) | (~always5(s84)) | always5(s85))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s84, s85)) | (~always5(s84)) | always5(s85))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8761,plain,
% 36.04/23.89 (((~always5(s84)) | (~trans(s84, s85)) | always5(s85)) <=> ((~trans(s84, s85)) | (~always5(s84)) | always5(s85))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8762,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s84)) | (~trans(s84, s85)) | always5(s85))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s84, s85)) | (~always5(s84)) | always5(s85)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8761])).
% 36.04/23.89 tff(8763,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s84)) | (~trans(s84, s85)) | always5(s85))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s84, s85)) | (~always5(s84)) | always5(s85))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8762, 8760])).
% 36.04/23.89 tff(8764,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s84)) | (~trans(s84, s85)) | always5(s85))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8765,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s84, s85)) | (~always5(s84)) | always5(s85)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8764, 8763])).
% 36.04/23.89 tff(8766,plain,
% 36.04/23.89 ((~always5(s84)) | always5(s85)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8765, 25, 2596])).
% 36.04/23.89 tff(8767,plain,
% 36.04/23.89 (~always5(s84)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8766, 8759])).
% 36.04/23.89 tff(8768,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s83, s84)) | (~always5(s83)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s83, s84)) | (~always5(s83)) | always5(s84))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8769,plain,
% 36.04/23.89 (((~always5(s83)) | (~trans(s83, s84)) | always5(s84)) <=> ((~trans(s83, s84)) | (~always5(s83)) | always5(s84))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8770,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s83)) | (~trans(s83, s84)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s83, s84)) | (~always5(s83)) | always5(s84)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8769])).
% 36.04/23.89 tff(8771,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s83)) | (~trans(s83, s84)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s83, s84)) | (~always5(s83)) | always5(s84))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8770, 8768])).
% 36.04/23.89 tff(8772,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s83)) | (~trans(s83, s84)) | always5(s84))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8773,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s83, s84)) | (~always5(s83)) | always5(s84)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8772, 8771])).
% 36.04/23.89 tff(8774,plain,
% 36.04/23.89 ((~always5(s83)) | always5(s84)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8773, 25, 2565])).
% 36.04/23.89 tff(8775,plain,
% 36.04/23.89 (~always5(s83)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8774, 8767])).
% 36.04/23.89 tff(8776,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s82, s83)) | (~always5(s82)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s82, s83)) | (~always5(s82)) | always5(s83))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8777,plain,
% 36.04/23.89 (((~always5(s82)) | (~trans(s82, s83)) | always5(s83)) <=> ((~trans(s82, s83)) | (~always5(s82)) | always5(s83))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8778,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s82)) | (~trans(s82, s83)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s82, s83)) | (~always5(s82)) | always5(s83)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8777])).
% 36.04/23.89 tff(8779,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s82)) | (~trans(s82, s83)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s82, s83)) | (~always5(s82)) | always5(s83))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8778, 8776])).
% 36.04/23.89 tff(8780,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s82)) | (~trans(s82, s83)) | always5(s83))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8781,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s82, s83)) | (~always5(s82)) | always5(s83)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8780, 8779])).
% 36.04/23.89 tff(8782,plain,
% 36.04/23.89 ((~always5(s82)) | always5(s83)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8781, 25, 2537])).
% 36.04/23.89 tff(8783,plain,
% 36.04/23.89 (~always5(s82)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8782, 8775])).
% 36.04/23.89 tff(8784,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s81, s82)) | (~always5(s81)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s81, s82)) | (~always5(s81)) | always5(s82))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8785,plain,
% 36.04/23.89 (((~always5(s81)) | (~trans(s81, s82)) | always5(s82)) <=> ((~trans(s81, s82)) | (~always5(s81)) | always5(s82))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8786,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s81)) | (~trans(s81, s82)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s81, s82)) | (~always5(s81)) | always5(s82)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8785])).
% 36.04/23.89 tff(8787,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s81)) | (~trans(s81, s82)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s81, s82)) | (~always5(s81)) | always5(s82))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8786, 8784])).
% 36.04/23.89 tff(8788,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s81)) | (~trans(s81, s82)) | always5(s82))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8789,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s81, s82)) | (~always5(s81)) | always5(s82)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8788, 8787])).
% 36.04/23.89 tff(8790,plain,
% 36.04/23.89 ((~always5(s81)) | always5(s82)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8789, 25, 2506])).
% 36.04/23.89 tff(8791,plain,
% 36.04/23.89 (~always5(s81)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8790, 8783])).
% 36.04/23.89 tff(8792,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s80, s81)) | (~always5(s80)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s80, s81)) | (~always5(s80)) | always5(s81))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8793,plain,
% 36.04/23.89 (((~always5(s80)) | (~trans(s80, s81)) | always5(s81)) <=> ((~trans(s80, s81)) | (~always5(s80)) | always5(s81))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8794,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s80)) | (~trans(s80, s81)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s80, s81)) | (~always5(s80)) | always5(s81)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8793])).
% 36.04/23.89 tff(8795,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s80)) | (~trans(s80, s81)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s80, s81)) | (~always5(s80)) | always5(s81))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8794, 8792])).
% 36.04/23.89 tff(8796,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s80)) | (~trans(s80, s81)) | always5(s81))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8797,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s80, s81)) | (~always5(s80)) | always5(s81)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8796, 8795])).
% 36.04/23.89 tff(8798,plain,
% 36.04/23.89 ((~always5(s80)) | always5(s81)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8797, 25, 2478])).
% 36.04/23.89 tff(8799,plain,
% 36.04/23.89 (~always5(s80)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8798, 8791])).
% 36.04/23.89 tff(8800,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s79, s80)) | (~always5(s79)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s79, s80)) | (~always5(s79)) | always5(s80))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8801,plain,
% 36.04/23.89 (((~always5(s79)) | (~trans(s79, s80)) | always5(s80)) <=> ((~trans(s79, s80)) | (~always5(s79)) | always5(s80))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8802,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s79)) | (~trans(s79, s80)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s79, s80)) | (~always5(s79)) | always5(s80)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8801])).
% 36.04/23.89 tff(8803,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s79)) | (~trans(s79, s80)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s79, s80)) | (~always5(s79)) | always5(s80))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8802, 8800])).
% 36.04/23.89 tff(8804,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s79)) | (~trans(s79, s80)) | always5(s80))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8805,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s79, s80)) | (~always5(s79)) | always5(s80)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8804, 8803])).
% 36.04/23.89 tff(8806,plain,
% 36.04/23.89 ((~always5(s79)) | always5(s80)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8805, 25, 2447])).
% 36.04/23.89 tff(8807,plain,
% 36.04/23.89 (~always5(s79)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8806, 8799])).
% 36.04/23.89 tff(8808,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s78, s79)) | (~always5(s78)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s78, s79)) | (~always5(s78)) | always5(s79))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8809,plain,
% 36.04/23.89 (((~always5(s78)) | (~trans(s78, s79)) | always5(s79)) <=> ((~trans(s78, s79)) | (~always5(s78)) | always5(s79))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8810,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s78)) | (~trans(s78, s79)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s78, s79)) | (~always5(s78)) | always5(s79)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8809])).
% 36.04/23.89 tff(8811,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s78)) | (~trans(s78, s79)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s78, s79)) | (~always5(s78)) | always5(s79))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8810, 8808])).
% 36.04/23.89 tff(8812,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s78)) | (~trans(s78, s79)) | always5(s79))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8813,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s78, s79)) | (~always5(s78)) | always5(s79)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8812, 8811])).
% 36.04/23.89 tff(8814,plain,
% 36.04/23.89 ((~always5(s78)) | always5(s79)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8813, 25, 2419])).
% 36.04/23.89 tff(8815,plain,
% 36.04/23.89 (~always5(s78)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8814, 8807])).
% 36.04/23.89 tff(8816,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s77, s78)) | (~always5(s77)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s77, s78)) | (~always5(s77)) | always5(s78))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8817,plain,
% 36.04/23.89 (((~always5(s77)) | (~trans(s77, s78)) | always5(s78)) <=> ((~trans(s77, s78)) | (~always5(s77)) | always5(s78))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8818,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s77)) | (~trans(s77, s78)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s77, s78)) | (~always5(s77)) | always5(s78)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8817])).
% 36.04/23.89 tff(8819,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s77)) | (~trans(s77, s78)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s77, s78)) | (~always5(s77)) | always5(s78))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8818, 8816])).
% 36.04/23.89 tff(8820,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s77)) | (~trans(s77, s78)) | always5(s78))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8821,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s77, s78)) | (~always5(s77)) | always5(s78)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8820, 8819])).
% 36.04/23.89 tff(8822,plain,
% 36.04/23.89 ((~always5(s77)) | always5(s78)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8821, 25, 2388])).
% 36.04/23.89 tff(8823,plain,
% 36.04/23.89 (~always5(s77)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8822, 8815])).
% 36.04/23.89 tff(8824,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s76, s77)) | (~always5(s76)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s76, s77)) | (~always5(s76)) | always5(s77))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8825,plain,
% 36.04/23.89 (((~always5(s76)) | (~trans(s76, s77)) | always5(s77)) <=> ((~trans(s76, s77)) | (~always5(s76)) | always5(s77))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8826,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s76)) | (~trans(s76, s77)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s76, s77)) | (~always5(s76)) | always5(s77)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8825])).
% 36.04/23.89 tff(8827,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s76)) | (~trans(s76, s77)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s76, s77)) | (~always5(s76)) | always5(s77))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8826, 8824])).
% 36.04/23.89 tff(8828,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s76)) | (~trans(s76, s77)) | always5(s77))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8829,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s76, s77)) | (~always5(s76)) | always5(s77)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8828, 8827])).
% 36.04/23.89 tff(8830,plain,
% 36.04/23.89 ((~always5(s76)) | always5(s77)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8829, 25, 2360])).
% 36.04/23.89 tff(8831,plain,
% 36.04/23.89 (~always5(s76)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8830, 8823])).
% 36.04/23.89 tff(8832,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s75, s76)) | (~always5(s75)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s75, s76)) | (~always5(s75)) | always5(s76))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8833,plain,
% 36.04/23.89 (((~always5(s75)) | (~trans(s75, s76)) | always5(s76)) <=> ((~trans(s75, s76)) | (~always5(s75)) | always5(s76))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8834,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s75)) | (~trans(s75, s76)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s75, s76)) | (~always5(s75)) | always5(s76)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8833])).
% 36.04/23.89 tff(8835,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s75)) | (~trans(s75, s76)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s75, s76)) | (~always5(s75)) | always5(s76))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8834, 8832])).
% 36.04/23.89 tff(8836,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s75)) | (~trans(s75, s76)) | always5(s76))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8837,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s75, s76)) | (~always5(s75)) | always5(s76)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8836, 8835])).
% 36.04/23.89 tff(8838,plain,
% 36.04/23.89 ((~always5(s75)) | always5(s76)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8837, 25, 2329])).
% 36.04/23.89 tff(8839,plain,
% 36.04/23.89 (~always5(s75)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8838, 8831])).
% 36.04/23.89 tff(8840,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s74, s75)) | (~always5(s74)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s74, s75)) | (~always5(s74)) | always5(s75))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8841,plain,
% 36.04/23.89 (((~always5(s74)) | (~trans(s74, s75)) | always5(s75)) <=> ((~trans(s74, s75)) | (~always5(s74)) | always5(s75))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8842,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s74)) | (~trans(s74, s75)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s74, s75)) | (~always5(s74)) | always5(s75)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8841])).
% 36.04/23.89 tff(8843,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s74)) | (~trans(s74, s75)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s74, s75)) | (~always5(s74)) | always5(s75))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8842, 8840])).
% 36.04/23.89 tff(8844,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s74)) | (~trans(s74, s75)) | always5(s75))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8845,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s74, s75)) | (~always5(s74)) | always5(s75)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8844, 8843])).
% 36.04/23.89 tff(8846,plain,
% 36.04/23.89 ((~always5(s74)) | always5(s75)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8845, 25, 2301])).
% 36.04/23.89 tff(8847,plain,
% 36.04/23.89 (~always5(s74)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8846, 8839])).
% 36.04/23.89 tff(8848,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s73, s74)) | (~always5(s73)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s73, s74)) | (~always5(s73)) | always5(s74))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8849,plain,
% 36.04/23.89 (((~always5(s73)) | (~trans(s73, s74)) | always5(s74)) <=> ((~trans(s73, s74)) | (~always5(s73)) | always5(s74))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8850,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s73)) | (~trans(s73, s74)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s73, s74)) | (~always5(s73)) | always5(s74)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8849])).
% 36.04/23.89 tff(8851,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s73)) | (~trans(s73, s74)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s73, s74)) | (~always5(s73)) | always5(s74))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8850, 8848])).
% 36.04/23.89 tff(8852,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s73)) | (~trans(s73, s74)) | always5(s74))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8853,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s73, s74)) | (~always5(s73)) | always5(s74)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8852, 8851])).
% 36.04/23.89 tff(8854,plain,
% 36.04/23.89 ((~always5(s73)) | always5(s74)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8853, 25, 2270])).
% 36.04/23.89 tff(8855,plain,
% 36.04/23.89 (~always5(s73)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8854, 8847])).
% 36.04/23.89 tff(8856,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s72, s73)) | (~always5(s72)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s72, s73)) | (~always5(s72)) | always5(s73))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8857,plain,
% 36.04/23.89 (((~always5(s72)) | (~trans(s72, s73)) | always5(s73)) <=> ((~trans(s72, s73)) | (~always5(s72)) | always5(s73))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8858,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s72)) | (~trans(s72, s73)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s72, s73)) | (~always5(s72)) | always5(s73)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8857])).
% 36.04/23.89 tff(8859,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s72)) | (~trans(s72, s73)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s72, s73)) | (~always5(s72)) | always5(s73))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8858, 8856])).
% 36.04/23.89 tff(8860,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s72)) | (~trans(s72, s73)) | always5(s73))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8861,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s72, s73)) | (~always5(s72)) | always5(s73)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8860, 8859])).
% 36.04/23.89 tff(8862,plain,
% 36.04/23.89 ((~always5(s72)) | always5(s73)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8861, 25, 2242])).
% 36.04/23.89 tff(8863,plain,
% 36.04/23.89 (~always5(s72)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8862, 8855])).
% 36.04/23.89 tff(8864,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s71, s72)) | (~always5(s71)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s71, s72)) | (~always5(s71)) | always5(s72))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8865,plain,
% 36.04/23.89 (((~always5(s71)) | (~trans(s71, s72)) | always5(s72)) <=> ((~trans(s71, s72)) | (~always5(s71)) | always5(s72))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8866,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s71)) | (~trans(s71, s72)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s71, s72)) | (~always5(s71)) | always5(s72)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8865])).
% 36.04/23.89 tff(8867,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s71)) | (~trans(s71, s72)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s71, s72)) | (~always5(s71)) | always5(s72))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8866, 8864])).
% 36.04/23.89 tff(8868,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s71)) | (~trans(s71, s72)) | always5(s72))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8869,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s71, s72)) | (~always5(s71)) | always5(s72)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8868, 8867])).
% 36.04/23.89 tff(8870,plain,
% 36.04/23.89 ((~always5(s71)) | always5(s72)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8869, 25, 2211])).
% 36.04/23.89 tff(8871,plain,
% 36.04/23.89 (~always5(s71)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8870, 8863])).
% 36.04/23.89 tff(8872,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s70, s71)) | (~always5(s70)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s70, s71)) | (~always5(s70)) | always5(s71))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8873,plain,
% 36.04/23.89 (((~always5(s70)) | (~trans(s70, s71)) | always5(s71)) <=> ((~trans(s70, s71)) | (~always5(s70)) | always5(s71))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8874,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s70)) | (~trans(s70, s71)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s70, s71)) | (~always5(s70)) | always5(s71)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8873])).
% 36.04/23.89 tff(8875,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s70)) | (~trans(s70, s71)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s70, s71)) | (~always5(s70)) | always5(s71))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8874, 8872])).
% 36.04/23.89 tff(8876,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s70)) | (~trans(s70, s71)) | always5(s71))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8877,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s70, s71)) | (~always5(s70)) | always5(s71)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8876, 8875])).
% 36.04/23.89 tff(8878,plain,
% 36.04/23.89 ((~always5(s70)) | always5(s71)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8877, 25, 2183])).
% 36.04/23.89 tff(8879,plain,
% 36.04/23.89 (~always5(s70)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8878, 8871])).
% 36.04/23.89 tff(8880,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s69, s70)) | (~always5(s69)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s69, s70)) | (~always5(s69)) | always5(s70))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8881,plain,
% 36.04/23.89 (((~always5(s69)) | (~trans(s69, s70)) | always5(s70)) <=> ((~trans(s69, s70)) | (~always5(s69)) | always5(s70))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8882,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s69)) | (~trans(s69, s70)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s69, s70)) | (~always5(s69)) | always5(s70)))),
% 36.04/23.89 inference(monotonicity,[status(thm)],[8881])).
% 36.04/23.89 tff(8883,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s69)) | (~trans(s69, s70)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s69, s70)) | (~always5(s69)) | always5(s70))),
% 36.04/23.89 inference(transitivity,[status(thm)],[8882, 8880])).
% 36.04/23.89 tff(8884,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s69)) | (~trans(s69, s70)) | always5(s70))),
% 36.04/23.89 inference(quant_inst,[status(thm)],[])).
% 36.04/23.89 tff(8885,plain,
% 36.04/23.89 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s69, s70)) | (~always5(s69)) | always5(s70)),
% 36.04/23.89 inference(modus_ponens,[status(thm)],[8884, 8883])).
% 36.04/23.89 tff(8886,plain,
% 36.04/23.89 ((~always5(s69)) | always5(s70)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8885, 25, 2152])).
% 36.04/23.89 tff(8887,plain,
% 36.04/23.89 (~always5(s69)),
% 36.04/23.89 inference(unit_resolution,[status(thm)],[8886, 8879])).
% 36.04/23.89 tff(8888,plain,
% 36.04/23.89 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s68, s69)) | (~always5(s68)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s68, s69)) | (~always5(s68)) | always5(s69))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.89 tff(8889,plain,
% 36.04/23.89 (((~always5(s68)) | (~trans(s68, s69)) | always5(s69)) <=> ((~trans(s68, s69)) | (~always5(s68)) | always5(s69))),
% 36.04/23.89 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8890,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s68)) | (~trans(s68, s69)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s68, s69)) | (~always5(s68)) | always5(s69)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8889])).
% 36.04/23.90 tff(8891,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s68)) | (~trans(s68, s69)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s68, s69)) | (~always5(s68)) | always5(s69))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8890, 8888])).
% 36.04/23.90 tff(8892,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s68)) | (~trans(s68, s69)) | always5(s69))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8893,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s68, s69)) | (~always5(s68)) | always5(s69)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8892, 8891])).
% 36.04/23.90 tff(8894,plain,
% 36.04/23.90 ((~always5(s68)) | always5(s69)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8893, 25, 2124])).
% 36.04/23.90 tff(8895,plain,
% 36.04/23.90 (~always5(s68)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8894, 8887])).
% 36.04/23.90 tff(8896,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s67, s68)) | (~always5(s67)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s67, s68)) | (~always5(s67)) | always5(s68))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8897,plain,
% 36.04/23.90 (((~always5(s67)) | (~trans(s67, s68)) | always5(s68)) <=> ((~trans(s67, s68)) | (~always5(s67)) | always5(s68))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8898,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s67)) | (~trans(s67, s68)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s67, s68)) | (~always5(s67)) | always5(s68)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8897])).
% 36.04/23.90 tff(8899,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s67)) | (~trans(s67, s68)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s67, s68)) | (~always5(s67)) | always5(s68))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8898, 8896])).
% 36.04/23.90 tff(8900,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s67)) | (~trans(s67, s68)) | always5(s68))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8901,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s67, s68)) | (~always5(s67)) | always5(s68)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8900, 8899])).
% 36.04/23.90 tff(8902,plain,
% 36.04/23.90 ((~always5(s67)) | always5(s68)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8901, 25, 2093])).
% 36.04/23.90 tff(8903,plain,
% 36.04/23.90 (~always5(s67)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8902, 8895])).
% 36.04/23.90 tff(8904,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s66, s67)) | (~always5(s66)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s66, s67)) | (~always5(s66)) | always5(s67))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8905,plain,
% 36.04/23.90 (((~always5(s66)) | (~trans(s66, s67)) | always5(s67)) <=> ((~trans(s66, s67)) | (~always5(s66)) | always5(s67))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8906,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s66)) | (~trans(s66, s67)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s66, s67)) | (~always5(s66)) | always5(s67)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8905])).
% 36.04/23.90 tff(8907,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s66)) | (~trans(s66, s67)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s66, s67)) | (~always5(s66)) | always5(s67))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8906, 8904])).
% 36.04/23.90 tff(8908,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s66)) | (~trans(s66, s67)) | always5(s67))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8909,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s66, s67)) | (~always5(s66)) | always5(s67)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8908, 8907])).
% 36.04/23.90 tff(8910,plain,
% 36.04/23.90 ((~always5(s66)) | always5(s67)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8909, 25, 2065])).
% 36.04/23.90 tff(8911,plain,
% 36.04/23.90 (~always5(s66)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8910, 8903])).
% 36.04/23.90 tff(8912,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s65, s66)) | (~always5(s65)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s65, s66)) | (~always5(s65)) | always5(s66))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8913,plain,
% 36.04/23.90 (((~always5(s65)) | (~trans(s65, s66)) | always5(s66)) <=> ((~trans(s65, s66)) | (~always5(s65)) | always5(s66))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8914,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s65)) | (~trans(s65, s66)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s65, s66)) | (~always5(s65)) | always5(s66)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8913])).
% 36.04/23.90 tff(8915,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s65)) | (~trans(s65, s66)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s65, s66)) | (~always5(s65)) | always5(s66))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8914, 8912])).
% 36.04/23.90 tff(8916,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s65)) | (~trans(s65, s66)) | always5(s66))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8917,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s65, s66)) | (~always5(s65)) | always5(s66)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8916, 8915])).
% 36.04/23.90 tff(8918,plain,
% 36.04/23.90 ((~always5(s65)) | always5(s66)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8917, 25, 2034])).
% 36.04/23.90 tff(8919,plain,
% 36.04/23.90 (~always5(s65)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8918, 8911])).
% 36.04/23.90 tff(8920,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s64, s65)) | (~always5(s64)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s64, s65)) | (~always5(s64)) | always5(s65))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8921,plain,
% 36.04/23.90 (((~always5(s64)) | (~trans(s64, s65)) | always5(s65)) <=> ((~trans(s64, s65)) | (~always5(s64)) | always5(s65))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8922,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s64)) | (~trans(s64, s65)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s64, s65)) | (~always5(s64)) | always5(s65)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8921])).
% 36.04/23.90 tff(8923,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s64)) | (~trans(s64, s65)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s64, s65)) | (~always5(s64)) | always5(s65))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8922, 8920])).
% 36.04/23.90 tff(8924,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s64)) | (~trans(s64, s65)) | always5(s65))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8925,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s64, s65)) | (~always5(s64)) | always5(s65)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8924, 8923])).
% 36.04/23.90 tff(8926,plain,
% 36.04/23.90 ((~always5(s64)) | always5(s65)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8925, 25, 2006])).
% 36.04/23.90 tff(8927,plain,
% 36.04/23.90 (~always5(s64)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8926, 8919])).
% 36.04/23.90 tff(8928,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s63, s64)) | (~always5(s63)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s63, s64)) | (~always5(s63)) | always5(s64))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8929,plain,
% 36.04/23.90 (((~always5(s63)) | (~trans(s63, s64)) | always5(s64)) <=> ((~trans(s63, s64)) | (~always5(s63)) | always5(s64))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8930,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s63)) | (~trans(s63, s64)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s63, s64)) | (~always5(s63)) | always5(s64)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8929])).
% 36.04/23.90 tff(8931,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s63)) | (~trans(s63, s64)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s63, s64)) | (~always5(s63)) | always5(s64))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8930, 8928])).
% 36.04/23.90 tff(8932,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s63)) | (~trans(s63, s64)) | always5(s64))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8933,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s63, s64)) | (~always5(s63)) | always5(s64)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8932, 8931])).
% 36.04/23.90 tff(8934,plain,
% 36.04/23.90 ((~always5(s63)) | always5(s64)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8933, 25, 1975])).
% 36.04/23.90 tff(8935,plain,
% 36.04/23.90 (~always5(s63)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8934, 8927])).
% 36.04/23.90 tff(8936,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s62, s63)) | (~always5(s62)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s62, s63)) | (~always5(s62)) | always5(s63))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8937,plain,
% 36.04/23.90 (((~always5(s62)) | (~trans(s62, s63)) | always5(s63)) <=> ((~trans(s62, s63)) | (~always5(s62)) | always5(s63))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8938,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s62)) | (~trans(s62, s63)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s62, s63)) | (~always5(s62)) | always5(s63)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8937])).
% 36.04/23.90 tff(8939,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s62)) | (~trans(s62, s63)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s62, s63)) | (~always5(s62)) | always5(s63))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8938, 8936])).
% 36.04/23.90 tff(8940,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s62)) | (~trans(s62, s63)) | always5(s63))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8941,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s62, s63)) | (~always5(s62)) | always5(s63)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8940, 8939])).
% 36.04/23.90 tff(8942,plain,
% 36.04/23.90 ((~always5(s62)) | always5(s63)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8941, 25, 1947])).
% 36.04/23.90 tff(8943,plain,
% 36.04/23.90 (~always5(s62)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8942, 8935])).
% 36.04/23.90 tff(8944,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s61, s62)) | (~always5(s61)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s61, s62)) | (~always5(s61)) | always5(s62))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8945,plain,
% 36.04/23.90 (((~always5(s61)) | (~trans(s61, s62)) | always5(s62)) <=> ((~trans(s61, s62)) | (~always5(s61)) | always5(s62))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8946,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s61)) | (~trans(s61, s62)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s61, s62)) | (~always5(s61)) | always5(s62)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8945])).
% 36.04/23.90 tff(8947,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s61)) | (~trans(s61, s62)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s61, s62)) | (~always5(s61)) | always5(s62))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8946, 8944])).
% 36.04/23.90 tff(8948,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s61)) | (~trans(s61, s62)) | always5(s62))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8949,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s61, s62)) | (~always5(s61)) | always5(s62)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8948, 8947])).
% 36.04/23.90 tff(8950,plain,
% 36.04/23.90 ((~always5(s61)) | always5(s62)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8949, 25, 1916])).
% 36.04/23.90 tff(8951,plain,
% 36.04/23.90 (~always5(s61)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8950, 8943])).
% 36.04/23.90 tff(8952,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s60, s61)) | (~always5(s60)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s60, s61)) | (~always5(s60)) | always5(s61))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8953,plain,
% 36.04/23.90 (((~always5(s60)) | (~trans(s60, s61)) | always5(s61)) <=> ((~trans(s60, s61)) | (~always5(s60)) | always5(s61))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8954,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s60)) | (~trans(s60, s61)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s60, s61)) | (~always5(s60)) | always5(s61)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8953])).
% 36.04/23.90 tff(8955,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s60)) | (~trans(s60, s61)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s60, s61)) | (~always5(s60)) | always5(s61))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8954, 8952])).
% 36.04/23.90 tff(8956,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s60)) | (~trans(s60, s61)) | always5(s61))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8957,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s60, s61)) | (~always5(s60)) | always5(s61)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8956, 8955])).
% 36.04/23.90 tff(8958,plain,
% 36.04/23.90 ((~always5(s60)) | always5(s61)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8957, 25, 1888])).
% 36.04/23.90 tff(8959,plain,
% 36.04/23.90 (~always5(s60)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8958, 8951])).
% 36.04/23.90 tff(8960,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s59, s60)) | (~always5(s59)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s59, s60)) | (~always5(s59)) | always5(s60))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8961,plain,
% 36.04/23.90 (((~always5(s59)) | (~trans(s59, s60)) | always5(s60)) <=> ((~trans(s59, s60)) | (~always5(s59)) | always5(s60))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8962,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s60)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s59, s60)) | (~always5(s59)) | always5(s60)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8961])).
% 36.04/23.90 tff(8963,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s60)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s59, s60)) | (~always5(s59)) | always5(s60))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8962, 8960])).
% 36.04/23.90 tff(8964,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s59)) | (~trans(s59, s60)) | always5(s60))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8965,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s59, s60)) | (~always5(s59)) | always5(s60)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8964, 8963])).
% 36.04/23.90 tff(8966,plain,
% 36.04/23.90 ((~always5(s59)) | always5(s60)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8965, 25, 74])).
% 36.04/23.90 tff(8967,plain,
% 36.04/23.90 (~always5(s59)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8966, 8959])).
% 36.04/23.90 tff(8968,assumption,(~always5(s87)), introduced(assumption)).
% 36.04/23.90 tff(8969,assumption,(~always5(s99)), introduced(assumption)).
% 36.04/23.90 tff(8970,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (always5(s99) | (~trans(s98, s99)) | (~always5(s98)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s99) | (~trans(s98, s99)) | (~always5(s98)))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8971,plain,
% 36.04/23.90 (((~always5(s98)) | (~trans(s98, s99)) | always5(s99)) <=> (always5(s99) | (~trans(s98, s99)) | (~always5(s98)))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8972,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s98)) | (~trans(s98, s99)) | always5(s99))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (always5(s99) | (~trans(s98, s99)) | (~always5(s98))))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8971])).
% 36.04/23.90 tff(8973,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s98)) | (~trans(s98, s99)) | always5(s99))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s99) | (~trans(s98, s99)) | (~always5(s98)))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8972, 8970])).
% 36.04/23.90 tff(8974,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s98)) | (~trans(s98, s99)) | always5(s99))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8975,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | always5(s99) | (~trans(s98, s99)) | (~always5(s98))),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8974, 8973])).
% 36.04/23.90 tff(8976,plain,
% 36.04/23.90 (always5(s99) | (~always5(s98))),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8975, 25, 8629])).
% 36.04/23.90 tff(8977,plain,
% 36.04/23.90 (~always5(s98)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8976, 8969])).
% 36.04/23.90 tff(8978,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s97, s98)) | (~always5(s97)) | always5(s98))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s97, s98)) | (~always5(s97)) | always5(s98))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8979,plain,
% 36.04/23.90 (((~always5(s97)) | (~trans(s97, s98)) | always5(s98)) <=> ((~trans(s97, s98)) | (~always5(s97)) | always5(s98))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(8980,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s97)) | (~trans(s97, s98)) | always5(s98))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s97, s98)) | (~always5(s97)) | always5(s98)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[8979])).
% 36.04/23.90 tff(8981,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s97)) | (~trans(s97, s98)) | always5(s98))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s97, s98)) | (~always5(s97)) | always5(s98))),
% 36.04/23.90 inference(transitivity,[status(thm)],[8980, 8978])).
% 36.04/23.90 tff(8982,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s97)) | (~trans(s97, s98)) | always5(s98))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(8983,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s97, s98)) | (~always5(s97)) | always5(s98)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[8982, 8981])).
% 36.04/23.90 tff(8984,plain,
% 36.04/23.90 ((~always5(s97)) | always5(s98)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8983, 25, 8565])).
% 36.04/23.90 tff(8985,plain,
% 36.04/23.90 (~always5(s97)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8984, 8977])).
% 36.04/23.90 tff(8986,plain,
% 36.04/23.90 (~always5(s96)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[47, 8985])).
% 36.04/23.90 tff(8987,plain,
% 36.04/23.90 (~always5(s95)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[32, 8986])).
% 36.04/23.90 tff(8988,plain,
% 36.04/23.90 (~always5(s94)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8686, 8987])).
% 36.04/23.90 tff(8989,plain,
% 36.04/23.90 (~always5(s93)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8694, 8988])).
% 36.04/23.90 tff(8990,plain,
% 36.04/23.90 (~always5(s92)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8702, 8989])).
% 36.04/23.90 tff(8991,plain,
% 36.04/23.90 (~always5(s91)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8710, 8990])).
% 36.04/23.90 tff(8992,plain,
% 36.04/23.90 (~always5(s90)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8718, 8991])).
% 36.04/23.90 tff(8993,plain,
% 36.04/23.90 (~always5(s89)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8726, 8992])).
% 36.04/23.90 tff(8994,plain,
% 36.04/23.90 (~always5(s88)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8734, 8993])).
% 36.04/23.90 tff(8995,plain,
% 36.04/23.90 (~always5(s87)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8742, 8994])).
% 36.04/23.90 tff(8996,plain,
% 36.04/23.90 (~always5(s86)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8750, 8995])).
% 36.04/23.90 tff(8997,plain,
% 36.04/23.90 (~always5(s85)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8758, 8996])).
% 36.04/23.90 tff(8998,plain,
% 36.04/23.90 (~always5(s84)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8766, 8997])).
% 36.04/23.90 tff(8999,plain,
% 36.04/23.90 (~always5(s83)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8774, 8998])).
% 36.04/23.90 tff(9000,plain,
% 36.04/23.90 (~always5(s82)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8782, 8999])).
% 36.04/23.90 tff(9001,plain,
% 36.04/23.90 (~always5(s81)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8790, 9000])).
% 36.04/23.90 tff(9002,plain,
% 36.04/23.90 (~always5(s80)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8798, 9001])).
% 36.04/23.90 tff(9003,plain,
% 36.04/23.90 (~always5(s79)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8806, 9002])).
% 36.04/23.90 tff(9004,plain,
% 36.04/23.90 (~always5(s78)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8814, 9003])).
% 36.04/23.90 tff(9005,plain,
% 36.04/23.90 (~always5(s77)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8822, 9004])).
% 36.04/23.90 tff(9006,plain,
% 36.04/23.90 (~always5(s76)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8830, 9005])).
% 36.04/23.90 tff(9007,plain,
% 36.04/23.90 (~always5(s75)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8838, 9006])).
% 36.04/23.90 tff(9008,plain,
% 36.04/23.90 (~always5(s74)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8846, 9007])).
% 36.04/23.90 tff(9009,plain,
% 36.04/23.90 (~always5(s73)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8854, 9008])).
% 36.04/23.90 tff(9010,plain,
% 36.04/23.90 (~always5(s72)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8862, 9009])).
% 36.04/23.90 tff(9011,plain,
% 36.04/23.90 (~always5(s71)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8870, 9010])).
% 36.04/23.90 tff(9012,plain,
% 36.04/23.90 (~always5(s70)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8878, 9011])).
% 36.04/23.90 tff(9013,plain,
% 36.04/23.90 (~always5(s69)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8886, 9012])).
% 36.04/23.90 tff(9014,plain,
% 36.04/23.90 (~always5(s68)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8894, 9013])).
% 36.04/23.90 tff(9015,plain,
% 36.04/23.90 (~always5(s67)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8902, 9014])).
% 36.04/23.90 tff(9016,plain,
% 36.04/23.90 (~always5(s66)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8910, 9015])).
% 36.04/23.90 tff(9017,plain,
% 36.04/23.90 (~always5(s65)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8918, 9016])).
% 36.04/23.90 tff(9018,plain,
% 36.04/23.90 (~always5(s64)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8926, 9017])).
% 36.04/23.90 tff(9019,plain,
% 36.04/23.90 (~always5(s63)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8934, 9018])).
% 36.04/23.90 tff(9020,plain,
% 36.04/23.90 (~always5(s62)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8942, 9019])).
% 36.04/23.90 tff(9021,plain,
% 36.04/23.90 (~always5(s61)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8950, 9020])).
% 36.04/23.90 tff(9022,plain,
% 36.04/23.90 (~always5(s60)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8958, 9021])).
% 36.04/23.90 tff(9023,plain,
% 36.04/23.90 (~always5(s59)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[8966, 9022])).
% 36.04/23.90 tff(9024,plain,
% 36.04/23.90 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~trans(s58, s59)) | (~always5(s58)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s58, s59)) | (~always5(s58)) | always5(s59))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9025,plain,
% 36.04/23.90 (((~always5(s58)) | (~trans(s58, s59)) | always5(s59)) <=> ((~trans(s58, s59)) | (~always5(s58)) | always5(s59))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9026,plain,
% 36.04/23.90 (((~![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))) | ((~trans(s58, s59)) | (~always5(s58)) | always5(s59)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[9025])).
% 36.04/23.90 tff(9027,plain,
% 36.04/23.90 (((~![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))) | (~trans(s58, s59)) | (~always5(s58)) | always5(s59))),
% 36.04/23.90 inference(transitivity,[status(thm)],[9026, 9024])).
% 36.04/23.90 tff(9028,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s58)) | (~trans(s58, s59)) | always5(s59))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(9029,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s58, s59)) | (~always5(s58)) | always5(s59)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[9028, 9027])).
% 36.04/23.90 tff(9030,plain,
% 36.04/23.90 ((~always5(s58)) | always5(s59)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9029, 25, 1841])).
% 36.04/23.90 tff(9031,plain,
% 36.04/23.90 (~always5(s58)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9030, 9023])).
% 36.04/23.90 tff(9032,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9033,plain,
% 36.04/23.90 (((~always5(s57)) | (~trans(s57, s58)) | always5(s58)) <=> ((~trans(s57, s58)) | (~always5(s57)) | always5(s58))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9034,plain,
% 36.04/23.90 (((~![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)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[9033])).
% 36.04/23.90 tff(9035,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(transitivity,[status(thm)],[9034, 9032])).
% 36.04/23.90 tff(9036,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s57)) | (~trans(s57, s58)) | always5(s58))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(9037,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s57, s58)) | (~always5(s57)) | always5(s58)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[9036, 9035])).
% 36.04/23.90 tff(9038,plain,
% 36.04/23.90 ((~always5(s57)) | always5(s58)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9037, 25, 1810])).
% 36.04/23.90 tff(9039,plain,
% 36.04/23.90 (~always5(s57)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9038, 9031])).
% 36.04/23.90 tff(9040,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9041,plain,
% 36.04/23.90 (((~always5(s56)) | (~trans(s56, s57)) | always5(s57)) <=> ((~trans(s56, s57)) | (~always5(s56)) | always5(s57))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9042,plain,
% 36.04/23.90 (((~![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)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[9041])).
% 36.04/23.90 tff(9043,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(transitivity,[status(thm)],[9042, 9040])).
% 36.04/23.90 tff(9044,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s56)) | (~trans(s56, s57)) | always5(s57))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(9045,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s56, s57)) | (~always5(s56)) | always5(s57)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[9044, 9043])).
% 36.04/23.90 tff(9046,plain,
% 36.04/23.90 ((~always5(s56)) | always5(s57)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9045, 25, 1782])).
% 36.04/23.90 tff(9047,plain,
% 36.04/23.90 (~always5(s56)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9046, 9039])).
% 36.04/23.90 tff(9048,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9049,plain,
% 36.04/23.90 (((~always5(s55)) | (~trans(s55, s56)) | always5(s56)) <=> ((~trans(s55, s56)) | (~always5(s55)) | always5(s56))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9050,plain,
% 36.04/23.90 (((~![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)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[9049])).
% 36.04/23.90 tff(9051,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(transitivity,[status(thm)],[9050, 9048])).
% 36.04/23.90 tff(9052,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s55)) | (~trans(s55, s56)) | always5(s56))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(9053,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s55, s56)) | (~always5(s55)) | always5(s56)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[9052, 9051])).
% 36.04/23.90 tff(9054,plain,
% 36.04/23.90 ((~always5(s55)) | always5(s56)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9053, 25, 1751])).
% 36.04/23.90 tff(9055,plain,
% 36.04/23.90 (~always5(s55)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9054, 9047])).
% 36.04/23.90 tff(9056,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9057,plain,
% 36.04/23.90 (((~always5(s54)) | (~trans(s54, s55)) | always5(s55)) <=> ((~trans(s54, s55)) | (~always5(s54)) | always5(s55))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9058,plain,
% 36.04/23.90 (((~![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)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[9057])).
% 36.04/23.90 tff(9059,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(transitivity,[status(thm)],[9058, 9056])).
% 36.04/23.90 tff(9060,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s54)) | (~trans(s54, s55)) | always5(s55))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(9061,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s54, s55)) | (~always5(s54)) | always5(s55)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[9060, 9059])).
% 36.04/23.90 tff(9062,plain,
% 36.04/23.90 ((~always5(s54)) | always5(s55)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9061, 25, 1723])).
% 36.04/23.90 tff(9063,plain,
% 36.04/23.90 (~always5(s54)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9062, 9055])).
% 36.04/23.90 tff(9064,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9065,plain,
% 36.04/23.90 (((~always5(s53)) | (~trans(s53, s54)) | always5(s54)) <=> ((~trans(s53, s54)) | (~always5(s53)) | always5(s54))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9066,plain,
% 36.04/23.90 (((~![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)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[9065])).
% 36.04/23.90 tff(9067,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(transitivity,[status(thm)],[9066, 9064])).
% 36.04/23.90 tff(9068,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s53)) | (~trans(s53, s54)) | always5(s54))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(9069,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s53, s54)) | (~always5(s53)) | always5(s54)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[9068, 9067])).
% 36.04/23.90 tff(9070,plain,
% 36.04/23.90 ((~always5(s53)) | always5(s54)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9069, 25, 1692])).
% 36.04/23.90 tff(9071,plain,
% 36.04/23.90 (~always5(s53)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9070, 9063])).
% 36.04/23.90 tff(9072,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9073,plain,
% 36.04/23.90 (((~always5(s52)) | (~trans(s52, s53)) | always5(s53)) <=> ((~trans(s52, s53)) | (~always5(s52)) | always5(s53))),
% 36.04/23.90 inference(rewrite,[status(thm)],[])).
% 36.04/23.90 tff(9074,plain,
% 36.04/23.90 (((~![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)))),
% 36.04/23.90 inference(monotonicity,[status(thm)],[9073])).
% 36.04/23.90 tff(9075,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.90 inference(transitivity,[status(thm)],[9074, 9072])).
% 36.04/23.90 tff(9076,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s52)) | (~trans(s52, s53)) | always5(s53))),
% 36.04/23.90 inference(quant_inst,[status(thm)],[])).
% 36.04/23.90 tff(9077,plain,
% 36.04/23.90 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s52, s53)) | (~always5(s52)) | always5(s53)),
% 36.04/23.90 inference(modus_ponens,[status(thm)],[9076, 9075])).
% 36.04/23.90 tff(9078,plain,
% 36.04/23.90 ((~always5(s52)) | always5(s53)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9077, 25, 1664])).
% 36.04/23.90 tff(9079,plain,
% 36.04/23.90 (~always5(s52)),
% 36.04/23.90 inference(unit_resolution,[status(thm)],[9078, 9071])).
% 36.04/23.90 tff(9080,plain,
% 36.04/23.90 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9081,plain,
% 36.04/23.91 (((~always5(s51)) | (~trans(s51, s52)) | always5(s52)) <=> ((~trans(s51, s52)) | (~always5(s51)) | always5(s52))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9082,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9081])).
% 36.04/23.91 tff(9083,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9082, 9080])).
% 36.04/23.91 tff(9084,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s51)) | (~trans(s51, s52)) | always5(s52))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9085,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s51, s52)) | (~always5(s51)) | always5(s52)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9084, 9083])).
% 36.04/23.91 tff(9086,plain,
% 36.04/23.91 ((~always5(s51)) | always5(s52)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9085, 25, 1633])).
% 36.04/23.91 tff(9087,plain,
% 36.04/23.91 (~always5(s51)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9086, 9079])).
% 36.04/23.91 tff(9088,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9089,plain,
% 36.04/23.91 (((~always5(s50)) | (~trans(s50, s51)) | always5(s51)) <=> ((~trans(s50, s51)) | (~always5(s50)) | always5(s51))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9090,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9089])).
% 36.04/23.91 tff(9091,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9090, 9088])).
% 36.04/23.91 tff(9092,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s50)) | (~trans(s50, s51)) | always5(s51))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9093,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s50, s51)) | (~always5(s50)) | always5(s51)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9092, 9091])).
% 36.04/23.91 tff(9094,plain,
% 36.04/23.91 ((~always5(s50)) | always5(s51)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9093, 25, 1605])).
% 36.04/23.91 tff(9095,plain,
% 36.04/23.91 (~always5(s50)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9094, 9087])).
% 36.04/23.91 tff(9096,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9097,plain,
% 36.04/23.91 (((~always5(s49)) | (~trans(s49, s50)) | always5(s50)) <=> ((~trans(s49, s50)) | (~always5(s49)) | always5(s50))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9098,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9097])).
% 36.04/23.91 tff(9099,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9098, 9096])).
% 36.04/23.91 tff(9100,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s49)) | (~trans(s49, s50)) | always5(s50))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9101,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s49, s50)) | (~always5(s49)) | always5(s50)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9100, 9099])).
% 36.04/23.91 tff(9102,plain,
% 36.04/23.91 ((~always5(s49)) | always5(s50)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9101, 25, 1574])).
% 36.04/23.91 tff(9103,plain,
% 36.04/23.91 (~always5(s49)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9102, 9095])).
% 36.04/23.91 tff(9104,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9105,plain,
% 36.04/23.91 (((~always5(s48)) | (~trans(s48, s49)) | always5(s49)) <=> ((~trans(s48, s49)) | (~always5(s48)) | always5(s49))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9106,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9105])).
% 36.04/23.91 tff(9107,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9106, 9104])).
% 36.04/23.91 tff(9108,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s48)) | (~trans(s48, s49)) | always5(s49))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9109,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s48, s49)) | (~always5(s48)) | always5(s49)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9108, 9107])).
% 36.04/23.91 tff(9110,plain,
% 36.04/23.91 ((~always5(s48)) | always5(s49)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9109, 25, 1546])).
% 36.04/23.91 tff(9111,plain,
% 36.04/23.91 (~always5(s48)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9110, 9103])).
% 36.04/23.91 tff(9112,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9113,plain,
% 36.04/23.91 (((~always5(s47)) | (~trans(s47, s48)) | always5(s48)) <=> ((~trans(s47, s48)) | (~always5(s47)) | always5(s48))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9114,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9113])).
% 36.04/23.91 tff(9115,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9114, 9112])).
% 36.04/23.91 tff(9116,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s47)) | (~trans(s47, s48)) | always5(s48))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9117,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s47, s48)) | (~always5(s47)) | always5(s48)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9116, 9115])).
% 36.04/23.91 tff(9118,plain,
% 36.04/23.91 ((~always5(s47)) | always5(s48)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9117, 25, 1515])).
% 36.04/23.91 tff(9119,plain,
% 36.04/23.91 (~always5(s47)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9118, 9111])).
% 36.04/23.91 tff(9120,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9121,plain,
% 36.04/23.91 (((~always5(s46)) | (~trans(s46, s47)) | always5(s47)) <=> ((~trans(s46, s47)) | (~always5(s46)) | always5(s47))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9122,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9121])).
% 36.04/23.91 tff(9123,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9122, 9120])).
% 36.04/23.91 tff(9124,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s46)) | (~trans(s46, s47)) | always5(s47))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9125,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s46, s47)) | (~always5(s46)) | always5(s47)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9124, 9123])).
% 36.04/23.91 tff(9126,plain,
% 36.04/23.91 ((~always5(s46)) | always5(s47)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9125, 25, 1487])).
% 36.04/23.91 tff(9127,plain,
% 36.04/23.91 (~always5(s46)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9126, 9119])).
% 36.04/23.91 tff(9128,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9129,plain,
% 36.04/23.91 (((~always5(s45)) | (~trans(s45, s46)) | always5(s46)) <=> ((~trans(s45, s46)) | (~always5(s45)) | always5(s46))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9130,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9129])).
% 36.04/23.91 tff(9131,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9130, 9128])).
% 36.04/23.91 tff(9132,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s45)) | (~trans(s45, s46)) | always5(s46))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9133,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s45, s46)) | (~always5(s45)) | always5(s46)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9132, 9131])).
% 36.04/23.91 tff(9134,plain,
% 36.04/23.91 ((~always5(s45)) | always5(s46)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9133, 25, 1456])).
% 36.04/23.91 tff(9135,plain,
% 36.04/23.91 (~always5(s45)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9134, 9127])).
% 36.04/23.91 tff(9136,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9137,plain,
% 36.04/23.91 (((~always5(s44)) | (~trans(s44, s45)) | always5(s45)) <=> ((~trans(s44, s45)) | (~always5(s44)) | always5(s45))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9138,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9137])).
% 36.04/23.91 tff(9139,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9138, 9136])).
% 36.04/23.91 tff(9140,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s44)) | (~trans(s44, s45)) | always5(s45))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9141,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s44, s45)) | (~always5(s44)) | always5(s45)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9140, 9139])).
% 36.04/23.91 tff(9142,plain,
% 36.04/23.91 ((~always5(s44)) | always5(s45)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9141, 25, 1430])).
% 36.04/23.91 tff(9143,plain,
% 36.04/23.91 (~always5(s44)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9142, 9135])).
% 36.04/23.91 tff(9144,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9145,plain,
% 36.04/23.91 (((~always5(s43)) | (~trans(s43, s44)) | always5(s44)) <=> ((~trans(s43, s44)) | (~always5(s43)) | always5(s44))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9146,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9145])).
% 36.04/23.91 tff(9147,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9146, 9144])).
% 36.04/23.91 tff(9148,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s43)) | (~trans(s43, s44)) | always5(s44))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9149,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s43, s44)) | (~always5(s43)) | always5(s44)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9148, 9147])).
% 36.04/23.91 tff(9150,plain,
% 36.04/23.91 ((~always5(s43)) | always5(s44)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9149, 25, 1399])).
% 36.04/23.91 tff(9151,plain,
% 36.04/23.91 (~always5(s43)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9150, 9143])).
% 36.04/23.91 tff(9152,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9153,plain,
% 36.04/23.91 (((~always5(s42)) | (~trans(s42, s43)) | always5(s43)) <=> ((~trans(s42, s43)) | (~always5(s42)) | always5(s43))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9154,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9153])).
% 36.04/23.91 tff(9155,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9154, 9152])).
% 36.04/23.91 tff(9156,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s42)) | (~trans(s42, s43)) | always5(s43))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9157,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s42, s43)) | (~always5(s42)) | always5(s43)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9156, 9155])).
% 36.04/23.91 tff(9158,plain,
% 36.04/23.91 ((~always5(s42)) | always5(s43)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9157, 25, 1371])).
% 36.04/23.91 tff(9159,plain,
% 36.04/23.91 (~always5(s42)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9158, 9151])).
% 36.04/23.91 tff(9160,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9161,plain,
% 36.04/23.91 (((~always5(s41)) | (~trans(s41, s42)) | always5(s42)) <=> ((~trans(s41, s42)) | (~always5(s41)) | always5(s42))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9162,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9161])).
% 36.04/23.91 tff(9163,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9162, 9160])).
% 36.04/23.91 tff(9164,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s41)) | (~trans(s41, s42)) | always5(s42))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9165,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s41, s42)) | (~always5(s41)) | always5(s42)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9164, 9163])).
% 36.04/23.91 tff(9166,plain,
% 36.04/23.91 ((~always5(s41)) | always5(s42)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9165, 25, 1340])).
% 36.04/23.91 tff(9167,plain,
% 36.04/23.91 (~always5(s41)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9166, 9159])).
% 36.04/23.91 tff(9168,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9169,plain,
% 36.04/23.91 (((~always5(s40)) | (~trans(s40, s41)) | always5(s41)) <=> ((~trans(s40, s41)) | (~always5(s40)) | always5(s41))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9170,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9169])).
% 36.04/23.91 tff(9171,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9170, 9168])).
% 36.04/23.91 tff(9172,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s40)) | (~trans(s40, s41)) | always5(s41))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9173,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s40, s41)) | (~always5(s40)) | always5(s41)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9172, 9171])).
% 36.04/23.91 tff(9174,plain,
% 36.04/23.91 ((~always5(s40)) | always5(s41)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9173, 25, 1312])).
% 36.04/23.91 tff(9175,plain,
% 36.04/23.91 (~always5(s40)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9174, 9167])).
% 36.04/23.91 tff(9176,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9177,plain,
% 36.04/23.91 (((~always5(s39)) | (~trans(s39, s40)) | always5(s40)) <=> ((~trans(s39, s40)) | (~always5(s39)) | always5(s40))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9178,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9177])).
% 36.04/23.91 tff(9179,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9178, 9176])).
% 36.04/23.91 tff(9180,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s39)) | (~trans(s39, s40)) | always5(s40))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9181,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s39, s40)) | (~always5(s39)) | always5(s40)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9180, 9179])).
% 36.04/23.91 tff(9182,plain,
% 36.04/23.91 ((~always5(s39)) | always5(s40)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9181, 25, 1281])).
% 36.04/23.91 tff(9183,plain,
% 36.04/23.91 (~always5(s39)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9182, 9175])).
% 36.04/23.91 tff(9184,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9185,plain,
% 36.04/23.91 (((~always5(s38)) | (~trans(s38, s39)) | always5(s39)) <=> ((~trans(s38, s39)) | (~always5(s38)) | always5(s39))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9186,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9185])).
% 36.04/23.91 tff(9187,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9186, 9184])).
% 36.04/23.91 tff(9188,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s38)) | (~trans(s38, s39)) | always5(s39))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9189,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s38, s39)) | (~always5(s38)) | always5(s39)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9188, 9187])).
% 36.04/23.91 tff(9190,plain,
% 36.04/23.91 ((~always5(s38)) | always5(s39)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9189, 25, 1253])).
% 36.04/23.91 tff(9191,plain,
% 36.04/23.91 (~always5(s38)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9190, 9183])).
% 36.04/23.91 tff(9192,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9193,plain,
% 36.04/23.91 (((~always5(s37)) | (~trans(s37, s38)) | always5(s38)) <=> ((~trans(s37, s38)) | (~always5(s37)) | always5(s38))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9194,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9193])).
% 36.04/23.91 tff(9195,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9194, 9192])).
% 36.04/23.91 tff(9196,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s37)) | (~trans(s37, s38)) | always5(s38))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9197,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s37, s38)) | (~always5(s37)) | always5(s38)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9196, 9195])).
% 36.04/23.91 tff(9198,plain,
% 36.04/23.91 ((~always5(s37)) | always5(s38)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9197, 25, 1222])).
% 36.04/23.91 tff(9199,plain,
% 36.04/23.91 (~always5(s37)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9198, 9191])).
% 36.04/23.91 tff(9200,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9201,plain,
% 36.04/23.91 (((~always5(s36)) | (~trans(s36, s37)) | always5(s37)) <=> ((~trans(s36, s37)) | (~always5(s36)) | always5(s37))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9202,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9201])).
% 36.04/23.91 tff(9203,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9202, 9200])).
% 36.04/23.91 tff(9204,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s36)) | (~trans(s36, s37)) | always5(s37))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9205,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s36, s37)) | (~always5(s36)) | always5(s37)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9204, 9203])).
% 36.04/23.91 tff(9206,plain,
% 36.04/23.91 ((~always5(s36)) | always5(s37)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9205, 25, 1194])).
% 36.04/23.91 tff(9207,plain,
% 36.04/23.91 (~always5(s36)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9206, 9199])).
% 36.04/23.91 tff(9208,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9209,plain,
% 36.04/23.91 (((~always5(s35)) | (~trans(s35, s36)) | always5(s36)) <=> ((~trans(s35, s36)) | (~always5(s35)) | always5(s36))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9210,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9209])).
% 36.04/23.91 tff(9211,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9210, 9208])).
% 36.04/23.91 tff(9212,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s35)) | (~trans(s35, s36)) | always5(s36))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9213,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s35, s36)) | (~always5(s35)) | always5(s36)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9212, 9211])).
% 36.04/23.91 tff(9214,plain,
% 36.04/23.91 ((~always5(s35)) | always5(s36)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9213, 25, 1163])).
% 36.04/23.91 tff(9215,plain,
% 36.04/23.91 (~always5(s35)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9214, 9207])).
% 36.04/23.91 tff(9216,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9217,plain,
% 36.04/23.91 (((~always5(s34)) | (~trans(s34, s35)) | always5(s35)) <=> ((~trans(s34, s35)) | (~always5(s34)) | always5(s35))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9218,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9217])).
% 36.04/23.91 tff(9219,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9218, 9216])).
% 36.04/23.91 tff(9220,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s34)) | (~trans(s34, s35)) | always5(s35))),
% 36.04/23.91 inference(quant_inst,[status(thm)],[])).
% 36.04/23.91 tff(9221,plain,
% 36.04/23.91 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s34, s35)) | (~always5(s34)) | always5(s35)),
% 36.04/23.91 inference(modus_ponens,[status(thm)],[9220, 9219])).
% 36.04/23.91 tff(9222,plain,
% 36.04/23.91 ((~always5(s34)) | always5(s35)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9221, 25, 1135])).
% 36.04/23.91 tff(9223,plain,
% 36.04/23.91 (~always5(s34)),
% 36.04/23.91 inference(unit_resolution,[status(thm)],[9222, 9215])).
% 36.04/23.91 tff(9224,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9225,plain,
% 36.04/23.91 (((~always5(s33)) | (~trans(s33, s34)) | always5(s34)) <=> ((~trans(s33, s34)) | (~always5(s33)) | always5(s34))),
% 36.04/23.91 inference(rewrite,[status(thm)],[])).
% 36.04/23.91 tff(9226,plain,
% 36.04/23.91 (((~![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)))),
% 36.04/23.91 inference(monotonicity,[status(thm)],[9225])).
% 36.04/23.91 tff(9227,plain,
% 36.04/23.91 (((~![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))),
% 36.04/23.91 inference(transitivity,[status(thm)],[9226, 9224])).
% 36.04/23.92 tff(9228,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s33)) | (~trans(s33, s34)) | always5(s34))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9229,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s33, s34)) | (~always5(s33)) | always5(s34)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9228, 9227])).
% 36.04/23.92 tff(9230,plain,
% 36.04/23.92 ((~always5(s33)) | always5(s34)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9229, 25, 1104])).
% 36.04/23.92 tff(9231,plain,
% 36.04/23.92 (~always5(s33)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9230, 9223])).
% 36.04/23.92 tff(9232,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9233,plain,
% 36.04/23.92 (((~always5(s32)) | (~trans(s32, s33)) | always5(s33)) <=> ((~trans(s32, s33)) | (~always5(s32)) | always5(s33))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9234,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9233])).
% 36.04/23.92 tff(9235,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9234, 9232])).
% 36.04/23.92 tff(9236,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s32)) | (~trans(s32, s33)) | always5(s33))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9237,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s32, s33)) | (~always5(s32)) | always5(s33)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9236, 9235])).
% 36.04/23.92 tff(9238,plain,
% 36.04/23.92 ((~always5(s32)) | always5(s33)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9237, 25, 1076])).
% 36.04/23.92 tff(9239,plain,
% 36.04/23.92 (~always5(s32)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9238, 9231])).
% 36.04/23.92 tff(9240,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9241,plain,
% 36.04/23.92 (((~always5(s31)) | (~trans(s31, s32)) | always5(s32)) <=> ((~trans(s31, s32)) | (~always5(s31)) | always5(s32))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9242,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9241])).
% 36.04/23.92 tff(9243,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9242, 9240])).
% 36.04/23.92 tff(9244,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s31)) | (~trans(s31, s32)) | always5(s32))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9245,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s31, s32)) | (~always5(s31)) | always5(s32)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9244, 9243])).
% 36.04/23.92 tff(9246,plain,
% 36.04/23.92 ((~always5(s31)) | always5(s32)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9245, 25, 1045])).
% 36.04/23.92 tff(9247,plain,
% 36.04/23.92 (~always5(s31)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9246, 9239])).
% 36.04/23.92 tff(9248,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9249,plain,
% 36.04/23.92 (((~always5(s30)) | (~trans(s30, s31)) | always5(s31)) <=> ((~trans(s30, s31)) | (~always5(s30)) | always5(s31))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9250,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9249])).
% 36.04/23.92 tff(9251,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9250, 9248])).
% 36.04/23.92 tff(9252,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s30)) | (~trans(s30, s31)) | always5(s31))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9253,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s30, s31)) | (~always5(s30)) | always5(s31)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9252, 9251])).
% 36.04/23.92 tff(9254,plain,
% 36.04/23.92 ((~always5(s30)) | always5(s31)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9253, 25, 1017])).
% 36.04/23.92 tff(9255,plain,
% 36.04/23.92 (~always5(s30)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9254, 9247])).
% 36.04/23.92 tff(9256,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9257,plain,
% 36.04/23.92 (((~always5(s29)) | (~trans(s29, s30)) | always5(s30)) <=> ((~trans(s29, s30)) | (~always5(s29)) | always5(s30))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9258,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9257])).
% 36.04/23.92 tff(9259,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9258, 9256])).
% 36.04/23.92 tff(9260,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s29)) | (~trans(s29, s30)) | always5(s30))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9261,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s29, s30)) | (~always5(s29)) | always5(s30)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9260, 9259])).
% 36.04/23.92 tff(9262,plain,
% 36.04/23.92 ((~always5(s29)) | always5(s30)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9261, 25, 986])).
% 36.04/23.92 tff(9263,plain,
% 36.04/23.92 (~always5(s29)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9262, 9255])).
% 36.04/23.92 tff(9264,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9265,plain,
% 36.04/23.92 (((~always5(s28)) | (~trans(s28, s29)) | always5(s29)) <=> ((~trans(s28, s29)) | (~always5(s28)) | always5(s29))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9266,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9265])).
% 36.04/23.92 tff(9267,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9266, 9264])).
% 36.04/23.92 tff(9268,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s28)) | (~trans(s28, s29)) | always5(s29))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9269,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s28, s29)) | (~always5(s28)) | always5(s29)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9268, 9267])).
% 36.04/23.92 tff(9270,plain,
% 36.04/23.92 ((~always5(s28)) | always5(s29)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9269, 25, 958])).
% 36.04/23.92 tff(9271,plain,
% 36.04/23.92 (~always5(s28)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9270, 9263])).
% 36.04/23.92 tff(9272,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9273,plain,
% 36.04/23.92 (((~always5(s27)) | (~trans(s27, s28)) | always5(s28)) <=> ((~trans(s27, s28)) | (~always5(s27)) | always5(s28))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9274,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9273])).
% 36.04/23.92 tff(9275,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9274, 9272])).
% 36.04/23.92 tff(9276,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s27)) | (~trans(s27, s28)) | always5(s28))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9277,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s27, s28)) | (~always5(s27)) | always5(s28)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9276, 9275])).
% 36.04/23.92 tff(9278,plain,
% 36.04/23.92 ((~always5(s27)) | always5(s28)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9277, 25, 929])).
% 36.04/23.92 tff(9279,plain,
% 36.04/23.92 (~always5(s27)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9278, 9271])).
% 36.04/23.92 tff(9280,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9281,plain,
% 36.04/23.92 (((~always5(s26)) | (~trans(s26, s27)) | always5(s27)) <=> ((~trans(s26, s27)) | (~always5(s26)) | always5(s27))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9282,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9281])).
% 36.04/23.92 tff(9283,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9282, 9280])).
% 36.04/23.92 tff(9284,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s26)) | (~trans(s26, s27)) | always5(s27))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9285,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s26, s27)) | (~always5(s26)) | always5(s27)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9284, 9283])).
% 36.04/23.92 tff(9286,plain,
% 36.04/23.92 ((~always5(s26)) | always5(s27)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9285, 25, 901])).
% 36.04/23.92 tff(9287,plain,
% 36.04/23.92 (~always5(s26)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9286, 9279])).
% 36.04/23.92 tff(9288,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9289,plain,
% 36.04/23.92 (((~always5(s25)) | (~trans(s25, s26)) | always5(s26)) <=> ((~trans(s25, s26)) | (~always5(s25)) | always5(s26))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9290,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9289])).
% 36.04/23.92 tff(9291,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9290, 9288])).
% 36.04/23.92 tff(9292,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s25)) | (~trans(s25, s26)) | always5(s26))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9293,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s25, s26)) | (~always5(s25)) | always5(s26)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9292, 9291])).
% 36.04/23.92 tff(9294,plain,
% 36.04/23.92 ((~always5(s25)) | always5(s26)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9293, 25, 870])).
% 36.04/23.92 tff(9295,plain,
% 36.04/23.92 (~always5(s25)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9294, 9287])).
% 36.04/23.92 tff(9296,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9297,plain,
% 36.04/23.92 (((~always5(s24)) | (~trans(s24, s25)) | always5(s25)) <=> ((~trans(s24, s25)) | (~always5(s24)) | always5(s25))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9298,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9297])).
% 36.04/23.92 tff(9299,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9298, 9296])).
% 36.04/23.92 tff(9300,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s24)) | (~trans(s24, s25)) | always5(s25))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9301,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s24, s25)) | (~always5(s24)) | always5(s25)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9300, 9299])).
% 36.04/23.92 tff(9302,plain,
% 36.04/23.92 ((~always5(s24)) | always5(s25)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9301, 25, 844])).
% 36.04/23.92 tff(9303,plain,
% 36.04/23.92 (~always5(s24)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9302, 9295])).
% 36.04/23.92 tff(9304,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9305,plain,
% 36.04/23.92 (((~always5(s23)) | (~trans(s23, s24)) | always5(s24)) <=> ((~trans(s23, s24)) | (~always5(s23)) | always5(s24))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9306,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9305])).
% 36.04/23.92 tff(9307,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9306, 9304])).
% 36.04/23.92 tff(9308,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s23)) | (~trans(s23, s24)) | always5(s24))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9309,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s23, s24)) | (~always5(s23)) | always5(s24)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9308, 9307])).
% 36.04/23.92 tff(9310,plain,
% 36.04/23.92 ((~always5(s23)) | always5(s24)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9309, 25, 813])).
% 36.04/23.92 tff(9311,plain,
% 36.04/23.92 (~always5(s23)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9310, 9303])).
% 36.04/23.92 tff(9312,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9313,plain,
% 36.04/23.92 (((~always5(s22)) | (~trans(s22, s23)) | always5(s23)) <=> ((~trans(s22, s23)) | (~always5(s22)) | always5(s23))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9314,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9313])).
% 36.04/23.92 tff(9315,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9314, 9312])).
% 36.04/23.92 tff(9316,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s22)) | (~trans(s22, s23)) | always5(s23))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9317,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s22, s23)) | (~always5(s22)) | always5(s23)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9316, 9315])).
% 36.04/23.92 tff(9318,plain,
% 36.04/23.92 ((~always5(s22)) | always5(s23)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9317, 25, 785])).
% 36.04/23.92 tff(9319,plain,
% 36.04/23.92 (~always5(s22)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9318, 9311])).
% 36.04/23.92 tff(9320,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9321,plain,
% 36.04/23.92 (((~always5(s21)) | (~trans(s21, s22)) | always5(s22)) <=> ((~trans(s21, s22)) | (~always5(s21)) | always5(s22))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9322,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9321])).
% 36.04/23.92 tff(9323,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9322, 9320])).
% 36.04/23.92 tff(9324,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s21)) | (~trans(s21, s22)) | always5(s22))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9325,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s21, s22)) | (~always5(s21)) | always5(s22)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9324, 9323])).
% 36.04/23.92 tff(9326,plain,
% 36.04/23.92 ((~always5(s21)) | always5(s22)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9325, 25, 754])).
% 36.04/23.92 tff(9327,plain,
% 36.04/23.92 (~always5(s21)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9326, 9319])).
% 36.04/23.92 tff(9328,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9329,plain,
% 36.04/23.92 (((~always5(s20)) | (~trans(s20, s21)) | always5(s21)) <=> ((~trans(s20, s21)) | (~always5(s20)) | always5(s21))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9330,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9329])).
% 36.04/23.92 tff(9331,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9330, 9328])).
% 36.04/23.92 tff(9332,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s20)) | (~trans(s20, s21)) | always5(s21))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9333,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s20, s21)) | (~always5(s20)) | always5(s21)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9332, 9331])).
% 36.04/23.92 tff(9334,plain,
% 36.04/23.92 ((~always5(s20)) | always5(s21)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9333, 25, 726])).
% 36.04/23.92 tff(9335,plain,
% 36.04/23.92 (~always5(s20)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9334, 9327])).
% 36.04/23.92 tff(9336,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9337,plain,
% 36.04/23.92 (((~always5(s19)) | (~trans(s19, s20)) | always5(s20)) <=> ((~trans(s19, s20)) | (~always5(s19)) | always5(s20))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9338,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9337])).
% 36.04/23.92 tff(9339,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9338, 9336])).
% 36.04/23.92 tff(9340,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s19)) | (~trans(s19, s20)) | always5(s20))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9341,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s19, s20)) | (~always5(s19)) | always5(s20)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9340, 9339])).
% 36.04/23.92 tff(9342,plain,
% 36.04/23.92 ((~always5(s19)) | always5(s20)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9341, 25, 697])).
% 36.04/23.92 tff(9343,plain,
% 36.04/23.92 (~always5(s19)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9342, 9335])).
% 36.04/23.92 tff(9344,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9345,plain,
% 36.04/23.92 (((~always5(s18)) | (~trans(s18, s19)) | always5(s19)) <=> ((~trans(s18, s19)) | (~always5(s18)) | always5(s19))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9346,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9345])).
% 36.04/23.92 tff(9347,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9346, 9344])).
% 36.04/23.92 tff(9348,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s18)) | (~trans(s18, s19)) | always5(s19))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9349,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s18, s19)) | (~always5(s18)) | always5(s19)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9348, 9347])).
% 36.04/23.92 tff(9350,plain,
% 36.04/23.92 ((~always5(s18)) | always5(s19)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9349, 25, 669])).
% 36.04/23.92 tff(9351,plain,
% 36.04/23.92 (~always5(s18)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9350, 9343])).
% 36.04/23.92 tff(9352,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9353,plain,
% 36.04/23.92 (((~always5(s17)) | (~trans(s17, s18)) | always5(s18)) <=> ((~trans(s17, s18)) | (~always5(s17)) | always5(s18))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9354,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9353])).
% 36.04/23.92 tff(9355,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9354, 9352])).
% 36.04/23.92 tff(9356,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s17)) | (~trans(s17, s18)) | always5(s18))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9357,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s17, s18)) | (~always5(s17)) | always5(s18)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9356, 9355])).
% 36.04/23.92 tff(9358,plain,
% 36.04/23.92 ((~always5(s17)) | always5(s18)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9357, 25, 638])).
% 36.04/23.92 tff(9359,plain,
% 36.04/23.92 (~always5(s17)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9358, 9351])).
% 36.04/23.92 tff(9360,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9361,plain,
% 36.04/23.92 (((~always5(s16)) | (~trans(s16, s17)) | always5(s17)) <=> ((~trans(s16, s17)) | (~always5(s16)) | always5(s17))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9362,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9361])).
% 36.04/23.92 tff(9363,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9362, 9360])).
% 36.04/23.92 tff(9364,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s16)) | (~trans(s16, s17)) | always5(s17))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9365,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s16, s17)) | (~always5(s16)) | always5(s17)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9364, 9363])).
% 36.04/23.92 tff(9366,plain,
% 36.04/23.92 ((~always5(s16)) | always5(s17)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9365, 25, 610])).
% 36.04/23.92 tff(9367,plain,
% 36.04/23.92 (~always5(s16)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9366, 9359])).
% 36.04/23.92 tff(9368,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9369,plain,
% 36.04/23.92 (((~always5(s15)) | (~trans(s15, s16)) | always5(s16)) <=> ((~trans(s15, s16)) | (~always5(s15)) | always5(s16))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9370,plain,
% 36.04/23.92 (((~![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)))),
% 36.04/23.92 inference(monotonicity,[status(thm)],[9369])).
% 36.04/23.92 tff(9371,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(transitivity,[status(thm)],[9370, 9368])).
% 36.04/23.92 tff(9372,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s15)) | (~trans(s15, s16)) | always5(s16))),
% 36.04/23.92 inference(quant_inst,[status(thm)],[])).
% 36.04/23.92 tff(9373,plain,
% 36.04/23.92 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s15, s16)) | (~always5(s15)) | always5(s16)),
% 36.04/23.92 inference(modus_ponens,[status(thm)],[9372, 9371])).
% 36.04/23.92 tff(9374,plain,
% 36.04/23.92 ((~always5(s15)) | always5(s16)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9373, 25, 581])).
% 36.04/23.92 tff(9375,plain,
% 36.04/23.92 (~always5(s15)),
% 36.04/23.92 inference(unit_resolution,[status(thm)],[9374, 9367])).
% 36.04/23.92 tff(9376,assumption,(~always5(s15)), introduced(assumption)).
% 36.04/23.92 tff(9377,plain,
% 36.04/23.92 (((~![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))),
% 36.04/23.92 inference(rewrite,[status(thm)],[])).
% 36.04/23.92 tff(9378,plain,
% 36.04/23.92 (((~always5(s14)) | (~trans(s14, s15)) | always5(s15)) <=> ((~trans(s14, s15)) | (~always5(s14)) | always5(s15))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9379,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9378])).
% 36.04/23.93 tff(9380,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9379, 9377])).
% 36.04/23.93 tff(9381,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s14)) | (~trans(s14, s15)) | always5(s15))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9382,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s14, s15)) | (~always5(s14)) | always5(s15)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9381, 9380])).
% 36.04/23.93 tff(9383,plain,
% 36.04/23.93 ((~always5(s14)) | always5(s15)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9382, 25, 553])).
% 36.04/23.93 tff(9384,plain,
% 36.04/23.93 (~always5(s14)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9383, 9376])).
% 36.04/23.93 tff(9385,assumption,(~xuntil7(s15)), introduced(assumption)).
% 36.04/23.93 tff(9386,plain,
% 36.04/23.93 (^[X: $i] : refl((always5(X) | (~until6(X)) | xuntil7(X)) <=> (always5(X) | (~until6(X)) | xuntil7(X)))),
% 36.04/23.93 inference(bind,[status(th)],[])).
% 36.04/23.93 tff(9387,plain,
% 36.04/23.93 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X)) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 36.04/23.93 inference(quant_intro,[status(thm)],[9386])).
% 36.04/23.93 tff(9388,plain,
% 36.04/23.93 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X)) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9389,plain,
% 36.04/23.93 (^[X: $i] : rewrite(((always5(X) | xuntil7(X)) | (~until6(X))) <=> (always5(X) | (~until6(X)) | xuntil7(X)))),
% 36.04/23.93 inference(bind,[status(th)],[])).
% 36.04/23.93 tff(9390,plain,
% 36.04/23.93 (![X: $i] : ((always5(X) | xuntil7(X)) | (~until6(X))) <=> ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 36.04/23.93 inference(quant_intro,[status(thm)],[9389])).
% 36.04/23.93 tff(9391,axiom,(![X: $i] : ((always5(X) | xuntil7(X)) | (~until6(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty4')).
% 36.04/23.93 tff(9392,plain,
% 36.04/23.93 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9391, 9390])).
% 36.04/23.93 tff(9393,plain,
% 36.04/23.93 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9392, 9388])).
% 36.04/23.93 tff(9394,plain,(
% 36.04/23.93 ![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 36.04/23.93 inference(skolemize,[status(sab)],[9393])).
% 36.04/23.93 tff(9395,plain,
% 36.04/23.93 (![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9394, 9387])).
% 36.04/23.93 tff(9396,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9397,plain,
% 36.04/23.93 ((always5(s15) | (~until6(s15)) | xuntil7(s15)) <=> (xuntil7(s15) | always5(s15) | (~until6(s15)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9398,plain,
% 36.04/23.93 (((~![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))))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9397])).
% 36.04/23.93 tff(9399,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9398, 9396])).
% 36.04/23.93 tff(9400,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s15) | (~until6(s15)) | xuntil7(s15))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9401,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s15) | always5(s15) | (~until6(s15))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9400, 9399])).
% 36.04/23.93 tff(9402,plain,
% 36.04/23.93 (always5(s15) | (~until6(s15))),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9401, 9395, 9385])).
% 36.04/23.93 tff(9403,plain,
% 36.04/23.93 (~until6(s15)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9402, 9376])).
% 36.04/23.93 tff(9404,plain,
% 36.04/23.93 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)))),
% 36.04/23.93 inference(bind,[status(th)],[])).
% 36.04/23.93 tff(9405,plain,
% 36.04/23.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 36.04/23.93 inference(quant_intro,[status(thm)],[9404])).
% 36.04/23.93 tff(9406,plain,
% 36.04/23.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9407,plain,
% 36.04/23.93 (^[Y: $i, X: $i] : rewrite(((until6(Y) | (~succ(X, Y))) | (~xuntil7(X))) <=> ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y)))),
% 36.04/23.93 inference(bind,[status(th)],[])).
% 36.04/23.93 tff(9408,plain,
% 36.04/23.93 (![Y: $i, X: $i] : ((until6(Y) | (~succ(X, Y))) | (~xuntil7(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 36.04/23.93 inference(quant_intro,[status(thm)],[9407])).
% 36.04/23.93 tff(9409,axiom,(![Y: $i, X: $i] : ((until6(Y) | (~succ(X, Y))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty5')).
% 36.04/23.93 tff(9410,plain,
% 36.04/23.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9409, 9408])).
% 36.04/23.93 tff(9411,plain,
% 36.04/23.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9410, 9406])).
% 36.04/23.93 tff(9412,plain,(
% 36.04/23.93 ![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 36.04/23.93 inference(skolemize,[status(sab)],[9411])).
% 36.04/23.93 tff(9413,plain,
% 36.04/23.93 (![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9412, 9405])).
% 36.04/23.93 tff(9414,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9415,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9416,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s14, s15)) | (~xuntil7(s14)) | until6(s15)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9415, 9414])).
% 36.04/23.93 tff(9417,plain,
% 36.04/23.93 ((~xuntil7(s14)) | until6(s15)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9416, 549, 9413])).
% 36.04/23.93 tff(9418,plain,
% 36.04/23.93 (~xuntil7(s14)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9417, 9403])).
% 36.04/23.93 tff(9419,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9420,plain,
% 36.04/23.93 ((always5(s14) | (~until6(s14)) | xuntil7(s14)) <=> (xuntil7(s14) | always5(s14) | (~until6(s14)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9421,plain,
% 36.04/23.93 (((~![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))))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9420])).
% 36.04/23.93 tff(9422,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9421, 9419])).
% 36.04/23.93 tff(9423,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s14) | (~until6(s14)) | xuntil7(s14))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9424,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s14) | always5(s14) | (~until6(s14))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9423, 9422])).
% 36.04/23.93 tff(9425,plain,
% 36.04/23.93 (~until6(s14)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9424, 9395, 9418, 9384])).
% 36.04/23.93 tff(9426,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9427,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9428,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s13, s14)) | (~xuntil7(s13)) | until6(s14)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9427, 9426])).
% 36.04/23.93 tff(9429,plain,
% 36.04/23.93 ((~xuntil7(s13)) | until6(s14)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9428, 518, 9413])).
% 36.04/23.93 tff(9430,plain,
% 36.04/23.93 (~xuntil7(s13)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9429, 9425])).
% 36.04/23.93 tff(9431,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9432,plain,
% 36.04/23.93 (((~always5(s13)) | (~trans(s13, s14)) | always5(s14)) <=> ((~trans(s13, s14)) | (~always5(s13)) | always5(s14))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9433,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9432])).
% 36.04/23.93 tff(9434,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9433, 9431])).
% 36.04/23.93 tff(9435,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s13)) | (~trans(s13, s14)) | always5(s14))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9436,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s13, s14)) | (~always5(s13)) | always5(s14)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9435, 9434])).
% 36.04/23.93 tff(9437,plain,
% 36.04/23.93 ((~always5(s13)) | always5(s14)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9436, 25, 522])).
% 36.04/23.93 tff(9438,plain,
% 36.04/23.93 (~always5(s13)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9437, 9384])).
% 36.04/23.93 tff(9439,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9440,plain,
% 36.04/23.93 ((always5(s13) | (~until6(s13)) | xuntil7(s13)) <=> (xuntil7(s13) | always5(s13) | (~until6(s13)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9441,plain,
% 36.04/23.93 (((~![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))))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9440])).
% 36.04/23.93 tff(9442,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9441, 9439])).
% 36.04/23.93 tff(9443,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s13) | (~until6(s13)) | xuntil7(s13))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9444,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s13) | always5(s13) | (~until6(s13))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9443, 9442])).
% 36.04/23.93 tff(9445,plain,
% 36.04/23.93 (xuntil7(s13) | (~until6(s13))),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9444, 9395, 9438])).
% 36.04/23.93 tff(9446,plain,
% 36.04/23.93 (~until6(s13)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9445, 9430])).
% 36.04/23.93 tff(9447,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9448,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9449,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s12, s13)) | (~xuntil7(s12)) | until6(s13)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9448, 9447])).
% 36.04/23.93 tff(9450,plain,
% 36.04/23.93 ((~xuntil7(s12)) | until6(s13)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9449, 490, 9413])).
% 36.04/23.93 tff(9451,plain,
% 36.04/23.93 (~xuntil7(s12)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9450, 9446])).
% 36.04/23.93 tff(9452,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9453,plain,
% 36.04/23.93 (((~always5(s12)) | (~trans(s12, s13)) | always5(s13)) <=> ((~trans(s12, s13)) | (~always5(s12)) | always5(s13))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9454,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9453])).
% 36.04/23.93 tff(9455,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9454, 9452])).
% 36.04/23.93 tff(9456,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s12)) | (~trans(s12, s13)) | always5(s13))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9457,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s12, s13)) | (~always5(s12)) | always5(s13)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9456, 9455])).
% 36.04/23.93 tff(9458,plain,
% 36.04/23.93 ((~always5(s12)) | always5(s13)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9457, 25, 494])).
% 36.04/23.93 tff(9459,plain,
% 36.04/23.93 (~always5(s12)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9458, 9438])).
% 36.04/23.93 tff(9460,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9461,plain,
% 36.04/23.93 ((always5(s12) | (~until6(s12)) | xuntil7(s12)) <=> (xuntil7(s12) | always5(s12) | (~until6(s12)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9462,plain,
% 36.04/23.93 (((~![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))))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9461])).
% 36.04/23.93 tff(9463,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9462, 9460])).
% 36.04/23.93 tff(9464,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s12) | (~until6(s12)) | xuntil7(s12))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9465,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s12) | always5(s12) | (~until6(s12))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9464, 9463])).
% 36.04/23.93 tff(9466,plain,
% 36.04/23.93 (xuntil7(s12) | (~until6(s12))),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9465, 9395, 9459])).
% 36.04/23.93 tff(9467,plain,
% 36.04/23.93 (~until6(s12)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9466, 9451])).
% 36.04/23.93 tff(9468,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9469,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s11, s12)) | (~xuntil7(s11)) | until6(s12))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9470,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s11, s12)) | (~xuntil7(s11)) | until6(s12)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9469, 9468])).
% 36.04/23.93 tff(9471,plain,
% 36.04/23.93 ((~xuntil7(s11)) | until6(s12)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9470, 459, 9413])).
% 36.04/23.93 tff(9472,plain,
% 36.04/23.93 (~xuntil7(s11)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9471, 9467])).
% 36.04/23.93 tff(9473,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9474,plain,
% 36.04/23.93 (((~always5(s11)) | (~trans(s11, s12)) | always5(s12)) <=> ((~trans(s11, s12)) | (~always5(s11)) | always5(s12))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9475,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9474])).
% 36.04/23.93 tff(9476,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9475, 9473])).
% 36.04/23.93 tff(9477,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s11)) | (~trans(s11, s12)) | always5(s12))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9478,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s11, s12)) | (~always5(s11)) | always5(s12)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9477, 9476])).
% 36.04/23.93 tff(9479,plain,
% 36.04/23.93 ((~always5(s11)) | always5(s12)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9478, 25, 463])).
% 36.04/23.93 tff(9480,plain,
% 36.04/23.93 (~always5(s11)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9479, 9459])).
% 36.04/23.93 tff(9481,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9482,plain,
% 36.04/23.93 ((always5(s11) | (~until6(s11)) | xuntil7(s11)) <=> (xuntil7(s11) | always5(s11) | (~until6(s11)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9483,plain,
% 36.04/23.93 (((~![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))))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9482])).
% 36.04/23.93 tff(9484,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9483, 9481])).
% 36.04/23.93 tff(9485,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s11) | (~until6(s11)) | xuntil7(s11))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9486,plain,
% 36.04/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s11) | always5(s11) | (~until6(s11))),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9485, 9484])).
% 36.04/23.93 tff(9487,plain,
% 36.04/23.93 (xuntil7(s11) | (~until6(s11))),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9486, 9395, 9480])).
% 36.04/23.93 tff(9488,plain,
% 36.04/23.93 (~until6(s11)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9487, 9472])).
% 36.04/23.93 tff(9489,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9490,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s10, s11)) | (~xuntil7(s10)) | until6(s11))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9491,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s10, s11)) | (~xuntil7(s10)) | until6(s11)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9490, 9489])).
% 36.04/23.93 tff(9492,plain,
% 36.04/23.93 ((~xuntil7(s10)) | until6(s11)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9491, 431, 9413])).
% 36.04/23.93 tff(9493,plain,
% 36.04/23.93 (~xuntil7(s10)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9492, 9488])).
% 36.04/23.93 tff(9494,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9495,plain,
% 36.04/23.93 (((~always5(s10)) | (~trans(s10, s11)) | always5(s11)) <=> ((~trans(s10, s11)) | (~always5(s10)) | always5(s11))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9496,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(monotonicity,[status(thm)],[9495])).
% 36.04/23.93 tff(9497,plain,
% 36.04/23.93 (((~![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))),
% 36.04/23.93 inference(transitivity,[status(thm)],[9496, 9494])).
% 36.04/23.93 tff(9498,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s10)) | (~trans(s10, s11)) | always5(s11))),
% 36.04/23.93 inference(quant_inst,[status(thm)],[])).
% 36.04/23.93 tff(9499,plain,
% 36.04/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s10, s11)) | (~always5(s10)) | always5(s11)),
% 36.04/23.93 inference(modus_ponens,[status(thm)],[9498, 9497])).
% 36.04/23.93 tff(9500,plain,
% 36.04/23.93 ((~always5(s10)) | always5(s11)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9499, 25, 435])).
% 36.04/23.93 tff(9501,plain,
% 36.04/23.93 (~always5(s10)),
% 36.04/23.93 inference(unit_resolution,[status(thm)],[9500, 9480])).
% 36.04/23.93 tff(9502,plain,
% 36.04/23.93 (((~![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)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9503,plain,
% 36.04/23.93 ((always5(s10) | (~until6(s10)) | xuntil7(s10)) <=> (xuntil7(s10) | always5(s10) | (~until6(s10)))),
% 36.04/23.93 inference(rewrite,[status(thm)],[])).
% 36.04/23.93 tff(9504,plain,
% 36.04/23.93 (((~![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))))),
% 36.13/23.93 inference(monotonicity,[status(thm)],[9503])).
% 36.13/23.93 tff(9505,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(transitivity,[status(thm)],[9504, 9502])).
% 36.13/23.93 tff(9506,plain,
% 36.13/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s10) | (~until6(s10)) | xuntil7(s10))),
% 36.13/23.93 inference(quant_inst,[status(thm)],[])).
% 36.13/23.93 tff(9507,plain,
% 36.13/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s10) | always5(s10) | (~until6(s10))),
% 36.13/23.93 inference(modus_ponens,[status(thm)],[9506, 9505])).
% 36.13/23.93 tff(9508,plain,
% 36.13/23.93 (xuntil7(s10) | (~until6(s10))),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9507, 9395, 9501])).
% 36.13/23.93 tff(9509,plain,
% 36.13/23.93 (~until6(s10)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9508, 9493])).
% 36.13/23.93 tff(9510,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9511,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s9, s10)) | (~xuntil7(s9)) | until6(s10))),
% 36.13/23.93 inference(quant_inst,[status(thm)],[])).
% 36.13/23.93 tff(9512,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s9, s10)) | (~xuntil7(s9)) | until6(s10)),
% 36.13/23.93 inference(modus_ponens,[status(thm)],[9511, 9510])).
% 36.13/23.93 tff(9513,plain,
% 36.13/23.93 ((~xuntil7(s9)) | until6(s10)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9512, 400, 9413])).
% 36.13/23.93 tff(9514,plain,
% 36.13/23.93 (~xuntil7(s9)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9513, 9509])).
% 36.13/23.93 tff(9515,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9516,plain,
% 36.13/23.93 (((~always5(s9)) | (~trans(s9, s10)) | always5(s10)) <=> ((~trans(s9, s10)) | (~always5(s9)) | always5(s10))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9517,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(monotonicity,[status(thm)],[9516])).
% 36.13/23.93 tff(9518,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(transitivity,[status(thm)],[9517, 9515])).
% 36.13/23.93 tff(9519,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s9)) | (~trans(s9, s10)) | always5(s10))),
% 36.13/23.93 inference(quant_inst,[status(thm)],[])).
% 36.13/23.93 tff(9520,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s9, s10)) | (~always5(s9)) | always5(s10)),
% 36.13/23.93 inference(modus_ponens,[status(thm)],[9519, 9518])).
% 36.13/23.93 tff(9521,plain,
% 36.13/23.93 ((~always5(s9)) | always5(s10)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9520, 25, 404])).
% 36.13/23.93 tff(9522,plain,
% 36.13/23.93 (~always5(s9)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9521, 9501])).
% 36.13/23.93 tff(9523,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9524,plain,
% 36.13/23.93 ((always5(s9) | (~until6(s9)) | xuntil7(s9)) <=> (xuntil7(s9) | always5(s9) | (~until6(s9)))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9525,plain,
% 36.13/23.93 (((~![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))))),
% 36.13/23.93 inference(monotonicity,[status(thm)],[9524])).
% 36.13/23.93 tff(9526,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(transitivity,[status(thm)],[9525, 9523])).
% 36.13/23.93 tff(9527,plain,
% 36.13/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s9) | (~until6(s9)) | xuntil7(s9))),
% 36.13/23.93 inference(quant_inst,[status(thm)],[])).
% 36.13/23.93 tff(9528,plain,
% 36.13/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s9) | always5(s9) | (~until6(s9))),
% 36.13/23.93 inference(modus_ponens,[status(thm)],[9527, 9526])).
% 36.13/23.93 tff(9529,plain,
% 36.13/23.93 (xuntil7(s9) | (~until6(s9))),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9528, 9395, 9522])).
% 36.13/23.93 tff(9530,plain,
% 36.13/23.93 (~until6(s9)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9529, 9514])).
% 36.13/23.93 tff(9531,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9532,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9))),
% 36.13/23.93 inference(quant_inst,[status(thm)],[])).
% 36.13/23.93 tff(9533,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s8, s9)) | (~xuntil7(s8)) | until6(s9)),
% 36.13/23.93 inference(modus_ponens,[status(thm)],[9532, 9531])).
% 36.13/23.93 tff(9534,plain,
% 36.13/23.93 ((~xuntil7(s8)) | until6(s9)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9533, 374, 9413])).
% 36.13/23.93 tff(9535,plain,
% 36.13/23.93 (~xuntil7(s8)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9534, 9530])).
% 36.13/23.93 tff(9536,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9537,plain,
% 36.13/23.93 (((~always5(s8)) | (~trans(s8, s9)) | always5(s9)) <=> ((~trans(s8, s9)) | (~always5(s8)) | always5(s9))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9538,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(monotonicity,[status(thm)],[9537])).
% 36.13/23.93 tff(9539,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(transitivity,[status(thm)],[9538, 9536])).
% 36.13/23.93 tff(9540,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s8)) | (~trans(s8, s9)) | always5(s9))),
% 36.13/23.93 inference(quant_inst,[status(thm)],[])).
% 36.13/23.93 tff(9541,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s8, s9)) | (~always5(s8)) | always5(s9)),
% 36.13/23.93 inference(modus_ponens,[status(thm)],[9540, 9539])).
% 36.13/23.93 tff(9542,plain,
% 36.13/23.93 ((~always5(s8)) | always5(s9)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9541, 25, 378])).
% 36.13/23.93 tff(9543,plain,
% 36.13/23.93 (~always5(s8)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9542, 9522])).
% 36.13/23.93 tff(9544,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9545,plain,
% 36.13/23.93 ((always5(s8) | (~until6(s8)) | xuntil7(s8)) <=> (xuntil7(s8) | always5(s8) | (~until6(s8)))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9546,plain,
% 36.13/23.93 (((~![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))))),
% 36.13/23.93 inference(monotonicity,[status(thm)],[9545])).
% 36.13/23.93 tff(9547,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(transitivity,[status(thm)],[9546, 9544])).
% 36.13/23.93 tff(9548,plain,
% 36.13/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s8) | (~until6(s8)) | xuntil7(s8))),
% 36.13/23.93 inference(quant_inst,[status(thm)],[])).
% 36.13/23.93 tff(9549,plain,
% 36.13/23.93 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s8) | always5(s8) | (~until6(s8))),
% 36.13/23.93 inference(modus_ponens,[status(thm)],[9548, 9547])).
% 36.13/23.93 tff(9550,plain,
% 36.13/23.93 (xuntil7(s8) | (~until6(s8))),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9549, 9395, 9543])).
% 36.13/23.93 tff(9551,plain,
% 36.13/23.93 (~until6(s8)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9550, 9535])).
% 36.13/23.93 tff(9552,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9553,plain,
% 36.13/23.93 (((~always5(s7)) | (~trans(s7, s8)) | always5(s8)) <=> ((~trans(s7, s8)) | (~always5(s7)) | always5(s8))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9554,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(monotonicity,[status(thm)],[9553])).
% 36.13/23.93 tff(9555,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(transitivity,[status(thm)],[9554, 9552])).
% 36.13/23.93 tff(9556,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s7)) | (~trans(s7, s8)) | always5(s8))),
% 36.13/23.93 inference(quant_inst,[status(thm)],[])).
% 36.13/23.93 tff(9557,plain,
% 36.13/23.93 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s7, s8)) | (~always5(s7)) | always5(s8)),
% 36.13/23.93 inference(modus_ponens,[status(thm)],[9556, 9555])).
% 36.13/23.93 tff(9558,plain,
% 36.13/23.93 ((~always5(s7)) | always5(s8)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9557, 25, 349])).
% 36.13/23.93 tff(9559,plain,
% 36.13/23.93 (~always5(s7)),
% 36.13/23.93 inference(unit_resolution,[status(thm)],[9558, 9543])).
% 36.13/23.93 tff(9560,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9561,plain,
% 36.13/23.93 (((~always5(s6)) | (~trans(s6, s7)) | always5(s7)) <=> ((~trans(s6, s7)) | (~always5(s6)) | always5(s7))),
% 36.13/23.93 inference(rewrite,[status(thm)],[])).
% 36.13/23.93 tff(9562,plain,
% 36.13/23.93 (((~![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)))),
% 36.13/23.93 inference(monotonicity,[status(thm)],[9561])).
% 36.13/23.93 tff(9563,plain,
% 36.13/23.93 (((~![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))),
% 36.13/23.93 inference(transitivity,[status(thm)],[9562, 9560])).
% 36.13/23.93 tff(9564,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s6)) | (~trans(s6, s7)) | always5(s7))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9565,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s6, s7)) | (~always5(s6)) | always5(s7)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9564, 9563])).
% 36.13/23.94 tff(9566,plain,
% 36.13/23.94 ((~always5(s6)) | always5(s7)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9565, 25, 321])).
% 36.13/23.94 tff(9567,plain,
% 36.13/23.94 (~always5(s6)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9566, 9559])).
% 36.13/23.94 tff(9568,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9569,plain,
% 36.13/23.94 (((~always5(s5)) | (~trans(s5, s6)) | always5(s6)) <=> ((~trans(s5, s6)) | (~always5(s5)) | always5(s6))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9570,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9569])).
% 36.13/23.94 tff(9571,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9570, 9568])).
% 36.13/23.94 tff(9572,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s5)) | (~trans(s5, s6)) | always5(s6))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9573,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s5, s6)) | (~always5(s5)) | always5(s6)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9572, 9571])).
% 36.13/23.94 tff(9574,plain,
% 36.13/23.94 ((~always5(s5)) | always5(s6)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9573, 25, 92])).
% 36.13/23.94 tff(9575,plain,
% 36.13/23.94 (~always5(s5)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9574, 9567])).
% 36.13/23.94 tff(9576,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9577,plain,
% 36.13/23.94 (((~always5(s4)) | (~trans(s4, s5)) | always5(s5)) <=> ((~trans(s4, s5)) | (~always5(s4)) | always5(s5))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9578,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9577])).
% 36.13/23.94 tff(9579,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9578, 9576])).
% 36.13/23.94 tff(9580,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s4)) | (~trans(s4, s5)) | always5(s5))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9581,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s4, s5)) | (~always5(s4)) | always5(s5)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9580, 9579])).
% 36.13/23.94 tff(9582,plain,
% 36.13/23.94 ((~always5(s4)) | always5(s5)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9581, 25, 103])).
% 36.13/23.94 tff(9583,plain,
% 36.13/23.94 (~always5(s4)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9582, 9575])).
% 36.13/23.94 tff(9584,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9585,plain,
% 36.13/23.94 (((~always5(s3)) | (~trans(s3, s4)) | always5(s4)) <=> ((~trans(s3, s4)) | (~always5(s3)) | always5(s4))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9586,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9585])).
% 36.13/23.94 tff(9587,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9586, 9584])).
% 36.13/23.94 tff(9588,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s3)) | (~trans(s3, s4)) | always5(s4))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9589,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s3, s4)) | (~always5(s3)) | always5(s4)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9588, 9587])).
% 36.13/23.94 tff(9590,plain,
% 36.13/23.94 ((~always5(s3)) | always5(s4)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9589, 25, 114])).
% 36.13/23.94 tff(9591,plain,
% 36.13/23.94 (~always5(s3)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9590, 9583])).
% 36.13/23.94 tff(9592,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9593,plain,
% 36.13/23.94 (((~always5(s2)) | (~trans(s2, s3)) | always5(s3)) <=> ((~trans(s2, s3)) | (~always5(s2)) | always5(s3))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9594,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9593])).
% 36.13/23.94 tff(9595,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9594, 9592])).
% 36.13/23.94 tff(9596,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s2)) | (~trans(s2, s3)) | always5(s3))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9597,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s2, s3)) | (~always5(s2)) | always5(s3)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9596, 9595])).
% 36.13/23.94 tff(9598,plain,
% 36.13/23.94 ((~always5(s2)) | always5(s3)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9597, 25, 125])).
% 36.13/23.94 tff(9599,plain,
% 36.13/23.94 (~always5(s2)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9598, 9591])).
% 36.13/23.94 tff(9600,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9601,plain,
% 36.13/23.94 (((~always5(s1)) | (~trans(s1, s2)) | always5(s2)) <=> ((~trans(s1, s2)) | (~always5(s1)) | always5(s2))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9602,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9601])).
% 36.13/23.94 tff(9603,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9602, 9600])).
% 36.13/23.94 tff(9604,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s1)) | (~trans(s1, s2)) | always5(s2))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9605,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s1, s2)) | (~always5(s1)) | always5(s2)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9604, 9603])).
% 36.13/23.94 tff(9606,plain,
% 36.13/23.94 ((~always5(s1)) | always5(s2)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9605, 25, 136])).
% 36.13/23.94 tff(9607,plain,
% 36.13/23.94 (~always5(s1)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9606, 9599])).
% 36.13/23.94 tff(9608,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9609,plain,
% 36.13/23.94 (((~always5(s0)) | (~trans(s0, s1)) | always5(s1)) <=> ((~trans(s0, s1)) | (~always5(s0)) | always5(s1))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9610,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9609])).
% 36.13/23.94 tff(9611,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9610, 9608])).
% 36.13/23.94 tff(9612,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s0)) | (~trans(s0, s1)) | always5(s1))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9613,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~trans(s0, s1)) | (~always5(s0)) | always5(s1)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9612, 9611])).
% 36.13/23.94 tff(9614,plain,
% 36.13/23.94 ((~always5(s0)) | always5(s1)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9613, 25, 185])).
% 36.13/23.94 tff(9615,plain,
% 36.13/23.94 (~always5(s0)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9614, 9607])).
% 36.13/23.94 tff(9616,plain,
% 36.13/23.94 (until6(s0) <=> until6(s0)),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9617,axiom,(until6(s0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty11')).
% 36.13/23.94 tff(9618,plain,
% 36.13/23.94 (until6(s0)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9617, 9616])).
% 36.13/23.94 tff(9619,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9620,plain,
% 36.13/23.94 ((always5(s0) | (~until6(s0)) | xuntil7(s0)) <=> (xuntil7(s0) | always5(s0) | (~until6(s0)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9621,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9620])).
% 36.13/23.94 tff(9622,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9621, 9619])).
% 36.13/23.94 tff(9623,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s0) | (~until6(s0)) | xuntil7(s0))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9624,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s0) | always5(s0) | (~until6(s0))),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9623, 9622])).
% 36.13/23.94 tff(9625,plain,
% 36.13/23.94 (xuntil7(s0) | always5(s0)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9624, 9395, 9618])).
% 36.13/23.94 tff(9626,plain,
% 36.13/23.94 (xuntil7(s0)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9625, 9615])).
% 36.13/23.94 tff(9627,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9628,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9629,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s0, s1)) | (~xuntil7(s0)) | until6(s1)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9628, 9627])).
% 36.13/23.94 tff(9630,plain,
% 36.13/23.94 ((~xuntil7(s0)) | until6(s1)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9629, 181, 9413])).
% 36.13/23.94 tff(9631,plain,
% 36.13/23.94 (until6(s1)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9630, 9626])).
% 36.13/23.94 tff(9632,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9633,plain,
% 36.13/23.94 ((always5(s1) | (~until6(s1)) | xuntil7(s1)) <=> (xuntil7(s1) | always5(s1) | (~until6(s1)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9634,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9633])).
% 36.13/23.94 tff(9635,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9634, 9632])).
% 36.13/23.94 tff(9636,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s1) | (~until6(s1)) | xuntil7(s1))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9637,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s1) | always5(s1) | (~until6(s1))),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9636, 9635])).
% 36.13/23.94 tff(9638,plain,
% 36.13/23.94 (xuntil7(s1)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9637, 9395, 9631, 9607])).
% 36.13/23.94 tff(9639,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9640,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9641,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s1, s2)) | (~xuntil7(s1)) | until6(s2)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9640, 9639])).
% 36.13/23.94 tff(9642,plain,
% 36.13/23.94 ((~xuntil7(s1)) | until6(s2)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9641, 132, 9413])).
% 36.13/23.94 tff(9643,plain,
% 36.13/23.94 (until6(s2)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9642, 9638])).
% 36.13/23.94 tff(9644,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9645,plain,
% 36.13/23.94 ((always5(s2) | (~until6(s2)) | xuntil7(s2)) <=> (xuntil7(s2) | always5(s2) | (~until6(s2)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9646,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9645])).
% 36.13/23.94 tff(9647,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9646, 9644])).
% 36.13/23.94 tff(9648,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s2) | (~until6(s2)) | xuntil7(s2))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9649,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s2) | always5(s2) | (~until6(s2))),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9648, 9647])).
% 36.13/23.94 tff(9650,plain,
% 36.13/23.94 (xuntil7(s2) | (~until6(s2))),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9649, 9395, 9599])).
% 36.13/23.94 tff(9651,plain,
% 36.13/23.94 (xuntil7(s2)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9650, 9643])).
% 36.13/23.94 tff(9652,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9653,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9654,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s2, s3)) | (~xuntil7(s2)) | until6(s3)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9653, 9652])).
% 36.13/23.94 tff(9655,plain,
% 36.13/23.94 ((~xuntil7(s2)) | until6(s3)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9654, 121, 9413])).
% 36.13/23.94 tff(9656,plain,
% 36.13/23.94 (until6(s3)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9655, 9651])).
% 36.13/23.94 tff(9657,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9658,plain,
% 36.13/23.94 ((always5(s3) | (~until6(s3)) | xuntil7(s3)) <=> (xuntil7(s3) | always5(s3) | (~until6(s3)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9659,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9658])).
% 36.13/23.94 tff(9660,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9659, 9657])).
% 36.13/23.94 tff(9661,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s3) | (~until6(s3)) | xuntil7(s3))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9662,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s3) | always5(s3) | (~until6(s3))),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9661, 9660])).
% 36.13/23.94 tff(9663,plain,
% 36.13/23.94 (xuntil7(s3) | (~until6(s3))),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9662, 9395, 9591])).
% 36.13/23.94 tff(9664,plain,
% 36.13/23.94 (xuntil7(s3)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9663, 9656])).
% 36.13/23.94 tff(9665,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9666,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9667,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s3, s4)) | (~xuntil7(s3)) | until6(s4)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9666, 9665])).
% 36.13/23.94 tff(9668,plain,
% 36.13/23.94 ((~xuntil7(s3)) | until6(s4)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9667, 110, 9413])).
% 36.13/23.94 tff(9669,plain,
% 36.13/23.94 (until6(s4)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9668, 9664])).
% 36.13/23.94 tff(9670,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9671,plain,
% 36.13/23.94 ((always5(s4) | (~until6(s4)) | xuntil7(s4)) <=> (xuntil7(s4) | always5(s4) | (~until6(s4)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9672,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9671])).
% 36.13/23.94 tff(9673,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9672, 9670])).
% 36.13/23.94 tff(9674,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s4) | (~until6(s4)) | xuntil7(s4))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9675,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s4) | always5(s4) | (~until6(s4))),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9674, 9673])).
% 36.13/23.94 tff(9676,plain,
% 36.13/23.94 (xuntil7(s4) | (~until6(s4))),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9675, 9395, 9583])).
% 36.13/23.94 tff(9677,plain,
% 36.13/23.94 (xuntil7(s4)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9676, 9669])).
% 36.13/23.94 tff(9678,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9679,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9680,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s4, s5)) | (~xuntil7(s4)) | until6(s5)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9679, 9678])).
% 36.13/23.94 tff(9681,plain,
% 36.13/23.94 ((~xuntil7(s4)) | until6(s5)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9680, 99, 9413])).
% 36.13/23.94 tff(9682,plain,
% 36.13/23.94 (until6(s5)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9681, 9677])).
% 36.13/23.94 tff(9683,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9684,plain,
% 36.13/23.94 ((always5(s5) | (~until6(s5)) | xuntil7(s5)) <=> (xuntil7(s5) | always5(s5) | (~until6(s5)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9685,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9684])).
% 36.13/23.94 tff(9686,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9685, 9683])).
% 36.13/23.94 tff(9687,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s5) | (~until6(s5)) | xuntil7(s5))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9688,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s5) | always5(s5) | (~until6(s5))),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9687, 9686])).
% 36.13/23.94 tff(9689,plain,
% 36.13/23.94 (xuntil7(s5) | (~until6(s5))),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9688, 9395, 9575])).
% 36.13/23.94 tff(9690,plain,
% 36.13/23.94 (xuntil7(s5)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9689, 9682])).
% 36.13/23.94 tff(9691,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9692,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9693,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s5, s6)) | (~xuntil7(s5)) | until6(s6)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9692, 9691])).
% 36.13/23.94 tff(9694,plain,
% 36.13/23.94 ((~xuntil7(s5)) | until6(s6)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9693, 88, 9413])).
% 36.13/23.94 tff(9695,plain,
% 36.13/23.94 (until6(s6)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9694, 9690])).
% 36.13/23.94 tff(9696,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9697,plain,
% 36.13/23.94 ((always5(s6) | (~until6(s6)) | xuntil7(s6)) <=> (xuntil7(s6) | always5(s6) | (~until6(s6)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9698,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9697])).
% 36.13/23.94 tff(9699,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9698, 9696])).
% 36.13/23.94 tff(9700,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s6) | (~until6(s6)) | xuntil7(s6))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9701,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s6) | always5(s6) | (~until6(s6))),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9700, 9699])).
% 36.13/23.94 tff(9702,plain,
% 36.13/23.94 (xuntil7(s6) | (~until6(s6))),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9701, 9395, 9567])).
% 36.13/23.94 tff(9703,plain,
% 36.13/23.94 (xuntil7(s6)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9702, 9695])).
% 36.13/23.94 tff(9704,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9705,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9706,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s6, s7)) | (~xuntil7(s6)) | until6(s7)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9705, 9704])).
% 36.13/23.94 tff(9707,plain,
% 36.13/23.94 ((~xuntil7(s6)) | until6(s7)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9706, 317, 9413])).
% 36.13/23.94 tff(9708,plain,
% 36.13/23.94 (until6(s7)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9707, 9703])).
% 36.13/23.94 tff(9709,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9710,plain,
% 36.13/23.94 ((always5(s7) | (~until6(s7)) | xuntil7(s7)) <=> (xuntil7(s7) | always5(s7) | (~until6(s7)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9711,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9710])).
% 36.13/23.94 tff(9712,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9711, 9709])).
% 36.13/23.94 tff(9713,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s7) | (~until6(s7)) | xuntil7(s7))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9714,plain,
% 36.13/23.94 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s7) | always5(s7) | (~until6(s7))),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9713, 9712])).
% 36.13/23.94 tff(9715,plain,
% 36.13/23.94 (xuntil7(s7) | (~until6(s7))),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9714, 9395, 9559])).
% 36.13/23.94 tff(9716,plain,
% 36.13/23.94 (xuntil7(s7)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9715, 9708])).
% 36.13/23.94 tff(9717,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9718,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9719,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s7, s8)) | (~xuntil7(s7)) | until6(s8)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9718, 9717])).
% 36.13/23.94 tff(9720,plain,
% 36.13/23.94 ((~xuntil7(s7)) | until6(s8)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9719, 345, 9413])).
% 36.13/23.94 tff(9721,plain,
% 36.13/23.94 ($false),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9720, 9716, 9551])).
% 36.13/23.94 tff(9722,plain,(always5(s15) | xuntil7(s15)), inference(lemma,lemma(discharge,[]))).
% 36.13/23.94 tff(9723,plain,
% 36.13/23.94 (xuntil7(s15)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9722, 9375])).
% 36.13/23.94 tff(9724,plain,
% 36.13/23.94 (((~![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))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9725,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16))),
% 36.13/23.94 inference(quant_inst,[status(thm)],[])).
% 36.13/23.94 tff(9726,plain,
% 36.13/23.94 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s15, s16)) | (~xuntil7(s15)) | until6(s16)),
% 36.13/23.94 inference(modus_ponens,[status(thm)],[9725, 9724])).
% 36.13/23.94 tff(9727,plain,
% 36.13/23.94 ((~xuntil7(s15)) | until6(s16)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9726, 577, 9413])).
% 36.13/23.94 tff(9728,plain,
% 36.13/23.94 (until6(s16)),
% 36.13/23.94 inference(unit_resolution,[status(thm)],[9727, 9723])).
% 36.13/23.94 tff(9729,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9730,plain,
% 36.13/23.94 ((always5(s16) | (~until6(s16)) | xuntil7(s16)) <=> (xuntil7(s16) | always5(s16) | (~until6(s16)))),
% 36.13/23.94 inference(rewrite,[status(thm)],[])).
% 36.13/23.94 tff(9731,plain,
% 36.13/23.94 (((~![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))))),
% 36.13/23.94 inference(monotonicity,[status(thm)],[9730])).
% 36.13/23.94 tff(9732,plain,
% 36.13/23.94 (((~![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)))),
% 36.13/23.94 inference(transitivity,[status(thm)],[9731, 9729])).
% 36.13/23.95 tff(9733,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s16) | (~until6(s16)) | xuntil7(s16))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9734,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s16) | always5(s16) | (~until6(s16))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9733, 9732])).
% 36.13/23.95 tff(9735,plain,
% 36.13/23.95 (xuntil7(s16)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9734, 9395, 9728, 9367])).
% 36.13/23.95 tff(9736,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9737,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9738,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s16, s17)) | (~xuntil7(s16)) | until6(s17)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9737, 9736])).
% 36.13/23.95 tff(9739,plain,
% 36.13/23.95 ((~xuntil7(s16)) | until6(s17)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9738, 606, 9413])).
% 36.13/23.95 tff(9740,plain,
% 36.13/23.95 (until6(s17)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9739, 9735])).
% 36.13/23.95 tff(9741,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9742,plain,
% 36.13/23.95 ((always5(s17) | (~until6(s17)) | xuntil7(s17)) <=> (xuntil7(s17) | always5(s17) | (~until6(s17)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9743,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9742])).
% 36.13/23.95 tff(9744,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9743, 9741])).
% 36.13/23.95 tff(9745,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s17) | (~until6(s17)) | xuntil7(s17))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9746,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s17) | always5(s17) | (~until6(s17))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9745, 9744])).
% 36.13/23.95 tff(9747,plain,
% 36.13/23.95 (xuntil7(s17) | (~until6(s17))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9746, 9395, 9359])).
% 36.13/23.95 tff(9748,plain,
% 36.13/23.95 (xuntil7(s17)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9747, 9740])).
% 36.13/23.95 tff(9749,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9750,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9751,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s17, s18)) | (~xuntil7(s17)) | until6(s18)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9750, 9749])).
% 36.13/23.95 tff(9752,plain,
% 36.13/23.95 ((~xuntil7(s17)) | until6(s18)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9751, 634, 9413])).
% 36.13/23.95 tff(9753,plain,
% 36.13/23.95 (until6(s18)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9752, 9748])).
% 36.13/23.95 tff(9754,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9755,plain,
% 36.13/23.95 ((always5(s18) | (~until6(s18)) | xuntil7(s18)) <=> (xuntil7(s18) | always5(s18) | (~until6(s18)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9756,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9755])).
% 36.13/23.95 tff(9757,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9756, 9754])).
% 36.13/23.95 tff(9758,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s18) | (~until6(s18)) | xuntil7(s18))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9759,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s18) | always5(s18) | (~until6(s18))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9758, 9757])).
% 36.13/23.95 tff(9760,plain,
% 36.13/23.95 (xuntil7(s18) | (~until6(s18))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9759, 9395, 9351])).
% 36.13/23.95 tff(9761,plain,
% 36.13/23.95 (xuntil7(s18)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9760, 9753])).
% 36.13/23.95 tff(9762,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9763,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9764,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s18, s19)) | (~xuntil7(s18)) | until6(s19)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9763, 9762])).
% 36.13/23.95 tff(9765,plain,
% 36.13/23.95 ((~xuntil7(s18)) | until6(s19)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9764, 665, 9413])).
% 36.13/23.95 tff(9766,plain,
% 36.13/23.95 (until6(s19)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9765, 9761])).
% 36.13/23.95 tff(9767,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9768,plain,
% 36.13/23.95 ((always5(s19) | (~until6(s19)) | xuntil7(s19)) <=> (xuntil7(s19) | always5(s19) | (~until6(s19)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9769,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9768])).
% 36.13/23.95 tff(9770,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9769, 9767])).
% 36.13/23.95 tff(9771,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s19) | (~until6(s19)) | xuntil7(s19))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9772,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s19) | always5(s19) | (~until6(s19))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9771, 9770])).
% 36.13/23.95 tff(9773,plain,
% 36.13/23.95 (xuntil7(s19) | (~until6(s19))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9772, 9395, 9343])).
% 36.13/23.95 tff(9774,plain,
% 36.13/23.95 (xuntil7(s19)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9773, 9766])).
% 36.13/23.95 tff(9775,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9776,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9777,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s19, s20)) | (~xuntil7(s19)) | until6(s20)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9776, 9775])).
% 36.13/23.95 tff(9778,plain,
% 36.13/23.95 ((~xuntil7(s19)) | until6(s20)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9777, 693, 9413])).
% 36.13/23.95 tff(9779,plain,
% 36.13/23.95 (until6(s20)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9778, 9774])).
% 36.13/23.95 tff(9780,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9781,plain,
% 36.13/23.95 ((always5(s20) | (~until6(s20)) | xuntil7(s20)) <=> (xuntil7(s20) | always5(s20) | (~until6(s20)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9782,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9781])).
% 36.13/23.95 tff(9783,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9782, 9780])).
% 36.13/23.95 tff(9784,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s20) | (~until6(s20)) | xuntil7(s20))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9785,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s20) | always5(s20) | (~until6(s20))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9784, 9783])).
% 36.13/23.95 tff(9786,plain,
% 36.13/23.95 (xuntil7(s20) | (~until6(s20))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9785, 9395, 9335])).
% 36.13/23.95 tff(9787,plain,
% 36.13/23.95 (xuntil7(s20)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9786, 9779])).
% 36.13/23.95 tff(9788,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9789,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9790,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s20, s21)) | (~xuntil7(s20)) | until6(s21)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9789, 9788])).
% 36.13/23.95 tff(9791,plain,
% 36.13/23.95 ((~xuntil7(s20)) | until6(s21)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9790, 722, 9413])).
% 36.13/23.95 tff(9792,plain,
% 36.13/23.95 (until6(s21)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9791, 9787])).
% 36.13/23.95 tff(9793,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9794,plain,
% 36.13/23.95 ((always5(s21) | (~until6(s21)) | xuntil7(s21)) <=> (xuntil7(s21) | always5(s21) | (~until6(s21)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9795,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9794])).
% 36.13/23.95 tff(9796,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9795, 9793])).
% 36.13/23.95 tff(9797,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s21) | (~until6(s21)) | xuntil7(s21))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9798,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s21) | always5(s21) | (~until6(s21))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9797, 9796])).
% 36.13/23.95 tff(9799,plain,
% 36.13/23.95 (xuntil7(s21) | (~until6(s21))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9798, 9395, 9327])).
% 36.13/23.95 tff(9800,plain,
% 36.13/23.95 (xuntil7(s21)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9799, 9792])).
% 36.13/23.95 tff(9801,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9802,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9803,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s21, s22)) | (~xuntil7(s21)) | until6(s22)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9802, 9801])).
% 36.13/23.95 tff(9804,plain,
% 36.13/23.95 ((~xuntil7(s21)) | until6(s22)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9803, 750, 9413])).
% 36.13/23.95 tff(9805,plain,
% 36.13/23.95 (until6(s22)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9804, 9800])).
% 36.13/23.95 tff(9806,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9807,plain,
% 36.13/23.95 ((always5(s22) | (~until6(s22)) | xuntil7(s22)) <=> (xuntil7(s22) | always5(s22) | (~until6(s22)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9808,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9807])).
% 36.13/23.95 tff(9809,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9808, 9806])).
% 36.13/23.95 tff(9810,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s22) | (~until6(s22)) | xuntil7(s22))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9811,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s22) | always5(s22) | (~until6(s22))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9810, 9809])).
% 36.13/23.95 tff(9812,plain,
% 36.13/23.95 (xuntil7(s22) | (~until6(s22))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9811, 9395, 9319])).
% 36.13/23.95 tff(9813,plain,
% 36.13/23.95 (xuntil7(s22)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9812, 9805])).
% 36.13/23.95 tff(9814,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9815,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9816,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s22, s23)) | (~xuntil7(s22)) | until6(s23)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9815, 9814])).
% 36.13/23.95 tff(9817,plain,
% 36.13/23.95 ((~xuntil7(s22)) | until6(s23)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9816, 781, 9413])).
% 36.13/23.95 tff(9818,plain,
% 36.13/23.95 (until6(s23)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9817, 9813])).
% 36.13/23.95 tff(9819,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9820,plain,
% 36.13/23.95 ((always5(s23) | (~until6(s23)) | xuntil7(s23)) <=> (xuntil7(s23) | always5(s23) | (~until6(s23)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9821,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9820])).
% 36.13/23.95 tff(9822,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9821, 9819])).
% 36.13/23.95 tff(9823,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s23) | (~until6(s23)) | xuntil7(s23))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9824,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s23) | always5(s23) | (~until6(s23))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9823, 9822])).
% 36.13/23.95 tff(9825,plain,
% 36.13/23.95 (xuntil7(s23) | (~until6(s23))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9824, 9395, 9311])).
% 36.13/23.95 tff(9826,plain,
% 36.13/23.95 (xuntil7(s23)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9825, 9818])).
% 36.13/23.95 tff(9827,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9828,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9829,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s23, s24)) | (~xuntil7(s23)) | until6(s24)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9828, 9827])).
% 36.13/23.95 tff(9830,plain,
% 36.13/23.95 ((~xuntil7(s23)) | until6(s24)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9829, 809, 9413])).
% 36.13/23.95 tff(9831,plain,
% 36.13/23.95 (until6(s24)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9830, 9826])).
% 36.13/23.95 tff(9832,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9833,plain,
% 36.13/23.95 ((always5(s24) | (~until6(s24)) | xuntil7(s24)) <=> (xuntil7(s24) | always5(s24) | (~until6(s24)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9834,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9833])).
% 36.13/23.95 tff(9835,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9834, 9832])).
% 36.13/23.95 tff(9836,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s24) | (~until6(s24)) | xuntil7(s24))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9837,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s24) | always5(s24) | (~until6(s24))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9836, 9835])).
% 36.13/23.95 tff(9838,plain,
% 36.13/23.95 (xuntil7(s24) | (~until6(s24))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9837, 9395, 9303])).
% 36.13/23.95 tff(9839,plain,
% 36.13/23.95 (xuntil7(s24)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9838, 9831])).
% 36.13/23.95 tff(9840,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9841,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9842,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s24, s25)) | (~xuntil7(s24)) | until6(s25)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9841, 9840])).
% 36.13/23.95 tff(9843,plain,
% 36.13/23.95 ((~xuntil7(s24)) | until6(s25)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9842, 840, 9413])).
% 36.13/23.95 tff(9844,plain,
% 36.13/23.95 (until6(s25)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9843, 9839])).
% 36.13/23.95 tff(9845,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9846,plain,
% 36.13/23.95 ((always5(s25) | (~until6(s25)) | xuntil7(s25)) <=> (xuntil7(s25) | always5(s25) | (~until6(s25)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9847,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9846])).
% 36.13/23.95 tff(9848,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9847, 9845])).
% 36.13/23.95 tff(9849,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s25) | (~until6(s25)) | xuntil7(s25))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9850,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s25) | always5(s25) | (~until6(s25))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9849, 9848])).
% 36.13/23.95 tff(9851,plain,
% 36.13/23.95 (xuntil7(s25) | (~until6(s25))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9850, 9395, 9295])).
% 36.13/23.95 tff(9852,plain,
% 36.13/23.95 (xuntil7(s25)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9851, 9844])).
% 36.13/23.95 tff(9853,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9854,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s25, s26)) | (~xuntil7(s25)) | until6(s26))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9855,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s25, s26)) | (~xuntil7(s25)) | until6(s26)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9854, 9853])).
% 36.13/23.95 tff(9856,plain,
% 36.13/23.95 ((~xuntil7(s25)) | until6(s26)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9855, 866, 9413])).
% 36.13/23.95 tff(9857,plain,
% 36.13/23.95 (until6(s26)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9856, 9852])).
% 36.13/23.95 tff(9858,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9859,plain,
% 36.13/23.95 ((always5(s26) | (~until6(s26)) | xuntil7(s26)) <=> (xuntil7(s26) | always5(s26) | (~until6(s26)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9860,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9859])).
% 36.13/23.95 tff(9861,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9860, 9858])).
% 36.13/23.95 tff(9862,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s26) | (~until6(s26)) | xuntil7(s26))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9863,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s26) | always5(s26) | (~until6(s26))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9862, 9861])).
% 36.13/23.95 tff(9864,plain,
% 36.13/23.95 (xuntil7(s26) | (~until6(s26))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9863, 9395, 9287])).
% 36.13/23.95 tff(9865,plain,
% 36.13/23.95 (xuntil7(s26)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9864, 9857])).
% 36.13/23.95 tff(9866,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9867,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s26, s27)) | (~xuntil7(s26)) | until6(s27))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9868,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s26, s27)) | (~xuntil7(s26)) | until6(s27)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9867, 9866])).
% 36.13/23.95 tff(9869,plain,
% 36.13/23.95 ((~xuntil7(s26)) | until6(s27)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9868, 897, 9413])).
% 36.13/23.95 tff(9870,plain,
% 36.13/23.95 (until6(s27)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9869, 9865])).
% 36.13/23.95 tff(9871,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9872,plain,
% 36.13/23.95 ((always5(s27) | (~until6(s27)) | xuntil7(s27)) <=> (xuntil7(s27) | always5(s27) | (~until6(s27)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9873,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9872])).
% 36.13/23.95 tff(9874,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9873, 9871])).
% 36.13/23.95 tff(9875,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s27) | (~until6(s27)) | xuntil7(s27))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9876,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s27) | always5(s27) | (~until6(s27))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9875, 9874])).
% 36.13/23.95 tff(9877,plain,
% 36.13/23.95 (xuntil7(s27) | (~until6(s27))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9876, 9395, 9279])).
% 36.13/23.95 tff(9878,plain,
% 36.13/23.95 (xuntil7(s27)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9877, 9870])).
% 36.13/23.95 tff(9879,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9880,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9881,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s27, s28)) | (~xuntil7(s27)) | until6(s28)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9880, 9879])).
% 36.13/23.95 tff(9882,plain,
% 36.13/23.95 ((~xuntil7(s27)) | until6(s28)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9881, 925, 9413])).
% 36.13/23.95 tff(9883,plain,
% 36.13/23.95 (until6(s28)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9882, 9878])).
% 36.13/23.95 tff(9884,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9885,plain,
% 36.13/23.95 ((always5(s28) | (~until6(s28)) | xuntil7(s28)) <=> (xuntil7(s28) | always5(s28) | (~until6(s28)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9886,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9885])).
% 36.13/23.95 tff(9887,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9886, 9884])).
% 36.13/23.95 tff(9888,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s28) | (~until6(s28)) | xuntil7(s28))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9889,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s28) | always5(s28) | (~until6(s28))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9888, 9887])).
% 36.13/23.95 tff(9890,plain,
% 36.13/23.95 (xuntil7(s28) | (~until6(s28))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9889, 9395, 9271])).
% 36.13/23.95 tff(9891,plain,
% 36.13/23.95 (xuntil7(s28)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9890, 9883])).
% 36.13/23.95 tff(9892,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9893,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9894,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s28, s29)) | (~xuntil7(s28)) | until6(s29)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9893, 9892])).
% 36.13/23.95 tff(9895,plain,
% 36.13/23.95 ((~xuntil7(s28)) | until6(s29)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9894, 954, 9413])).
% 36.13/23.95 tff(9896,plain,
% 36.13/23.95 (until6(s29)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9895, 9891])).
% 36.13/23.95 tff(9897,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9898,plain,
% 36.13/23.95 ((always5(s29) | (~until6(s29)) | xuntil7(s29)) <=> (xuntil7(s29) | always5(s29) | (~until6(s29)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9899,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9898])).
% 36.13/23.95 tff(9900,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9899, 9897])).
% 36.13/23.95 tff(9901,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s29) | (~until6(s29)) | xuntil7(s29))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9902,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s29) | always5(s29) | (~until6(s29))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9901, 9900])).
% 36.13/23.95 tff(9903,plain,
% 36.13/23.95 (xuntil7(s29) | (~until6(s29))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9902, 9395, 9263])).
% 36.13/23.95 tff(9904,plain,
% 36.13/23.95 (xuntil7(s29)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9903, 9896])).
% 36.13/23.95 tff(9905,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9906,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9907,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s29, s30)) | (~xuntil7(s29)) | until6(s30)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9906, 9905])).
% 36.13/23.95 tff(9908,plain,
% 36.13/23.95 ((~xuntil7(s29)) | until6(s30)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9907, 982, 9413])).
% 36.13/23.95 tff(9909,plain,
% 36.13/23.95 (until6(s30)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9908, 9904])).
% 36.13/23.95 tff(9910,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9911,plain,
% 36.13/23.95 ((always5(s30) | (~until6(s30)) | xuntil7(s30)) <=> (xuntil7(s30) | always5(s30) | (~until6(s30)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9912,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.95 inference(monotonicity,[status(thm)],[9911])).
% 36.13/23.95 tff(9913,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(transitivity,[status(thm)],[9912, 9910])).
% 36.13/23.95 tff(9914,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s30) | (~until6(s30)) | xuntil7(s30))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9915,plain,
% 36.13/23.95 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s30) | always5(s30) | (~until6(s30))),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9914, 9913])).
% 36.13/23.95 tff(9916,plain,
% 36.13/23.95 (xuntil7(s30) | (~until6(s30))),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9915, 9395, 9255])).
% 36.13/23.95 tff(9917,plain,
% 36.13/23.95 (xuntil7(s30)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9916, 9909])).
% 36.13/23.95 tff(9918,plain,
% 36.13/23.95 (((~![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))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9919,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31))),
% 36.13/23.95 inference(quant_inst,[status(thm)],[])).
% 36.13/23.95 tff(9920,plain,
% 36.13/23.95 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s30, s31)) | (~xuntil7(s30)) | until6(s31)),
% 36.13/23.95 inference(modus_ponens,[status(thm)],[9919, 9918])).
% 36.13/23.95 tff(9921,plain,
% 36.13/23.95 ((~xuntil7(s30)) | until6(s31)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9920, 1013, 9413])).
% 36.13/23.95 tff(9922,plain,
% 36.13/23.95 (until6(s31)),
% 36.13/23.95 inference(unit_resolution,[status(thm)],[9921, 9917])).
% 36.13/23.95 tff(9923,plain,
% 36.13/23.95 (((~![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)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9924,plain,
% 36.13/23.95 ((always5(s31) | (~until6(s31)) | xuntil7(s31)) <=> (xuntil7(s31) | always5(s31) | (~until6(s31)))),
% 36.13/23.95 inference(rewrite,[status(thm)],[])).
% 36.13/23.95 tff(9925,plain,
% 36.13/23.95 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[9924])).
% 36.13/23.96 tff(9926,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[9925, 9923])).
% 36.13/23.96 tff(9927,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s31) | (~until6(s31)) | xuntil7(s31))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9928,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s31) | always5(s31) | (~until6(s31))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9927, 9926])).
% 36.13/23.96 tff(9929,plain,
% 36.13/23.96 (xuntil7(s31) | (~until6(s31))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9928, 9395, 9247])).
% 36.13/23.96 tff(9930,plain,
% 36.13/23.96 (xuntil7(s31)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9929, 9922])).
% 36.13/23.96 tff(9931,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9932,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9933,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s31, s32)) | (~xuntil7(s31)) | until6(s32)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9932, 9931])).
% 36.13/23.96 tff(9934,plain,
% 36.13/23.96 ((~xuntil7(s31)) | until6(s32)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9933, 1041, 9413])).
% 36.13/23.96 tff(9935,plain,
% 36.13/23.96 (until6(s32)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9934, 9930])).
% 36.13/23.96 tff(9936,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9937,plain,
% 36.13/23.96 ((always5(s32) | (~until6(s32)) | xuntil7(s32)) <=> (xuntil7(s32) | always5(s32) | (~until6(s32)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9938,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[9937])).
% 36.13/23.96 tff(9939,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[9938, 9936])).
% 36.13/23.96 tff(9940,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s32) | (~until6(s32)) | xuntil7(s32))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9941,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s32) | always5(s32) | (~until6(s32))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9940, 9939])).
% 36.13/23.96 tff(9942,plain,
% 36.13/23.96 (xuntil7(s32) | (~until6(s32))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9941, 9395, 9239])).
% 36.13/23.96 tff(9943,plain,
% 36.13/23.96 (xuntil7(s32)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9942, 9935])).
% 36.13/23.96 tff(9944,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9945,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9946,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s32, s33)) | (~xuntil7(s32)) | until6(s33)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9945, 9944])).
% 36.13/23.96 tff(9947,plain,
% 36.13/23.96 ((~xuntil7(s32)) | until6(s33)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9946, 1072, 9413])).
% 36.13/23.96 tff(9948,plain,
% 36.13/23.96 (until6(s33)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9947, 9943])).
% 36.13/23.96 tff(9949,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9950,plain,
% 36.13/23.96 ((always5(s33) | (~until6(s33)) | xuntil7(s33)) <=> (xuntil7(s33) | always5(s33) | (~until6(s33)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9951,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[9950])).
% 36.13/23.96 tff(9952,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[9951, 9949])).
% 36.13/23.96 tff(9953,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s33) | (~until6(s33)) | xuntil7(s33))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9954,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s33) | always5(s33) | (~until6(s33))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9953, 9952])).
% 36.13/23.96 tff(9955,plain,
% 36.13/23.96 (xuntil7(s33) | (~until6(s33))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9954, 9395, 9231])).
% 36.13/23.96 tff(9956,plain,
% 36.13/23.96 (xuntil7(s33)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9955, 9948])).
% 36.13/23.96 tff(9957,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9958,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9959,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s33, s34)) | (~xuntil7(s33)) | until6(s34)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9958, 9957])).
% 36.13/23.96 tff(9960,plain,
% 36.13/23.96 ((~xuntil7(s33)) | until6(s34)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9959, 1100, 9413])).
% 36.13/23.96 tff(9961,plain,
% 36.13/23.96 (until6(s34)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9960, 9956])).
% 36.13/23.96 tff(9962,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9963,plain,
% 36.13/23.96 ((always5(s34) | (~until6(s34)) | xuntil7(s34)) <=> (xuntil7(s34) | always5(s34) | (~until6(s34)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9964,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[9963])).
% 36.13/23.96 tff(9965,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[9964, 9962])).
% 36.13/23.96 tff(9966,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s34) | (~until6(s34)) | xuntil7(s34))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9967,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s34) | always5(s34) | (~until6(s34))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9966, 9965])).
% 36.13/23.96 tff(9968,plain,
% 36.13/23.96 (xuntil7(s34) | (~until6(s34))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9967, 9395, 9223])).
% 36.13/23.96 tff(9969,plain,
% 36.13/23.96 (xuntil7(s34)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9968, 9961])).
% 36.13/23.96 tff(9970,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9971,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9972,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s34, s35)) | (~xuntil7(s34)) | until6(s35)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9971, 9970])).
% 36.13/23.96 tff(9973,plain,
% 36.13/23.96 ((~xuntil7(s34)) | until6(s35)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9972, 1131, 9413])).
% 36.13/23.96 tff(9974,plain,
% 36.13/23.96 (until6(s35)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9973, 9969])).
% 36.13/23.96 tff(9975,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9976,plain,
% 36.13/23.96 ((always5(s35) | (~until6(s35)) | xuntil7(s35)) <=> (xuntil7(s35) | always5(s35) | (~until6(s35)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9977,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[9976])).
% 36.13/23.96 tff(9978,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[9977, 9975])).
% 36.13/23.96 tff(9979,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s35) | (~until6(s35)) | xuntil7(s35))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9980,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s35) | always5(s35) | (~until6(s35))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9979, 9978])).
% 36.13/23.96 tff(9981,plain,
% 36.13/23.96 (xuntil7(s35) | (~until6(s35))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9980, 9395, 9215])).
% 36.13/23.96 tff(9982,plain,
% 36.13/23.96 (xuntil7(s35)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9981, 9974])).
% 36.13/23.96 tff(9983,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9984,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9985,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s35, s36)) | (~xuntil7(s35)) | until6(s36)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9984, 9983])).
% 36.13/23.96 tff(9986,plain,
% 36.13/23.96 ((~xuntil7(s35)) | until6(s36)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9985, 1159, 9413])).
% 36.13/23.96 tff(9987,plain,
% 36.13/23.96 (until6(s36)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9986, 9982])).
% 36.13/23.96 tff(9988,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9989,plain,
% 36.13/23.96 ((always5(s36) | (~until6(s36)) | xuntil7(s36)) <=> (xuntil7(s36) | always5(s36) | (~until6(s36)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9990,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[9989])).
% 36.13/23.96 tff(9991,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[9990, 9988])).
% 36.13/23.96 tff(9992,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s36) | (~until6(s36)) | xuntil7(s36))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9993,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s36) | always5(s36) | (~until6(s36))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9992, 9991])).
% 36.13/23.96 tff(9994,plain,
% 36.13/23.96 (xuntil7(s36) | (~until6(s36))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9993, 9395, 9207])).
% 36.13/23.96 tff(9995,plain,
% 36.13/23.96 (xuntil7(s36)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9994, 9987])).
% 36.13/23.96 tff(9996,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(9997,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s36, s37)) | (~xuntil7(s36)) | until6(s37))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(9998,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s36, s37)) | (~xuntil7(s36)) | until6(s37)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[9997, 9996])).
% 36.13/23.96 tff(9999,plain,
% 36.13/23.96 ((~xuntil7(s36)) | until6(s37)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9998, 1190, 9413])).
% 36.13/23.96 tff(10000,plain,
% 36.13/23.96 (until6(s37)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[9999, 9995])).
% 36.13/23.96 tff(10001,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10002,plain,
% 36.13/23.96 ((always5(s37) | (~until6(s37)) | xuntil7(s37)) <=> (xuntil7(s37) | always5(s37) | (~until6(s37)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10003,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10002])).
% 36.13/23.96 tff(10004,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10003, 10001])).
% 36.13/23.96 tff(10005,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s37) | (~until6(s37)) | xuntil7(s37))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10006,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s37) | always5(s37) | (~until6(s37))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10005, 10004])).
% 36.13/23.96 tff(10007,plain,
% 36.13/23.96 (xuntil7(s37) | (~until6(s37))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10006, 9395, 9199])).
% 36.13/23.96 tff(10008,plain,
% 36.13/23.96 (xuntil7(s37)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10007, 10000])).
% 36.13/23.96 tff(10009,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10010,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10011,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s37, s38)) | (~xuntil7(s37)) | until6(s38)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10010, 10009])).
% 36.13/23.96 tff(10012,plain,
% 36.13/23.96 ((~xuntil7(s37)) | until6(s38)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10011, 1218, 9413])).
% 36.13/23.96 tff(10013,plain,
% 36.13/23.96 (until6(s38)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10012, 10008])).
% 36.13/23.96 tff(10014,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10015,plain,
% 36.13/23.96 ((always5(s38) | (~until6(s38)) | xuntil7(s38)) <=> (xuntil7(s38) | always5(s38) | (~until6(s38)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10016,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10015])).
% 36.13/23.96 tff(10017,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10016, 10014])).
% 36.13/23.96 tff(10018,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s38) | (~until6(s38)) | xuntil7(s38))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10019,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s38) | always5(s38) | (~until6(s38))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10018, 10017])).
% 36.13/23.96 tff(10020,plain,
% 36.13/23.96 (xuntil7(s38) | (~until6(s38))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10019, 9395, 9191])).
% 36.13/23.96 tff(10021,plain,
% 36.13/23.96 (xuntil7(s38)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10020, 10013])).
% 36.13/23.96 tff(10022,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10023,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10024,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s38, s39)) | (~xuntil7(s38)) | until6(s39)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10023, 10022])).
% 36.13/23.96 tff(10025,plain,
% 36.13/23.96 ((~xuntil7(s38)) | until6(s39)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10024, 1249, 9413])).
% 36.13/23.96 tff(10026,plain,
% 36.13/23.96 (until6(s39)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10025, 10021])).
% 36.13/23.96 tff(10027,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10028,plain,
% 36.13/23.96 ((always5(s39) | (~until6(s39)) | xuntil7(s39)) <=> (xuntil7(s39) | always5(s39) | (~until6(s39)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10029,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10028])).
% 36.13/23.96 tff(10030,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10029, 10027])).
% 36.13/23.96 tff(10031,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s39) | (~until6(s39)) | xuntil7(s39))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10032,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s39) | always5(s39) | (~until6(s39))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10031, 10030])).
% 36.13/23.96 tff(10033,plain,
% 36.13/23.96 (xuntil7(s39) | (~until6(s39))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10032, 9395, 9183])).
% 36.13/23.96 tff(10034,plain,
% 36.13/23.96 (xuntil7(s39)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10033, 10026])).
% 36.13/23.96 tff(10035,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10036,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10037,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s39, s40)) | (~xuntil7(s39)) | until6(s40)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10036, 10035])).
% 36.13/23.96 tff(10038,plain,
% 36.13/23.96 ((~xuntil7(s39)) | until6(s40)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10037, 1277, 9413])).
% 36.13/23.96 tff(10039,plain,
% 36.13/23.96 (until6(s40)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10038, 10034])).
% 36.13/23.96 tff(10040,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10041,plain,
% 36.13/23.96 ((always5(s40) | (~until6(s40)) | xuntil7(s40)) <=> (xuntil7(s40) | always5(s40) | (~until6(s40)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10042,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10041])).
% 36.13/23.96 tff(10043,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10042, 10040])).
% 36.13/23.96 tff(10044,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s40) | (~until6(s40)) | xuntil7(s40))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10045,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s40) | always5(s40) | (~until6(s40))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10044, 10043])).
% 36.13/23.96 tff(10046,plain,
% 36.13/23.96 (xuntil7(s40) | (~until6(s40))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10045, 9395, 9175])).
% 36.13/23.96 tff(10047,plain,
% 36.13/23.96 (xuntil7(s40)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10046, 10039])).
% 36.13/23.96 tff(10048,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10049,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10050,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s40, s41)) | (~xuntil7(s40)) | until6(s41)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10049, 10048])).
% 36.13/23.96 tff(10051,plain,
% 36.13/23.96 ((~xuntil7(s40)) | until6(s41)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10050, 1308, 9413])).
% 36.13/23.96 tff(10052,plain,
% 36.13/23.96 (until6(s41)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10051, 10047])).
% 36.13/23.96 tff(10053,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10054,plain,
% 36.13/23.96 ((always5(s41) | (~until6(s41)) | xuntil7(s41)) <=> (xuntil7(s41) | always5(s41) | (~until6(s41)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10055,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10054])).
% 36.13/23.96 tff(10056,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10055, 10053])).
% 36.13/23.96 tff(10057,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s41) | (~until6(s41)) | xuntil7(s41))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10058,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s41) | always5(s41) | (~until6(s41))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10057, 10056])).
% 36.13/23.96 tff(10059,plain,
% 36.13/23.96 (xuntil7(s41) | (~until6(s41))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10058, 9395, 9167])).
% 36.13/23.96 tff(10060,plain,
% 36.13/23.96 (xuntil7(s41)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10059, 10052])).
% 36.13/23.96 tff(10061,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10062,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10063,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s41, s42)) | (~xuntil7(s41)) | until6(s42)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10062, 10061])).
% 36.13/23.96 tff(10064,plain,
% 36.13/23.96 ((~xuntil7(s41)) | until6(s42)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10063, 1336, 9413])).
% 36.13/23.96 tff(10065,plain,
% 36.13/23.96 (until6(s42)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10064, 10060])).
% 36.13/23.96 tff(10066,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10067,plain,
% 36.13/23.96 ((always5(s42) | (~until6(s42)) | xuntil7(s42)) <=> (xuntil7(s42) | always5(s42) | (~until6(s42)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10068,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10067])).
% 36.13/23.96 tff(10069,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10068, 10066])).
% 36.13/23.96 tff(10070,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s42) | (~until6(s42)) | xuntil7(s42))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10071,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s42) | always5(s42) | (~until6(s42))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10070, 10069])).
% 36.13/23.96 tff(10072,plain,
% 36.13/23.96 (xuntil7(s42) | (~until6(s42))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10071, 9395, 9159])).
% 36.13/23.96 tff(10073,plain,
% 36.13/23.96 (xuntil7(s42)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10072, 10065])).
% 36.13/23.96 tff(10074,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10075,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10076,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s42, s43)) | (~xuntil7(s42)) | until6(s43)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10075, 10074])).
% 36.13/23.96 tff(10077,plain,
% 36.13/23.96 ((~xuntil7(s42)) | until6(s43)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10076, 1367, 9413])).
% 36.13/23.96 tff(10078,plain,
% 36.13/23.96 (until6(s43)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10077, 10073])).
% 36.13/23.96 tff(10079,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10080,plain,
% 36.13/23.96 ((always5(s43) | (~until6(s43)) | xuntil7(s43)) <=> (xuntil7(s43) | always5(s43) | (~until6(s43)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10081,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10080])).
% 36.13/23.96 tff(10082,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10081, 10079])).
% 36.13/23.96 tff(10083,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s43) | (~until6(s43)) | xuntil7(s43))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10084,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s43) | always5(s43) | (~until6(s43))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10083, 10082])).
% 36.13/23.96 tff(10085,plain,
% 36.13/23.96 (xuntil7(s43) | (~until6(s43))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10084, 9395, 9151])).
% 36.13/23.96 tff(10086,plain,
% 36.13/23.96 (xuntil7(s43)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10085, 10078])).
% 36.13/23.96 tff(10087,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10088,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10089,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s43, s44)) | (~xuntil7(s43)) | until6(s44)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10088, 10087])).
% 36.13/23.96 tff(10090,plain,
% 36.13/23.96 ((~xuntil7(s43)) | until6(s44)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10089, 1395, 9413])).
% 36.13/23.96 tff(10091,plain,
% 36.13/23.96 (until6(s44)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10090, 10086])).
% 36.13/23.96 tff(10092,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10093,plain,
% 36.13/23.96 ((always5(s44) | (~until6(s44)) | xuntil7(s44)) <=> (xuntil7(s44) | always5(s44) | (~until6(s44)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10094,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10093])).
% 36.13/23.96 tff(10095,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10094, 10092])).
% 36.13/23.96 tff(10096,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s44) | (~until6(s44)) | xuntil7(s44))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10097,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s44) | always5(s44) | (~until6(s44))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10096, 10095])).
% 36.13/23.96 tff(10098,plain,
% 36.13/23.96 (xuntil7(s44) | (~until6(s44))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10097, 9395, 9143])).
% 36.13/23.96 tff(10099,plain,
% 36.13/23.96 (xuntil7(s44)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10098, 10091])).
% 36.13/23.96 tff(10100,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10101,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10102,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s44, s45)) | (~xuntil7(s44)) | until6(s45)),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10101, 10100])).
% 36.13/23.96 tff(10103,plain,
% 36.13/23.96 ((~xuntil7(s44)) | until6(s45)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10102, 1426, 9413])).
% 36.13/23.96 tff(10104,plain,
% 36.13/23.96 (until6(s45)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10103, 10099])).
% 36.13/23.96 tff(10105,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10106,plain,
% 36.13/23.96 ((always5(s45) | (~until6(s45)) | xuntil7(s45)) <=> (xuntil7(s45) | always5(s45) | (~until6(s45)))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10107,plain,
% 36.13/23.96 (((~![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))))),
% 36.13/23.96 inference(monotonicity,[status(thm)],[10106])).
% 36.13/23.96 tff(10108,plain,
% 36.13/23.96 (((~![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)))),
% 36.13/23.96 inference(transitivity,[status(thm)],[10107, 10105])).
% 36.13/23.96 tff(10109,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s45) | (~until6(s45)) | xuntil7(s45))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.96 tff(10110,plain,
% 36.13/23.96 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s45) | always5(s45) | (~until6(s45))),
% 36.13/23.96 inference(modus_ponens,[status(thm)],[10109, 10108])).
% 36.13/23.96 tff(10111,plain,
% 36.13/23.96 (xuntil7(s45) | (~until6(s45))),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10110, 9395, 9135])).
% 36.13/23.96 tff(10112,plain,
% 36.13/23.96 (xuntil7(s45)),
% 36.13/23.96 inference(unit_resolution,[status(thm)],[10111, 10104])).
% 36.13/23.96 tff(10113,plain,
% 36.13/23.96 (((~![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))),
% 36.13/23.96 inference(rewrite,[status(thm)],[])).
% 36.13/23.96 tff(10114,plain,
% 36.13/23.96 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46))),
% 36.13/23.96 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10115,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s45, s46)) | (~xuntil7(s45)) | until6(s46)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10114, 10113])).
% 36.13/23.97 tff(10116,plain,
% 36.13/23.97 ((~xuntil7(s45)) | until6(s46)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10115, 1452, 9413])).
% 36.13/23.97 tff(10117,plain,
% 36.13/23.97 (until6(s46)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10116, 10112])).
% 36.13/23.97 tff(10118,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10119,plain,
% 36.13/23.97 ((always5(s46) | (~until6(s46)) | xuntil7(s46)) <=> (xuntil7(s46) | always5(s46) | (~until6(s46)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10120,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10119])).
% 36.13/23.97 tff(10121,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10120, 10118])).
% 36.13/23.97 tff(10122,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s46) | (~until6(s46)) | xuntil7(s46))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10123,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s46) | always5(s46) | (~until6(s46))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10122, 10121])).
% 36.13/23.97 tff(10124,plain,
% 36.13/23.97 (xuntil7(s46) | (~until6(s46))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10123, 9395, 9127])).
% 36.13/23.97 tff(10125,plain,
% 36.13/23.97 (xuntil7(s46)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10124, 10117])).
% 36.13/23.97 tff(10126,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10127,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10128,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s46, s47)) | (~xuntil7(s46)) | until6(s47)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10127, 10126])).
% 36.13/23.97 tff(10129,plain,
% 36.13/23.97 ((~xuntil7(s46)) | until6(s47)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10128, 1483, 9413])).
% 36.13/23.97 tff(10130,plain,
% 36.13/23.97 (until6(s47)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10129, 10125])).
% 36.13/23.97 tff(10131,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10132,plain,
% 36.13/23.97 ((always5(s47) | (~until6(s47)) | xuntil7(s47)) <=> (xuntil7(s47) | always5(s47) | (~until6(s47)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10133,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10132])).
% 36.13/23.97 tff(10134,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10133, 10131])).
% 36.13/23.97 tff(10135,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s47) | (~until6(s47)) | xuntil7(s47))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10136,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s47) | always5(s47) | (~until6(s47))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10135, 10134])).
% 36.13/23.97 tff(10137,plain,
% 36.13/23.97 (xuntil7(s47) | (~until6(s47))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10136, 9395, 9119])).
% 36.13/23.97 tff(10138,plain,
% 36.13/23.97 (xuntil7(s47)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10137, 10130])).
% 36.13/23.97 tff(10139,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10140,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s47, s48)) | (~xuntil7(s47)) | until6(s48))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10141,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s47, s48)) | (~xuntil7(s47)) | until6(s48)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10140, 10139])).
% 36.13/23.97 tff(10142,plain,
% 36.13/23.97 ((~xuntil7(s47)) | until6(s48)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10141, 1511, 9413])).
% 36.13/23.97 tff(10143,plain,
% 36.13/23.97 (until6(s48)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10142, 10138])).
% 36.13/23.97 tff(10144,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10145,plain,
% 36.13/23.97 ((always5(s48) | (~until6(s48)) | xuntil7(s48)) <=> (xuntil7(s48) | always5(s48) | (~until6(s48)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10146,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10145])).
% 36.13/23.97 tff(10147,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10146, 10144])).
% 36.13/23.97 tff(10148,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s48) | (~until6(s48)) | xuntil7(s48))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10149,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s48) | always5(s48) | (~until6(s48))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10148, 10147])).
% 36.13/23.97 tff(10150,plain,
% 36.13/23.97 (xuntil7(s48) | (~until6(s48))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10149, 9395, 9111])).
% 36.13/23.97 tff(10151,plain,
% 36.13/23.97 (xuntil7(s48)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10150, 10143])).
% 36.13/23.97 tff(10152,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10153,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10154,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s48, s49)) | (~xuntil7(s48)) | until6(s49)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10153, 10152])).
% 36.13/23.97 tff(10155,plain,
% 36.13/23.97 ((~xuntil7(s48)) | until6(s49)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10154, 1542, 9413])).
% 36.13/23.97 tff(10156,plain,
% 36.13/23.97 (until6(s49)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10155, 10151])).
% 36.13/23.97 tff(10157,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10158,plain,
% 36.13/23.97 ((always5(s49) | (~until6(s49)) | xuntil7(s49)) <=> (xuntil7(s49) | always5(s49) | (~until6(s49)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10159,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10158])).
% 36.13/23.97 tff(10160,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10159, 10157])).
% 36.13/23.97 tff(10161,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s49) | (~until6(s49)) | xuntil7(s49))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10162,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s49) | always5(s49) | (~until6(s49))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10161, 10160])).
% 36.13/23.97 tff(10163,plain,
% 36.13/23.97 (xuntil7(s49) | (~until6(s49))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10162, 9395, 9103])).
% 36.13/23.97 tff(10164,plain,
% 36.13/23.97 (xuntil7(s49)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10163, 10156])).
% 36.13/23.97 tff(10165,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10166,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10167,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s49, s50)) | (~xuntil7(s49)) | until6(s50)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10166, 10165])).
% 36.13/23.97 tff(10168,plain,
% 36.13/23.97 ((~xuntil7(s49)) | until6(s50)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10167, 1570, 9413])).
% 36.13/23.97 tff(10169,plain,
% 36.13/23.97 (until6(s50)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10168, 10164])).
% 36.13/23.97 tff(10170,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10171,plain,
% 36.13/23.97 ((always5(s50) | (~until6(s50)) | xuntil7(s50)) <=> (xuntil7(s50) | always5(s50) | (~until6(s50)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10172,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10171])).
% 36.13/23.97 tff(10173,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10172, 10170])).
% 36.13/23.97 tff(10174,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s50) | (~until6(s50)) | xuntil7(s50))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10175,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s50) | always5(s50) | (~until6(s50))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10174, 10173])).
% 36.13/23.97 tff(10176,plain,
% 36.13/23.97 (xuntil7(s50) | (~until6(s50))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10175, 9395, 9095])).
% 36.13/23.97 tff(10177,plain,
% 36.13/23.97 (xuntil7(s50)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10176, 10169])).
% 36.13/23.97 tff(10178,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10179,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10180,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s50, s51)) | (~xuntil7(s50)) | until6(s51)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10179, 10178])).
% 36.13/23.97 tff(10181,plain,
% 36.13/23.97 ((~xuntil7(s50)) | until6(s51)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10180, 1601, 9413])).
% 36.13/23.97 tff(10182,plain,
% 36.13/23.97 (until6(s51)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10181, 10177])).
% 36.13/23.97 tff(10183,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10184,plain,
% 36.13/23.97 ((always5(s51) | (~until6(s51)) | xuntil7(s51)) <=> (xuntil7(s51) | always5(s51) | (~until6(s51)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10185,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10184])).
% 36.13/23.97 tff(10186,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10185, 10183])).
% 36.13/23.97 tff(10187,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s51) | (~until6(s51)) | xuntil7(s51))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10188,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s51) | always5(s51) | (~until6(s51))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10187, 10186])).
% 36.13/23.97 tff(10189,plain,
% 36.13/23.97 (xuntil7(s51) | (~until6(s51))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10188, 9395, 9087])).
% 36.13/23.97 tff(10190,plain,
% 36.13/23.97 (xuntil7(s51)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10189, 10182])).
% 36.13/23.97 tff(10191,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10192,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10193,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s51, s52)) | (~xuntil7(s51)) | until6(s52)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10192, 10191])).
% 36.13/23.97 tff(10194,plain,
% 36.13/23.97 ((~xuntil7(s51)) | until6(s52)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10193, 1629, 9413])).
% 36.13/23.97 tff(10195,plain,
% 36.13/23.97 (until6(s52)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10194, 10190])).
% 36.13/23.97 tff(10196,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10197,plain,
% 36.13/23.97 ((always5(s52) | (~until6(s52)) | xuntil7(s52)) <=> (xuntil7(s52) | always5(s52) | (~until6(s52)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10198,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10197])).
% 36.13/23.97 tff(10199,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10198, 10196])).
% 36.13/23.97 tff(10200,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s52) | (~until6(s52)) | xuntil7(s52))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10201,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s52) | always5(s52) | (~until6(s52))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10200, 10199])).
% 36.13/23.97 tff(10202,plain,
% 36.13/23.97 (xuntil7(s52) | (~until6(s52))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10201, 9395, 9079])).
% 36.13/23.97 tff(10203,plain,
% 36.13/23.97 (xuntil7(s52)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10202, 10195])).
% 36.13/23.97 tff(10204,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10205,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10206,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s52, s53)) | (~xuntil7(s52)) | until6(s53)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10205, 10204])).
% 36.13/23.97 tff(10207,plain,
% 36.13/23.97 ((~xuntil7(s52)) | until6(s53)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10206, 1660, 9413])).
% 36.13/23.97 tff(10208,plain,
% 36.13/23.97 (until6(s53)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10207, 10203])).
% 36.13/23.97 tff(10209,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10210,plain,
% 36.13/23.97 ((always5(s53) | (~until6(s53)) | xuntil7(s53)) <=> (xuntil7(s53) | always5(s53) | (~until6(s53)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10211,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10210])).
% 36.13/23.97 tff(10212,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10211, 10209])).
% 36.13/23.97 tff(10213,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s53) | (~until6(s53)) | xuntil7(s53))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10214,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s53) | always5(s53) | (~until6(s53))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10213, 10212])).
% 36.13/23.97 tff(10215,plain,
% 36.13/23.97 (xuntil7(s53) | (~until6(s53))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10214, 9395, 9071])).
% 36.13/23.97 tff(10216,plain,
% 36.13/23.97 (xuntil7(s53)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10215, 10208])).
% 36.13/23.97 tff(10217,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10218,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10219,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s53, s54)) | (~xuntil7(s53)) | until6(s54)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10218, 10217])).
% 36.13/23.97 tff(10220,plain,
% 36.13/23.97 ((~xuntil7(s53)) | until6(s54)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10219, 1688, 9413])).
% 36.13/23.97 tff(10221,plain,
% 36.13/23.97 (until6(s54)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10220, 10216])).
% 36.13/23.97 tff(10222,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10223,plain,
% 36.13/23.97 ((always5(s54) | (~until6(s54)) | xuntil7(s54)) <=> (xuntil7(s54) | always5(s54) | (~until6(s54)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10224,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10223])).
% 36.13/23.97 tff(10225,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10224, 10222])).
% 36.13/23.97 tff(10226,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s54) | (~until6(s54)) | xuntil7(s54))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10227,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s54) | always5(s54) | (~until6(s54))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10226, 10225])).
% 36.13/23.97 tff(10228,plain,
% 36.13/23.97 (xuntil7(s54) | (~until6(s54))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10227, 9395, 9063])).
% 36.13/23.97 tff(10229,plain,
% 36.13/23.97 (xuntil7(s54)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10228, 10221])).
% 36.13/23.97 tff(10230,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10231,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10232,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s54, s55)) | (~xuntil7(s54)) | until6(s55)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10231, 10230])).
% 36.13/23.97 tff(10233,plain,
% 36.13/23.97 ((~xuntil7(s54)) | until6(s55)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10232, 1719, 9413])).
% 36.13/23.97 tff(10234,plain,
% 36.13/23.97 (until6(s55)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10233, 10229])).
% 36.13/23.97 tff(10235,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10236,plain,
% 36.13/23.97 ((always5(s55) | (~until6(s55)) | xuntil7(s55)) <=> (xuntil7(s55) | always5(s55) | (~until6(s55)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10237,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10236])).
% 36.13/23.97 tff(10238,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10237, 10235])).
% 36.13/23.97 tff(10239,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s55) | (~until6(s55)) | xuntil7(s55))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10240,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s55) | always5(s55) | (~until6(s55))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10239, 10238])).
% 36.13/23.97 tff(10241,plain,
% 36.13/23.97 (xuntil7(s55) | (~until6(s55))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10240, 9395, 9055])).
% 36.13/23.97 tff(10242,plain,
% 36.13/23.97 (xuntil7(s55)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10241, 10234])).
% 36.13/23.97 tff(10243,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10244,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10245,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s55, s56)) | (~xuntil7(s55)) | until6(s56)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10244, 10243])).
% 36.13/23.97 tff(10246,plain,
% 36.13/23.97 ((~xuntil7(s55)) | until6(s56)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10245, 1747, 9413])).
% 36.13/23.97 tff(10247,plain,
% 36.13/23.97 (until6(s56)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10246, 10242])).
% 36.13/23.97 tff(10248,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10249,plain,
% 36.13/23.97 ((always5(s56) | (~until6(s56)) | xuntil7(s56)) <=> (xuntil7(s56) | always5(s56) | (~until6(s56)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10250,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10249])).
% 36.13/23.97 tff(10251,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10250, 10248])).
% 36.13/23.97 tff(10252,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s56) | (~until6(s56)) | xuntil7(s56))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10253,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s56) | always5(s56) | (~until6(s56))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10252, 10251])).
% 36.13/23.97 tff(10254,plain,
% 36.13/23.97 (xuntil7(s56) | (~until6(s56))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10253, 9395, 9047])).
% 36.13/23.97 tff(10255,plain,
% 36.13/23.97 (xuntil7(s56)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10254, 10247])).
% 36.13/23.97 tff(10256,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10257,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s56, s57)) | (~xuntil7(s56)) | until6(s57))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10258,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s56, s57)) | (~xuntil7(s56)) | until6(s57)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10257, 10256])).
% 36.13/23.97 tff(10259,plain,
% 36.13/23.97 ((~xuntil7(s56)) | until6(s57)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10258, 1778, 9413])).
% 36.13/23.97 tff(10260,plain,
% 36.13/23.97 (until6(s57)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10259, 10255])).
% 36.13/23.97 tff(10261,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10262,plain,
% 36.13/23.97 ((always5(s57) | (~until6(s57)) | xuntil7(s57)) <=> (xuntil7(s57) | always5(s57) | (~until6(s57)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10263,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10262])).
% 36.13/23.97 tff(10264,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10263, 10261])).
% 36.13/23.97 tff(10265,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s57) | (~until6(s57)) | xuntil7(s57))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10266,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s57) | always5(s57) | (~until6(s57))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10265, 10264])).
% 36.13/23.97 tff(10267,plain,
% 36.13/23.97 (xuntil7(s57) | (~until6(s57))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10266, 9395, 9039])).
% 36.13/23.97 tff(10268,plain,
% 36.13/23.97 (xuntil7(s57)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10267, 10260])).
% 36.13/23.97 tff(10269,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10270,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s57, s58)) | (~xuntil7(s57)) | until6(s58))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10271,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s57, s58)) | (~xuntil7(s57)) | until6(s58)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10270, 10269])).
% 36.13/23.97 tff(10272,plain,
% 36.13/23.97 ((~xuntil7(s57)) | until6(s58)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10271, 1806, 9413])).
% 36.13/23.97 tff(10273,plain,
% 36.13/23.97 (until6(s58)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10272, 10268])).
% 36.13/23.97 tff(10274,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10275,plain,
% 36.13/23.97 ((always5(s58) | (~until6(s58)) | xuntil7(s58)) <=> (xuntil7(s58) | always5(s58) | (~until6(s58)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10276,plain,
% 36.13/23.97 (((~![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))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10275])).
% 36.13/23.97 tff(10277,plain,
% 36.13/23.97 (((~![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)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10276, 10274])).
% 36.13/23.97 tff(10278,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s58) | (~until6(s58)) | xuntil7(s58))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10279,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s58) | always5(s58) | (~until6(s58))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10278, 10277])).
% 36.13/23.97 tff(10280,plain,
% 36.13/23.97 (xuntil7(s58) | (~until6(s58))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10279, 9395, 9031])).
% 36.13/23.97 tff(10281,plain,
% 36.13/23.97 (xuntil7(s58)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10280, 10273])).
% 36.13/23.97 tff(10282,plain,
% 36.13/23.97 (((~![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))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10283,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s58, s59)) | (~xuntil7(s58)) | until6(s59))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10284,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s58, s59)) | (~xuntil7(s58)) | until6(s59)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10283, 10282])).
% 36.13/23.97 tff(10285,plain,
% 36.13/23.97 ((~xuntil7(s58)) | until6(s59)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10284, 1837, 9413])).
% 36.13/23.97 tff(10286,plain,
% 36.13/23.97 (until6(s59)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10285, 10281])).
% 36.13/23.97 tff(10287,plain,
% 36.13/23.97 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s59) | always5(s59) | (~until6(s59)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s59) | always5(s59) | (~until6(s59)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10288,plain,
% 36.13/23.97 ((always5(s59) | (~until6(s59)) | xuntil7(s59)) <=> (xuntil7(s59) | always5(s59) | (~until6(s59)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10289,plain,
% 36.13/23.97 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | (~until6(s59)) | xuntil7(s59))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s59) | always5(s59) | (~until6(s59))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10288])).
% 36.13/23.97 tff(10290,plain,
% 36.13/23.97 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | (~until6(s59)) | xuntil7(s59))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s59) | always5(s59) | (~until6(s59)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10289, 10287])).
% 36.13/23.97 tff(10291,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s59) | (~until6(s59)) | xuntil7(s59))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10292,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s59) | always5(s59) | (~until6(s59))),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10291, 10290])).
% 36.13/23.97 tff(10293,plain,
% 36.13/23.97 (xuntil7(s59) | (~until6(s59))),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10292, 9395, 9023])).
% 36.13/23.97 tff(10294,plain,
% 36.13/23.97 (xuntil7(s59)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10293, 10286])).
% 36.13/23.97 tff(10295,plain,
% 36.13/23.97 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s59, s60)) | (~xuntil7(s59)) | until6(s60))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s59, s60)) | (~xuntil7(s59)) | until6(s60))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10296,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s59, s60)) | (~xuntil7(s59)) | until6(s60))),
% 36.13/23.97 inference(quant_inst,[status(thm)],[])).
% 36.13/23.97 tff(10297,plain,
% 36.13/23.97 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s59, s60)) | (~xuntil7(s59)) | until6(s60)),
% 36.13/23.97 inference(modus_ponens,[status(thm)],[10296, 10295])).
% 36.13/23.97 tff(10298,plain,
% 36.13/23.97 ((~xuntil7(s59)) | until6(s60)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10297, 70, 9413])).
% 36.13/23.97 tff(10299,plain,
% 36.13/23.97 (until6(s60)),
% 36.13/23.97 inference(unit_resolution,[status(thm)],[10298, 10294])).
% 36.13/23.97 tff(10300,plain,
% 36.13/23.97 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s60) | always5(s60) | (~until6(s60)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s60) | always5(s60) | (~until6(s60)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10301,plain,
% 36.13/23.97 ((always5(s60) | (~until6(s60)) | xuntil7(s60)) <=> (xuntil7(s60) | always5(s60) | (~until6(s60)))),
% 36.13/23.97 inference(rewrite,[status(thm)],[])).
% 36.13/23.97 tff(10302,plain,
% 36.13/23.97 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s60) | (~until6(s60)) | xuntil7(s60))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s60) | always5(s60) | (~until6(s60))))),
% 36.13/23.97 inference(monotonicity,[status(thm)],[10301])).
% 36.13/23.97 tff(10303,plain,
% 36.13/23.97 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s60) | (~until6(s60)) | xuntil7(s60))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s60) | always5(s60) | (~until6(s60)))),
% 36.13/23.97 inference(transitivity,[status(thm)],[10302, 10300])).
% 36.13/23.97 tff(10304,plain,
% 36.13/23.97 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s60) | (~until6(s60)) | xuntil7(s60))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10305,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s60) | always5(s60) | (~until6(s60))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10304, 10303])).
% 36.13/23.98 tff(10306,plain,
% 36.13/23.98 (xuntil7(s60) | (~until6(s60))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10305, 9395, 9022])).
% 36.13/23.98 tff(10307,plain,
% 36.13/23.98 (xuntil7(s60)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10306, 10299])).
% 36.13/23.98 tff(10308,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s60, s61)) | (~xuntil7(s60)) | until6(s61))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s60, s61)) | (~xuntil7(s60)) | until6(s61))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10309,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s60, s61)) | (~xuntil7(s60)) | until6(s61))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10310,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s60, s61)) | (~xuntil7(s60)) | until6(s61)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10309, 10308])).
% 36.13/23.98 tff(10311,plain,
% 36.13/23.98 ((~xuntil7(s60)) | until6(s61)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10310, 1884, 9413])).
% 36.13/23.98 tff(10312,plain,
% 36.13/23.98 (until6(s61)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10311, 10307])).
% 36.13/23.98 tff(10313,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s61) | always5(s61) | (~until6(s61)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s61) | always5(s61) | (~until6(s61)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10314,plain,
% 36.13/23.98 ((always5(s61) | (~until6(s61)) | xuntil7(s61)) <=> (xuntil7(s61) | always5(s61) | (~until6(s61)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10315,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s61) | (~until6(s61)) | xuntil7(s61))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s61) | always5(s61) | (~until6(s61))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10314])).
% 36.13/23.98 tff(10316,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s61) | (~until6(s61)) | xuntil7(s61))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s61) | always5(s61) | (~until6(s61)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10315, 10313])).
% 36.13/23.98 tff(10317,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s61) | (~until6(s61)) | xuntil7(s61))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10318,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s61) | always5(s61) | (~until6(s61))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10317, 10316])).
% 36.13/23.98 tff(10319,plain,
% 36.13/23.98 (xuntil7(s61) | (~until6(s61))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10318, 9395, 9021])).
% 36.13/23.98 tff(10320,plain,
% 36.13/23.98 (xuntil7(s61)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10319, 10312])).
% 36.13/23.98 tff(10321,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s61, s62)) | (~xuntil7(s61)) | until6(s62))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s61, s62)) | (~xuntil7(s61)) | until6(s62))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10322,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s61, s62)) | (~xuntil7(s61)) | until6(s62))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10323,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s61, s62)) | (~xuntil7(s61)) | until6(s62)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10322, 10321])).
% 36.13/23.98 tff(10324,plain,
% 36.13/23.98 ((~xuntil7(s61)) | until6(s62)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10323, 1912, 9413])).
% 36.13/23.98 tff(10325,plain,
% 36.13/23.98 (until6(s62)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10324, 10320])).
% 36.13/23.98 tff(10326,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s62) | always5(s62) | (~until6(s62)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s62) | always5(s62) | (~until6(s62)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10327,plain,
% 36.13/23.98 ((always5(s62) | (~until6(s62)) | xuntil7(s62)) <=> (xuntil7(s62) | always5(s62) | (~until6(s62)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10328,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s62) | (~until6(s62)) | xuntil7(s62))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s62) | always5(s62) | (~until6(s62))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10327])).
% 36.13/23.98 tff(10329,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s62) | (~until6(s62)) | xuntil7(s62))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s62) | always5(s62) | (~until6(s62)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10328, 10326])).
% 36.13/23.98 tff(10330,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s62) | (~until6(s62)) | xuntil7(s62))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10331,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s62) | always5(s62) | (~until6(s62))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10330, 10329])).
% 36.13/23.98 tff(10332,plain,
% 36.13/23.98 (xuntil7(s62) | (~until6(s62))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10331, 9395, 9020])).
% 36.13/23.98 tff(10333,plain,
% 36.13/23.98 (xuntil7(s62)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10332, 10325])).
% 36.13/23.98 tff(10334,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s62, s63)) | (~xuntil7(s62)) | until6(s63))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s62, s63)) | (~xuntil7(s62)) | until6(s63))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10335,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s62, s63)) | (~xuntil7(s62)) | until6(s63))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10336,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s62, s63)) | (~xuntil7(s62)) | until6(s63)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10335, 10334])).
% 36.13/23.98 tff(10337,plain,
% 36.13/23.98 ((~xuntil7(s62)) | until6(s63)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10336, 1943, 9413])).
% 36.13/23.98 tff(10338,plain,
% 36.13/23.98 (until6(s63)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10337, 10333])).
% 36.13/23.98 tff(10339,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s63) | always5(s63) | (~until6(s63)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s63) | always5(s63) | (~until6(s63)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10340,plain,
% 36.13/23.98 ((always5(s63) | (~until6(s63)) | xuntil7(s63)) <=> (xuntil7(s63) | always5(s63) | (~until6(s63)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10341,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s63) | (~until6(s63)) | xuntil7(s63))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s63) | always5(s63) | (~until6(s63))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10340])).
% 36.13/23.98 tff(10342,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s63) | (~until6(s63)) | xuntil7(s63))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s63) | always5(s63) | (~until6(s63)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10341, 10339])).
% 36.13/23.98 tff(10343,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s63) | (~until6(s63)) | xuntil7(s63))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10344,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s63) | always5(s63) | (~until6(s63))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10343, 10342])).
% 36.13/23.98 tff(10345,plain,
% 36.13/23.98 (xuntil7(s63) | (~until6(s63))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10344, 9395, 9019])).
% 36.13/23.98 tff(10346,plain,
% 36.13/23.98 (xuntil7(s63)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10345, 10338])).
% 36.13/23.98 tff(10347,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s63, s64)) | (~xuntil7(s63)) | until6(s64))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s63, s64)) | (~xuntil7(s63)) | until6(s64))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10348,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s63, s64)) | (~xuntil7(s63)) | until6(s64))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10349,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s63, s64)) | (~xuntil7(s63)) | until6(s64)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10348, 10347])).
% 36.13/23.98 tff(10350,plain,
% 36.13/23.98 ((~xuntil7(s63)) | until6(s64)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10349, 1971, 9413])).
% 36.13/23.98 tff(10351,plain,
% 36.13/23.98 (until6(s64)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10350, 10346])).
% 36.13/23.98 tff(10352,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s64) | always5(s64) | (~until6(s64)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s64) | always5(s64) | (~until6(s64)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10353,plain,
% 36.13/23.98 ((always5(s64) | (~until6(s64)) | xuntil7(s64)) <=> (xuntil7(s64) | always5(s64) | (~until6(s64)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10354,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s64) | (~until6(s64)) | xuntil7(s64))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s64) | always5(s64) | (~until6(s64))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10353])).
% 36.13/23.98 tff(10355,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s64) | (~until6(s64)) | xuntil7(s64))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s64) | always5(s64) | (~until6(s64)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10354, 10352])).
% 36.13/23.98 tff(10356,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s64) | (~until6(s64)) | xuntil7(s64))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10357,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s64) | always5(s64) | (~until6(s64))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10356, 10355])).
% 36.13/23.98 tff(10358,plain,
% 36.13/23.98 (xuntil7(s64) | (~until6(s64))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10357, 9395, 9018])).
% 36.13/23.98 tff(10359,plain,
% 36.13/23.98 (xuntil7(s64)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10358, 10351])).
% 36.13/23.98 tff(10360,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s64, s65)) | (~xuntil7(s64)) | until6(s65))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s64, s65)) | (~xuntil7(s64)) | until6(s65))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10361,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s64, s65)) | (~xuntil7(s64)) | until6(s65))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10362,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s64, s65)) | (~xuntil7(s64)) | until6(s65)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10361, 10360])).
% 36.13/23.98 tff(10363,plain,
% 36.13/23.98 ((~xuntil7(s64)) | until6(s65)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10362, 2002, 9413])).
% 36.13/23.98 tff(10364,plain,
% 36.13/23.98 (until6(s65)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10363, 10359])).
% 36.13/23.98 tff(10365,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s65) | always5(s65) | (~until6(s65)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s65) | always5(s65) | (~until6(s65)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10366,plain,
% 36.13/23.98 ((always5(s65) | (~until6(s65)) | xuntil7(s65)) <=> (xuntil7(s65) | always5(s65) | (~until6(s65)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10367,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s65) | (~until6(s65)) | xuntil7(s65))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s65) | always5(s65) | (~until6(s65))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10366])).
% 36.13/23.98 tff(10368,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s65) | (~until6(s65)) | xuntil7(s65))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s65) | always5(s65) | (~until6(s65)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10367, 10365])).
% 36.13/23.98 tff(10369,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s65) | (~until6(s65)) | xuntil7(s65))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10370,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s65) | always5(s65) | (~until6(s65))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10369, 10368])).
% 36.13/23.98 tff(10371,plain,
% 36.13/23.98 (xuntil7(s65) | (~until6(s65))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10370, 9395, 9017])).
% 36.13/23.98 tff(10372,plain,
% 36.13/23.98 (xuntil7(s65)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10371, 10364])).
% 36.13/23.98 tff(10373,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s65, s66)) | (~xuntil7(s65)) | until6(s66))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s65, s66)) | (~xuntil7(s65)) | until6(s66))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10374,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s65, s66)) | (~xuntil7(s65)) | until6(s66))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10375,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s65, s66)) | (~xuntil7(s65)) | until6(s66)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10374, 10373])).
% 36.13/23.98 tff(10376,plain,
% 36.13/23.98 ((~xuntil7(s65)) | until6(s66)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10375, 2030, 9413])).
% 36.13/23.98 tff(10377,plain,
% 36.13/23.98 (until6(s66)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10376, 10372])).
% 36.13/23.98 tff(10378,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s66) | always5(s66) | (~until6(s66)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s66) | always5(s66) | (~until6(s66)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10379,plain,
% 36.13/23.98 ((always5(s66) | (~until6(s66)) | xuntil7(s66)) <=> (xuntil7(s66) | always5(s66) | (~until6(s66)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10380,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s66) | (~until6(s66)) | xuntil7(s66))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s66) | always5(s66) | (~until6(s66))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10379])).
% 36.13/23.98 tff(10381,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s66) | (~until6(s66)) | xuntil7(s66))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s66) | always5(s66) | (~until6(s66)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10380, 10378])).
% 36.13/23.98 tff(10382,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s66) | (~until6(s66)) | xuntil7(s66))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10383,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s66) | always5(s66) | (~until6(s66))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10382, 10381])).
% 36.13/23.98 tff(10384,plain,
% 36.13/23.98 (xuntil7(s66) | (~until6(s66))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10383, 9395, 9016])).
% 36.13/23.98 tff(10385,plain,
% 36.13/23.98 (xuntil7(s66)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10384, 10377])).
% 36.13/23.98 tff(10386,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s66, s67)) | (~xuntil7(s66)) | until6(s67))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s66, s67)) | (~xuntil7(s66)) | until6(s67))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10387,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s66, s67)) | (~xuntil7(s66)) | until6(s67))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10388,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s66, s67)) | (~xuntil7(s66)) | until6(s67)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10387, 10386])).
% 36.13/23.98 tff(10389,plain,
% 36.13/23.98 ((~xuntil7(s66)) | until6(s67)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10388, 2061, 9413])).
% 36.13/23.98 tff(10390,plain,
% 36.13/23.98 (until6(s67)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10389, 10385])).
% 36.13/23.98 tff(10391,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s67) | always5(s67) | (~until6(s67)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s67) | always5(s67) | (~until6(s67)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10392,plain,
% 36.13/23.98 ((always5(s67) | (~until6(s67)) | xuntil7(s67)) <=> (xuntil7(s67) | always5(s67) | (~until6(s67)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10393,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s67) | (~until6(s67)) | xuntil7(s67))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s67) | always5(s67) | (~until6(s67))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10392])).
% 36.13/23.98 tff(10394,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s67) | (~until6(s67)) | xuntil7(s67))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s67) | always5(s67) | (~until6(s67)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10393, 10391])).
% 36.13/23.98 tff(10395,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s67) | (~until6(s67)) | xuntil7(s67))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10396,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s67) | always5(s67) | (~until6(s67))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10395, 10394])).
% 36.13/23.98 tff(10397,plain,
% 36.13/23.98 (xuntil7(s67) | (~until6(s67))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10396, 9395, 9015])).
% 36.13/23.98 tff(10398,plain,
% 36.13/23.98 (xuntil7(s67)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10397, 10390])).
% 36.13/23.98 tff(10399,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s67, s68)) | (~xuntil7(s67)) | until6(s68))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s67, s68)) | (~xuntil7(s67)) | until6(s68))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10400,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s67, s68)) | (~xuntil7(s67)) | until6(s68))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10401,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s67, s68)) | (~xuntil7(s67)) | until6(s68)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10400, 10399])).
% 36.13/23.98 tff(10402,plain,
% 36.13/23.98 ((~xuntil7(s67)) | until6(s68)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10401, 2089, 9413])).
% 36.13/23.98 tff(10403,plain,
% 36.13/23.98 (until6(s68)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10402, 10398])).
% 36.13/23.98 tff(10404,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s68) | always5(s68) | (~until6(s68)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s68) | always5(s68) | (~until6(s68)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10405,plain,
% 36.13/23.98 ((always5(s68) | (~until6(s68)) | xuntil7(s68)) <=> (xuntil7(s68) | always5(s68) | (~until6(s68)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10406,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s68) | (~until6(s68)) | xuntil7(s68))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s68) | always5(s68) | (~until6(s68))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10405])).
% 36.13/23.98 tff(10407,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s68) | (~until6(s68)) | xuntil7(s68))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s68) | always5(s68) | (~until6(s68)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10406, 10404])).
% 36.13/23.98 tff(10408,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s68) | (~until6(s68)) | xuntil7(s68))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10409,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s68) | always5(s68) | (~until6(s68))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10408, 10407])).
% 36.13/23.98 tff(10410,plain,
% 36.13/23.98 (xuntil7(s68) | (~until6(s68))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10409, 9395, 9014])).
% 36.13/23.98 tff(10411,plain,
% 36.13/23.98 (xuntil7(s68)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10410, 10403])).
% 36.13/23.98 tff(10412,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s68, s69)) | (~xuntil7(s68)) | until6(s69))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s68, s69)) | (~xuntil7(s68)) | until6(s69))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10413,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s68, s69)) | (~xuntil7(s68)) | until6(s69))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10414,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s68, s69)) | (~xuntil7(s68)) | until6(s69)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10413, 10412])).
% 36.13/23.98 tff(10415,plain,
% 36.13/23.98 ((~xuntil7(s68)) | until6(s69)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10414, 2120, 9413])).
% 36.13/23.98 tff(10416,plain,
% 36.13/23.98 (until6(s69)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10415, 10411])).
% 36.13/23.98 tff(10417,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s69) | always5(s69) | (~until6(s69)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s69) | always5(s69) | (~until6(s69)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10418,plain,
% 36.13/23.98 ((always5(s69) | (~until6(s69)) | xuntil7(s69)) <=> (xuntil7(s69) | always5(s69) | (~until6(s69)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10419,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s69) | (~until6(s69)) | xuntil7(s69))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s69) | always5(s69) | (~until6(s69))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10418])).
% 36.13/23.98 tff(10420,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s69) | (~until6(s69)) | xuntil7(s69))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s69) | always5(s69) | (~until6(s69)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10419, 10417])).
% 36.13/23.98 tff(10421,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s69) | (~until6(s69)) | xuntil7(s69))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10422,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s69) | always5(s69) | (~until6(s69))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10421, 10420])).
% 36.13/23.98 tff(10423,plain,
% 36.13/23.98 (xuntil7(s69) | (~until6(s69))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10422, 9395, 9013])).
% 36.13/23.98 tff(10424,plain,
% 36.13/23.98 (xuntil7(s69)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10423, 10416])).
% 36.13/23.98 tff(10425,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s69, s70)) | (~xuntil7(s69)) | until6(s70))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s69, s70)) | (~xuntil7(s69)) | until6(s70))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10426,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s69, s70)) | (~xuntil7(s69)) | until6(s70))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10427,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s69, s70)) | (~xuntil7(s69)) | until6(s70)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10426, 10425])).
% 36.13/23.98 tff(10428,plain,
% 36.13/23.98 ((~xuntil7(s69)) | until6(s70)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10427, 2148, 9413])).
% 36.13/23.98 tff(10429,plain,
% 36.13/23.98 (until6(s70)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10428, 10424])).
% 36.13/23.98 tff(10430,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s70) | always5(s70) | (~until6(s70)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s70) | always5(s70) | (~until6(s70)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10431,plain,
% 36.13/23.98 ((always5(s70) | (~until6(s70)) | xuntil7(s70)) <=> (xuntil7(s70) | always5(s70) | (~until6(s70)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10432,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s70) | (~until6(s70)) | xuntil7(s70))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s70) | always5(s70) | (~until6(s70))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10431])).
% 36.13/23.98 tff(10433,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s70) | (~until6(s70)) | xuntil7(s70))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s70) | always5(s70) | (~until6(s70)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10432, 10430])).
% 36.13/23.98 tff(10434,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s70) | (~until6(s70)) | xuntil7(s70))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10435,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s70) | always5(s70) | (~until6(s70))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10434, 10433])).
% 36.13/23.98 tff(10436,plain,
% 36.13/23.98 (xuntil7(s70) | (~until6(s70))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10435, 9395, 9012])).
% 36.13/23.98 tff(10437,plain,
% 36.13/23.98 (xuntil7(s70)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10436, 10429])).
% 36.13/23.98 tff(10438,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s70, s71)) | (~xuntil7(s70)) | until6(s71))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s70, s71)) | (~xuntil7(s70)) | until6(s71))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10439,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s70, s71)) | (~xuntil7(s70)) | until6(s71))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10440,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s70, s71)) | (~xuntil7(s70)) | until6(s71)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10439, 10438])).
% 36.13/23.98 tff(10441,plain,
% 36.13/23.98 ((~xuntil7(s70)) | until6(s71)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10440, 2179, 9413])).
% 36.13/23.98 tff(10442,plain,
% 36.13/23.98 (until6(s71)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10441, 10437])).
% 36.13/23.98 tff(10443,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s71) | always5(s71) | (~until6(s71)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s71) | always5(s71) | (~until6(s71)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10444,plain,
% 36.13/23.98 ((always5(s71) | (~until6(s71)) | xuntil7(s71)) <=> (xuntil7(s71) | always5(s71) | (~until6(s71)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10445,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s71) | (~until6(s71)) | xuntil7(s71))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s71) | always5(s71) | (~until6(s71))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10444])).
% 36.13/23.98 tff(10446,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s71) | (~until6(s71)) | xuntil7(s71))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s71) | always5(s71) | (~until6(s71)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10445, 10443])).
% 36.13/23.98 tff(10447,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s71) | (~until6(s71)) | xuntil7(s71))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10448,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s71) | always5(s71) | (~until6(s71))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10447, 10446])).
% 36.13/23.98 tff(10449,plain,
% 36.13/23.98 (xuntil7(s71) | (~until6(s71))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10448, 9395, 9011])).
% 36.13/23.98 tff(10450,plain,
% 36.13/23.98 (xuntil7(s71)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10449, 10442])).
% 36.13/23.98 tff(10451,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s71, s72)) | (~xuntil7(s71)) | until6(s72))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s71, s72)) | (~xuntil7(s71)) | until6(s72))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10452,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s71, s72)) | (~xuntil7(s71)) | until6(s72))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10453,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s71, s72)) | (~xuntil7(s71)) | until6(s72)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10452, 10451])).
% 36.13/23.98 tff(10454,plain,
% 36.13/23.98 ((~xuntil7(s71)) | until6(s72)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10453, 2207, 9413])).
% 36.13/23.98 tff(10455,plain,
% 36.13/23.98 (until6(s72)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10454, 10450])).
% 36.13/23.98 tff(10456,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s72) | always5(s72) | (~until6(s72)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s72) | always5(s72) | (~until6(s72)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10457,plain,
% 36.13/23.98 ((always5(s72) | (~until6(s72)) | xuntil7(s72)) <=> (xuntil7(s72) | always5(s72) | (~until6(s72)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10458,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s72) | (~until6(s72)) | xuntil7(s72))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s72) | always5(s72) | (~until6(s72))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10457])).
% 36.13/23.98 tff(10459,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s72) | (~until6(s72)) | xuntil7(s72))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s72) | always5(s72) | (~until6(s72)))),
% 36.13/23.98 inference(transitivity,[status(thm)],[10458, 10456])).
% 36.13/23.98 tff(10460,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s72) | (~until6(s72)) | xuntil7(s72))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10461,plain,
% 36.13/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s72) | always5(s72) | (~until6(s72))),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10460, 10459])).
% 36.13/23.98 tff(10462,plain,
% 36.13/23.98 (xuntil7(s72) | (~until6(s72))),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10461, 9395, 9010])).
% 36.13/23.98 tff(10463,plain,
% 36.13/23.98 (xuntil7(s72)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10462, 10455])).
% 36.13/23.98 tff(10464,plain,
% 36.13/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s72, s73)) | (~xuntil7(s72)) | until6(s73))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s72, s73)) | (~xuntil7(s72)) | until6(s73))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10465,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s72, s73)) | (~xuntil7(s72)) | until6(s73))),
% 36.13/23.98 inference(quant_inst,[status(thm)],[])).
% 36.13/23.98 tff(10466,plain,
% 36.13/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s72, s73)) | (~xuntil7(s72)) | until6(s73)),
% 36.13/23.98 inference(modus_ponens,[status(thm)],[10465, 10464])).
% 36.13/23.98 tff(10467,plain,
% 36.13/23.98 ((~xuntil7(s72)) | until6(s73)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10466, 2238, 9413])).
% 36.13/23.98 tff(10468,plain,
% 36.13/23.98 (until6(s73)),
% 36.13/23.98 inference(unit_resolution,[status(thm)],[10467, 10463])).
% 36.13/23.98 tff(10469,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s73) | always5(s73) | (~until6(s73)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s73) | always5(s73) | (~until6(s73)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10470,plain,
% 36.13/23.98 ((always5(s73) | (~until6(s73)) | xuntil7(s73)) <=> (xuntil7(s73) | always5(s73) | (~until6(s73)))),
% 36.13/23.98 inference(rewrite,[status(thm)],[])).
% 36.13/23.98 tff(10471,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s73) | (~until6(s73)) | xuntil7(s73))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s73) | always5(s73) | (~until6(s73))))),
% 36.13/23.98 inference(monotonicity,[status(thm)],[10470])).
% 36.13/23.98 tff(10472,plain,
% 36.13/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s73) | (~until6(s73)) | xuntil7(s73))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s73) | always5(s73) | (~until6(s73)))),
% 36.18/23.98 inference(transitivity,[status(thm)],[10471, 10469])).
% 36.18/23.98 tff(10473,plain,
% 36.18/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s73) | (~until6(s73)) | xuntil7(s73))),
% 36.18/23.98 inference(quant_inst,[status(thm)],[])).
% 36.18/23.98 tff(10474,plain,
% 36.18/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s73) | always5(s73) | (~until6(s73))),
% 36.18/23.98 inference(modus_ponens,[status(thm)],[10473, 10472])).
% 36.18/23.98 tff(10475,plain,
% 36.18/23.98 (xuntil7(s73) | (~until6(s73))),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10474, 9395, 9009])).
% 36.18/23.98 tff(10476,plain,
% 36.18/23.98 (xuntil7(s73)),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10475, 10468])).
% 36.18/23.98 tff(10477,plain,
% 36.18/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s73, s74)) | (~xuntil7(s73)) | until6(s74))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s73, s74)) | (~xuntil7(s73)) | until6(s74))),
% 36.18/23.98 inference(rewrite,[status(thm)],[])).
% 36.18/23.98 tff(10478,plain,
% 36.18/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s73, s74)) | (~xuntil7(s73)) | until6(s74))),
% 36.18/23.98 inference(quant_inst,[status(thm)],[])).
% 36.18/23.98 tff(10479,plain,
% 36.18/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s73, s74)) | (~xuntil7(s73)) | until6(s74)),
% 36.18/23.98 inference(modus_ponens,[status(thm)],[10478, 10477])).
% 36.18/23.98 tff(10480,plain,
% 36.18/23.98 ((~xuntil7(s73)) | until6(s74)),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10479, 2266, 9413])).
% 36.18/23.98 tff(10481,plain,
% 36.18/23.98 (until6(s74)),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10480, 10476])).
% 36.18/23.98 tff(10482,plain,
% 36.18/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s74) | always5(s74) | (~until6(s74)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s74) | always5(s74) | (~until6(s74)))),
% 36.18/23.98 inference(rewrite,[status(thm)],[])).
% 36.18/23.98 tff(10483,plain,
% 36.18/23.98 ((always5(s74) | (~until6(s74)) | xuntil7(s74)) <=> (xuntil7(s74) | always5(s74) | (~until6(s74)))),
% 36.18/23.98 inference(rewrite,[status(thm)],[])).
% 36.18/23.98 tff(10484,plain,
% 36.18/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s74) | (~until6(s74)) | xuntil7(s74))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s74) | always5(s74) | (~until6(s74))))),
% 36.18/23.98 inference(monotonicity,[status(thm)],[10483])).
% 36.18/23.98 tff(10485,plain,
% 36.18/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s74) | (~until6(s74)) | xuntil7(s74))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s74) | always5(s74) | (~until6(s74)))),
% 36.18/23.98 inference(transitivity,[status(thm)],[10484, 10482])).
% 36.18/23.98 tff(10486,plain,
% 36.18/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s74) | (~until6(s74)) | xuntil7(s74))),
% 36.18/23.98 inference(quant_inst,[status(thm)],[])).
% 36.18/23.98 tff(10487,plain,
% 36.18/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s74) | always5(s74) | (~until6(s74))),
% 36.18/23.98 inference(modus_ponens,[status(thm)],[10486, 10485])).
% 36.18/23.98 tff(10488,plain,
% 36.18/23.98 (xuntil7(s74) | (~until6(s74))),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10487, 9395, 9008])).
% 36.18/23.98 tff(10489,plain,
% 36.18/23.98 (xuntil7(s74)),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10488, 10481])).
% 36.18/23.98 tff(10490,plain,
% 36.18/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s74, s75)) | (~xuntil7(s74)) | until6(s75))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s74, s75)) | (~xuntil7(s74)) | until6(s75))),
% 36.18/23.98 inference(rewrite,[status(thm)],[])).
% 36.18/23.98 tff(10491,plain,
% 36.18/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s74, s75)) | (~xuntil7(s74)) | until6(s75))),
% 36.18/23.98 inference(quant_inst,[status(thm)],[])).
% 36.18/23.98 tff(10492,plain,
% 36.18/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s74, s75)) | (~xuntil7(s74)) | until6(s75)),
% 36.18/23.98 inference(modus_ponens,[status(thm)],[10491, 10490])).
% 36.18/23.98 tff(10493,plain,
% 36.18/23.98 ((~xuntil7(s74)) | until6(s75)),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10492, 2297, 9413])).
% 36.18/23.98 tff(10494,plain,
% 36.18/23.98 (until6(s75)),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10493, 10489])).
% 36.18/23.98 tff(10495,plain,
% 36.18/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s75) | always5(s75) | (~until6(s75)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s75) | always5(s75) | (~until6(s75)))),
% 36.18/23.98 inference(rewrite,[status(thm)],[])).
% 36.18/23.98 tff(10496,plain,
% 36.18/23.98 ((always5(s75) | (~until6(s75)) | xuntil7(s75)) <=> (xuntil7(s75) | always5(s75) | (~until6(s75)))),
% 36.18/23.98 inference(rewrite,[status(thm)],[])).
% 36.18/23.98 tff(10497,plain,
% 36.18/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s75) | (~until6(s75)) | xuntil7(s75))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s75) | always5(s75) | (~until6(s75))))),
% 36.18/23.98 inference(monotonicity,[status(thm)],[10496])).
% 36.18/23.98 tff(10498,plain,
% 36.18/23.98 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s75) | (~until6(s75)) | xuntil7(s75))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s75) | always5(s75) | (~until6(s75)))),
% 36.18/23.98 inference(transitivity,[status(thm)],[10497, 10495])).
% 36.18/23.98 tff(10499,plain,
% 36.18/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s75) | (~until6(s75)) | xuntil7(s75))),
% 36.18/23.98 inference(quant_inst,[status(thm)],[])).
% 36.18/23.98 tff(10500,plain,
% 36.18/23.98 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s75) | always5(s75) | (~until6(s75))),
% 36.18/23.98 inference(modus_ponens,[status(thm)],[10499, 10498])).
% 36.18/23.98 tff(10501,plain,
% 36.18/23.98 (xuntil7(s75) | (~until6(s75))),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10500, 9395, 9007])).
% 36.18/23.98 tff(10502,plain,
% 36.18/23.98 (xuntil7(s75)),
% 36.18/23.98 inference(unit_resolution,[status(thm)],[10501, 10494])).
% 36.18/23.98 tff(10503,plain,
% 36.18/23.98 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s75, s76)) | (~xuntil7(s75)) | until6(s76))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s75, s76)) | (~xuntil7(s75)) | until6(s76))),
% 36.18/23.98 inference(rewrite,[status(thm)],[])).
% 36.18/23.98 tff(10504,plain,
% 36.18/23.98 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s75, s76)) | (~xuntil7(s75)) | until6(s76))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10505,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s75, s76)) | (~xuntil7(s75)) | until6(s76)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10504, 10503])).
% 36.18/23.99 tff(10506,plain,
% 36.18/23.99 ((~xuntil7(s75)) | until6(s76)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10505, 2325, 9413])).
% 36.18/23.99 tff(10507,plain,
% 36.18/23.99 (until6(s76)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10506, 10502])).
% 36.18/23.99 tff(10508,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s76) | always5(s76) | (~until6(s76)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s76) | always5(s76) | (~until6(s76)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10509,plain,
% 36.18/23.99 ((always5(s76) | (~until6(s76)) | xuntil7(s76)) <=> (xuntil7(s76) | always5(s76) | (~until6(s76)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10510,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s76) | (~until6(s76)) | xuntil7(s76))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s76) | always5(s76) | (~until6(s76))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10509])).
% 36.18/23.99 tff(10511,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s76) | (~until6(s76)) | xuntil7(s76))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s76) | always5(s76) | (~until6(s76)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10510, 10508])).
% 36.18/23.99 tff(10512,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s76) | (~until6(s76)) | xuntil7(s76))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10513,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s76) | always5(s76) | (~until6(s76))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10512, 10511])).
% 36.18/23.99 tff(10514,plain,
% 36.18/23.99 (xuntil7(s76) | (~until6(s76))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10513, 9395, 9006])).
% 36.18/23.99 tff(10515,plain,
% 36.18/23.99 (xuntil7(s76)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10514, 10507])).
% 36.18/23.99 tff(10516,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s76, s77)) | (~xuntil7(s76)) | until6(s77))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s76, s77)) | (~xuntil7(s76)) | until6(s77))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10517,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s76, s77)) | (~xuntil7(s76)) | until6(s77))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10518,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s76, s77)) | (~xuntil7(s76)) | until6(s77)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10517, 10516])).
% 36.18/23.99 tff(10519,plain,
% 36.18/23.99 ((~xuntil7(s76)) | until6(s77)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10518, 2356, 9413])).
% 36.18/23.99 tff(10520,plain,
% 36.18/23.99 (until6(s77)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10519, 10515])).
% 36.18/23.99 tff(10521,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s77) | always5(s77) | (~until6(s77)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s77) | always5(s77) | (~until6(s77)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10522,plain,
% 36.18/23.99 ((always5(s77) | (~until6(s77)) | xuntil7(s77)) <=> (xuntil7(s77) | always5(s77) | (~until6(s77)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10523,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s77) | (~until6(s77)) | xuntil7(s77))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s77) | always5(s77) | (~until6(s77))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10522])).
% 36.18/23.99 tff(10524,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s77) | (~until6(s77)) | xuntil7(s77))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s77) | always5(s77) | (~until6(s77)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10523, 10521])).
% 36.18/23.99 tff(10525,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s77) | (~until6(s77)) | xuntil7(s77))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10526,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s77) | always5(s77) | (~until6(s77))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10525, 10524])).
% 36.18/23.99 tff(10527,plain,
% 36.18/23.99 (xuntil7(s77) | (~until6(s77))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10526, 9395, 9005])).
% 36.18/23.99 tff(10528,plain,
% 36.18/23.99 (xuntil7(s77)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10527, 10520])).
% 36.18/23.99 tff(10529,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s77, s78)) | (~xuntil7(s77)) | until6(s78))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s77, s78)) | (~xuntil7(s77)) | until6(s78))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10530,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s77, s78)) | (~xuntil7(s77)) | until6(s78))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10531,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s77, s78)) | (~xuntil7(s77)) | until6(s78)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10530, 10529])).
% 36.18/23.99 tff(10532,plain,
% 36.18/23.99 ((~xuntil7(s77)) | until6(s78)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10531, 2384, 9413])).
% 36.18/23.99 tff(10533,plain,
% 36.18/23.99 (until6(s78)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10532, 10528])).
% 36.18/23.99 tff(10534,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s78) | always5(s78) | (~until6(s78)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s78) | always5(s78) | (~until6(s78)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10535,plain,
% 36.18/23.99 ((always5(s78) | (~until6(s78)) | xuntil7(s78)) <=> (xuntil7(s78) | always5(s78) | (~until6(s78)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10536,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s78) | (~until6(s78)) | xuntil7(s78))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s78) | always5(s78) | (~until6(s78))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10535])).
% 36.18/23.99 tff(10537,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s78) | (~until6(s78)) | xuntil7(s78))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s78) | always5(s78) | (~until6(s78)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10536, 10534])).
% 36.18/23.99 tff(10538,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s78) | (~until6(s78)) | xuntil7(s78))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10539,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s78) | always5(s78) | (~until6(s78))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10538, 10537])).
% 36.18/23.99 tff(10540,plain,
% 36.18/23.99 (xuntil7(s78) | (~until6(s78))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10539, 9395, 9004])).
% 36.18/23.99 tff(10541,plain,
% 36.18/23.99 (xuntil7(s78)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10540, 10533])).
% 36.18/23.99 tff(10542,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s78, s79)) | (~xuntil7(s78)) | until6(s79))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s78, s79)) | (~xuntil7(s78)) | until6(s79))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10543,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s78, s79)) | (~xuntil7(s78)) | until6(s79))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10544,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s78, s79)) | (~xuntil7(s78)) | until6(s79)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10543, 10542])).
% 36.18/23.99 tff(10545,plain,
% 36.18/23.99 ((~xuntil7(s78)) | until6(s79)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10544, 2415, 9413])).
% 36.18/23.99 tff(10546,plain,
% 36.18/23.99 (until6(s79)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10545, 10541])).
% 36.18/23.99 tff(10547,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s79) | always5(s79) | (~until6(s79)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s79) | always5(s79) | (~until6(s79)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10548,plain,
% 36.18/23.99 ((always5(s79) | (~until6(s79)) | xuntil7(s79)) <=> (xuntil7(s79) | always5(s79) | (~until6(s79)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10549,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s79) | (~until6(s79)) | xuntil7(s79))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s79) | always5(s79) | (~until6(s79))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10548])).
% 36.18/23.99 tff(10550,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s79) | (~until6(s79)) | xuntil7(s79))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s79) | always5(s79) | (~until6(s79)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10549, 10547])).
% 36.18/23.99 tff(10551,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s79) | (~until6(s79)) | xuntil7(s79))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10552,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s79) | always5(s79) | (~until6(s79))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10551, 10550])).
% 36.18/23.99 tff(10553,plain,
% 36.18/23.99 (xuntil7(s79) | (~until6(s79))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10552, 9395, 9003])).
% 36.18/23.99 tff(10554,plain,
% 36.18/23.99 (xuntil7(s79)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10553, 10546])).
% 36.18/23.99 tff(10555,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s79, s80)) | (~xuntil7(s79)) | until6(s80))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s79, s80)) | (~xuntil7(s79)) | until6(s80))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10556,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s79, s80)) | (~xuntil7(s79)) | until6(s80))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10557,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s79, s80)) | (~xuntil7(s79)) | until6(s80)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10556, 10555])).
% 36.18/23.99 tff(10558,plain,
% 36.18/23.99 ((~xuntil7(s79)) | until6(s80)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10557, 2443, 9413])).
% 36.18/23.99 tff(10559,plain,
% 36.18/23.99 (until6(s80)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10558, 10554])).
% 36.18/23.99 tff(10560,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s80) | always5(s80) | (~until6(s80)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s80) | always5(s80) | (~until6(s80)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10561,plain,
% 36.18/23.99 ((always5(s80) | (~until6(s80)) | xuntil7(s80)) <=> (xuntil7(s80) | always5(s80) | (~until6(s80)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10562,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s80) | (~until6(s80)) | xuntil7(s80))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s80) | always5(s80) | (~until6(s80))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10561])).
% 36.18/23.99 tff(10563,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s80) | (~until6(s80)) | xuntil7(s80))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s80) | always5(s80) | (~until6(s80)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10562, 10560])).
% 36.18/23.99 tff(10564,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s80) | (~until6(s80)) | xuntil7(s80))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10565,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s80) | always5(s80) | (~until6(s80))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10564, 10563])).
% 36.18/23.99 tff(10566,plain,
% 36.18/23.99 (xuntil7(s80) | (~until6(s80))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10565, 9395, 9002])).
% 36.18/23.99 tff(10567,plain,
% 36.18/23.99 (xuntil7(s80)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10566, 10559])).
% 36.18/23.99 tff(10568,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s80, s81)) | (~xuntil7(s80)) | until6(s81))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s80, s81)) | (~xuntil7(s80)) | until6(s81))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10569,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s80, s81)) | (~xuntil7(s80)) | until6(s81))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10570,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s80, s81)) | (~xuntil7(s80)) | until6(s81)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10569, 10568])).
% 36.18/23.99 tff(10571,plain,
% 36.18/23.99 ((~xuntil7(s80)) | until6(s81)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10570, 2474, 9413])).
% 36.18/23.99 tff(10572,plain,
% 36.18/23.99 (until6(s81)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10571, 10567])).
% 36.18/23.99 tff(10573,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s81) | always5(s81) | (~until6(s81)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s81) | always5(s81) | (~until6(s81)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10574,plain,
% 36.18/23.99 ((always5(s81) | (~until6(s81)) | xuntil7(s81)) <=> (xuntil7(s81) | always5(s81) | (~until6(s81)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10575,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s81) | (~until6(s81)) | xuntil7(s81))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s81) | always5(s81) | (~until6(s81))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10574])).
% 36.18/23.99 tff(10576,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s81) | (~until6(s81)) | xuntil7(s81))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s81) | always5(s81) | (~until6(s81)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10575, 10573])).
% 36.18/23.99 tff(10577,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s81) | (~until6(s81)) | xuntil7(s81))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10578,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s81) | always5(s81) | (~until6(s81))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10577, 10576])).
% 36.18/23.99 tff(10579,plain,
% 36.18/23.99 (xuntil7(s81) | (~until6(s81))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10578, 9395, 9001])).
% 36.18/23.99 tff(10580,plain,
% 36.18/23.99 (xuntil7(s81)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10579, 10572])).
% 36.18/23.99 tff(10581,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s81, s82)) | (~xuntil7(s81)) | until6(s82))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s81, s82)) | (~xuntil7(s81)) | until6(s82))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10582,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s81, s82)) | (~xuntil7(s81)) | until6(s82))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10583,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s81, s82)) | (~xuntil7(s81)) | until6(s82)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10582, 10581])).
% 36.18/23.99 tff(10584,plain,
% 36.18/23.99 ((~xuntil7(s81)) | until6(s82)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10583, 2502, 9413])).
% 36.18/23.99 tff(10585,plain,
% 36.18/23.99 (until6(s82)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10584, 10580])).
% 36.18/23.99 tff(10586,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s82) | always5(s82) | (~until6(s82)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s82) | always5(s82) | (~until6(s82)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10587,plain,
% 36.18/23.99 ((always5(s82) | (~until6(s82)) | xuntil7(s82)) <=> (xuntil7(s82) | always5(s82) | (~until6(s82)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10588,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s82) | (~until6(s82)) | xuntil7(s82))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s82) | always5(s82) | (~until6(s82))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10587])).
% 36.18/23.99 tff(10589,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s82) | (~until6(s82)) | xuntil7(s82))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s82) | always5(s82) | (~until6(s82)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10588, 10586])).
% 36.18/23.99 tff(10590,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s82) | (~until6(s82)) | xuntil7(s82))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10591,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s82) | always5(s82) | (~until6(s82))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10590, 10589])).
% 36.18/23.99 tff(10592,plain,
% 36.18/23.99 (xuntil7(s82) | (~until6(s82))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10591, 9395, 9000])).
% 36.18/23.99 tff(10593,plain,
% 36.18/23.99 (xuntil7(s82)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10592, 10585])).
% 36.18/23.99 tff(10594,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s82, s83)) | (~xuntil7(s82)) | until6(s83))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s82, s83)) | (~xuntil7(s82)) | until6(s83))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10595,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s82, s83)) | (~xuntil7(s82)) | until6(s83))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10596,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s82, s83)) | (~xuntil7(s82)) | until6(s83)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10595, 10594])).
% 36.18/23.99 tff(10597,plain,
% 36.18/23.99 ((~xuntil7(s82)) | until6(s83)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10596, 2533, 9413])).
% 36.18/23.99 tff(10598,plain,
% 36.18/23.99 (until6(s83)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10597, 10593])).
% 36.18/23.99 tff(10599,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s83) | always5(s83) | (~until6(s83)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s83) | always5(s83) | (~until6(s83)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10600,plain,
% 36.18/23.99 ((always5(s83) | (~until6(s83)) | xuntil7(s83)) <=> (xuntil7(s83) | always5(s83) | (~until6(s83)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10601,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s83) | (~until6(s83)) | xuntil7(s83))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s83) | always5(s83) | (~until6(s83))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10600])).
% 36.18/23.99 tff(10602,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s83) | (~until6(s83)) | xuntil7(s83))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s83) | always5(s83) | (~until6(s83)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10601, 10599])).
% 36.18/23.99 tff(10603,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s83) | (~until6(s83)) | xuntil7(s83))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10604,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s83) | always5(s83) | (~until6(s83))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10603, 10602])).
% 36.18/23.99 tff(10605,plain,
% 36.18/23.99 (xuntil7(s83) | (~until6(s83))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10604, 9395, 8999])).
% 36.18/23.99 tff(10606,plain,
% 36.18/23.99 (xuntil7(s83)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10605, 10598])).
% 36.18/23.99 tff(10607,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s83, s84)) | (~xuntil7(s83)) | until6(s84))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s83, s84)) | (~xuntil7(s83)) | until6(s84))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10608,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s83, s84)) | (~xuntil7(s83)) | until6(s84))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10609,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s83, s84)) | (~xuntil7(s83)) | until6(s84)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10608, 10607])).
% 36.18/23.99 tff(10610,plain,
% 36.18/23.99 ((~xuntil7(s83)) | until6(s84)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10609, 2561, 9413])).
% 36.18/23.99 tff(10611,plain,
% 36.18/23.99 (until6(s84)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10610, 10606])).
% 36.18/23.99 tff(10612,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s84) | always5(s84) | (~until6(s84)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s84) | always5(s84) | (~until6(s84)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10613,plain,
% 36.18/23.99 ((always5(s84) | (~until6(s84)) | xuntil7(s84)) <=> (xuntil7(s84) | always5(s84) | (~until6(s84)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10614,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s84) | (~until6(s84)) | xuntil7(s84))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s84) | always5(s84) | (~until6(s84))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10613])).
% 36.18/23.99 tff(10615,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s84) | (~until6(s84)) | xuntil7(s84))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s84) | always5(s84) | (~until6(s84)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10614, 10612])).
% 36.18/23.99 tff(10616,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s84) | (~until6(s84)) | xuntil7(s84))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10617,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s84) | always5(s84) | (~until6(s84))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10616, 10615])).
% 36.18/23.99 tff(10618,plain,
% 36.18/23.99 (xuntil7(s84) | (~until6(s84))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10617, 9395, 8998])).
% 36.18/23.99 tff(10619,plain,
% 36.18/23.99 (xuntil7(s84)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10618, 10611])).
% 36.18/23.99 tff(10620,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s84, s85)) | (~xuntil7(s84)) | until6(s85))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s84, s85)) | (~xuntil7(s84)) | until6(s85))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10621,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s84, s85)) | (~xuntil7(s84)) | until6(s85))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10622,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s84, s85)) | (~xuntil7(s84)) | until6(s85)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10621, 10620])).
% 36.18/23.99 tff(10623,plain,
% 36.18/23.99 ((~xuntil7(s84)) | until6(s85)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10622, 2592, 9413])).
% 36.18/23.99 tff(10624,plain,
% 36.18/23.99 (until6(s85)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10623, 10619])).
% 36.18/23.99 tff(10625,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s85) | always5(s85) | (~until6(s85)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s85) | always5(s85) | (~until6(s85)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10626,plain,
% 36.18/23.99 ((always5(s85) | (~until6(s85)) | xuntil7(s85)) <=> (xuntil7(s85) | always5(s85) | (~until6(s85)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10627,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s85) | (~until6(s85)) | xuntil7(s85))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s85) | always5(s85) | (~until6(s85))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10626])).
% 36.18/23.99 tff(10628,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s85) | (~until6(s85)) | xuntil7(s85))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s85) | always5(s85) | (~until6(s85)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10627, 10625])).
% 36.18/23.99 tff(10629,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s85) | (~until6(s85)) | xuntil7(s85))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10630,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s85) | always5(s85) | (~until6(s85))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10629, 10628])).
% 36.18/23.99 tff(10631,plain,
% 36.18/23.99 (xuntil7(s85) | (~until6(s85))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10630, 9395, 8997])).
% 36.18/23.99 tff(10632,plain,
% 36.18/23.99 (xuntil7(s85)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10631, 10624])).
% 36.18/23.99 tff(10633,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s85, s86)) | (~xuntil7(s85)) | until6(s86))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s85, s86)) | (~xuntil7(s85)) | until6(s86))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10634,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s85, s86)) | (~xuntil7(s85)) | until6(s86))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10635,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s85, s86)) | (~xuntil7(s85)) | until6(s86)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10634, 10633])).
% 36.18/23.99 tff(10636,plain,
% 36.18/23.99 ((~xuntil7(s85)) | until6(s86)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10635, 2620, 9413])).
% 36.18/23.99 tff(10637,plain,
% 36.18/23.99 (until6(s86)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10636, 10632])).
% 36.18/23.99 tff(10638,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s86) | always5(s86) | (~until6(s86)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s86) | always5(s86) | (~until6(s86)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10639,plain,
% 36.18/23.99 ((always5(s86) | (~until6(s86)) | xuntil7(s86)) <=> (xuntil7(s86) | always5(s86) | (~until6(s86)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10640,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s86) | (~until6(s86)) | xuntil7(s86))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s86) | always5(s86) | (~until6(s86))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10639])).
% 36.18/23.99 tff(10641,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s86) | (~until6(s86)) | xuntil7(s86))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s86) | always5(s86) | (~until6(s86)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10640, 10638])).
% 36.18/23.99 tff(10642,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s86) | (~until6(s86)) | xuntil7(s86))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10643,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s86) | always5(s86) | (~until6(s86))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10642, 10641])).
% 36.18/23.99 tff(10644,plain,
% 36.18/23.99 (xuntil7(s86) | (~until6(s86))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10643, 9395, 8996])).
% 36.18/23.99 tff(10645,plain,
% 36.18/23.99 (xuntil7(s86)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10644, 10637])).
% 36.18/23.99 tff(10646,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s86, s87)) | (~xuntil7(s86)) | until6(s87))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s86, s87)) | (~xuntil7(s86)) | until6(s87))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10647,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s86, s87)) | (~xuntil7(s86)) | until6(s87))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10648,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s86, s87)) | (~xuntil7(s86)) | until6(s87)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10647, 10646])).
% 36.18/23.99 tff(10649,plain,
% 36.18/23.99 ((~xuntil7(s86)) | until6(s87)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10648, 2651, 9413])).
% 36.18/23.99 tff(10650,plain,
% 36.18/23.99 (until6(s87)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10649, 10645])).
% 36.18/23.99 tff(10651,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s87) | always5(s87) | (~until6(s87)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s87) | always5(s87) | (~until6(s87)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10652,plain,
% 36.18/23.99 ((always5(s87) | (~until6(s87)) | xuntil7(s87)) <=> (xuntil7(s87) | always5(s87) | (~until6(s87)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10653,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s87) | (~until6(s87)) | xuntil7(s87))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s87) | always5(s87) | (~until6(s87))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10652])).
% 36.18/23.99 tff(10654,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s87) | (~until6(s87)) | xuntil7(s87))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s87) | always5(s87) | (~until6(s87)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10653, 10651])).
% 36.18/23.99 tff(10655,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s87) | (~until6(s87)) | xuntil7(s87))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10656,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s87) | always5(s87) | (~until6(s87))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10655, 10654])).
% 36.18/23.99 tff(10657,plain,
% 36.18/23.99 (xuntil7(s87) | (~until6(s87))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10656, 9395, 8995])).
% 36.18/23.99 tff(10658,plain,
% 36.18/23.99 (xuntil7(s87)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10657, 10650])).
% 36.18/23.99 tff(10659,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s87, s88)) | (~xuntil7(s87)) | until6(s88))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s87, s88)) | (~xuntil7(s87)) | until6(s88))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10660,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s87, s88)) | (~xuntil7(s87)) | until6(s88))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10661,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s87, s88)) | (~xuntil7(s87)) | until6(s88)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10660, 10659])).
% 36.18/23.99 tff(10662,plain,
% 36.18/23.99 ((~xuntil7(s87)) | until6(s88)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10661, 2679, 9413])).
% 36.18/23.99 tff(10663,plain,
% 36.18/23.99 (until6(s88)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10662, 10658])).
% 36.18/23.99 tff(10664,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s88) | always5(s88) | (~until6(s88)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s88) | always5(s88) | (~until6(s88)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10665,plain,
% 36.18/23.99 ((always5(s88) | (~until6(s88)) | xuntil7(s88)) <=> (xuntil7(s88) | always5(s88) | (~until6(s88)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10666,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s88) | (~until6(s88)) | xuntil7(s88))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s88) | always5(s88) | (~until6(s88))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10665])).
% 36.18/23.99 tff(10667,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s88) | (~until6(s88)) | xuntil7(s88))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s88) | always5(s88) | (~until6(s88)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10666, 10664])).
% 36.18/23.99 tff(10668,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s88) | (~until6(s88)) | xuntil7(s88))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10669,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s88) | always5(s88) | (~until6(s88))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10668, 10667])).
% 36.18/23.99 tff(10670,plain,
% 36.18/23.99 (xuntil7(s88) | (~until6(s88))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10669, 9395, 8994])).
% 36.18/23.99 tff(10671,plain,
% 36.18/23.99 (xuntil7(s88)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10670, 10663])).
% 36.18/23.99 tff(10672,plain,
% 36.18/23.99 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s88, s89)) | (~xuntil7(s88)) | until6(s89))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s88, s89)) | (~xuntil7(s88)) | until6(s89))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10673,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s88, s89)) | (~xuntil7(s88)) | until6(s89))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10674,plain,
% 36.18/23.99 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s88, s89)) | (~xuntil7(s88)) | until6(s89)),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10673, 10672])).
% 36.18/23.99 tff(10675,plain,
% 36.18/23.99 ((~xuntil7(s88)) | until6(s89)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10674, 2710, 9413])).
% 36.18/23.99 tff(10676,plain,
% 36.18/23.99 (until6(s89)),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10675, 10671])).
% 36.18/23.99 tff(10677,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s89) | always5(s89) | (~until6(s89)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s89) | always5(s89) | (~until6(s89)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10678,plain,
% 36.18/23.99 ((always5(s89) | (~until6(s89)) | xuntil7(s89)) <=> (xuntil7(s89) | always5(s89) | (~until6(s89)))),
% 36.18/23.99 inference(rewrite,[status(thm)],[])).
% 36.18/23.99 tff(10679,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s89) | (~until6(s89)) | xuntil7(s89))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s89) | always5(s89) | (~until6(s89))))),
% 36.18/23.99 inference(monotonicity,[status(thm)],[10678])).
% 36.18/23.99 tff(10680,plain,
% 36.18/23.99 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s89) | (~until6(s89)) | xuntil7(s89))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s89) | always5(s89) | (~until6(s89)))),
% 36.18/23.99 inference(transitivity,[status(thm)],[10679, 10677])).
% 36.18/23.99 tff(10681,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s89) | (~until6(s89)) | xuntil7(s89))),
% 36.18/23.99 inference(quant_inst,[status(thm)],[])).
% 36.18/23.99 tff(10682,plain,
% 36.18/23.99 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s89) | always5(s89) | (~until6(s89))),
% 36.18/23.99 inference(modus_ponens,[status(thm)],[10681, 10680])).
% 36.18/23.99 tff(10683,plain,
% 36.18/23.99 (xuntil7(s89) | (~until6(s89))),
% 36.18/23.99 inference(unit_resolution,[status(thm)],[10682, 9395, 8993])).
% 36.18/24.00 tff(10684,plain,
% 36.18/24.00 (xuntil7(s89)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10683, 10676])).
% 36.18/24.00 tff(10685,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s89, s90)) | (~xuntil7(s89)) | until6(s90))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s89, s90)) | (~xuntil7(s89)) | until6(s90))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10686,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s89, s90)) | (~xuntil7(s89)) | until6(s90))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10687,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s89, s90)) | (~xuntil7(s89)) | until6(s90)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10686, 10685])).
% 36.18/24.00 tff(10688,plain,
% 36.18/24.00 ((~xuntil7(s89)) | until6(s90)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10687, 2738, 9413])).
% 36.18/24.00 tff(10689,plain,
% 36.18/24.00 (until6(s90)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10688, 10684])).
% 36.18/24.00 tff(10690,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s90) | always5(s90) | (~until6(s90)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s90) | always5(s90) | (~until6(s90)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10691,plain,
% 36.18/24.00 ((always5(s90) | (~until6(s90)) | xuntil7(s90)) <=> (xuntil7(s90) | always5(s90) | (~until6(s90)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10692,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s90) | (~until6(s90)) | xuntil7(s90))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s90) | always5(s90) | (~until6(s90))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10691])).
% 36.18/24.00 tff(10693,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s90) | (~until6(s90)) | xuntil7(s90))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s90) | always5(s90) | (~until6(s90)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10692, 10690])).
% 36.18/24.00 tff(10694,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s90) | (~until6(s90)) | xuntil7(s90))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10695,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s90) | always5(s90) | (~until6(s90))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10694, 10693])).
% 36.18/24.00 tff(10696,plain,
% 36.18/24.00 (xuntil7(s90) | (~until6(s90))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10695, 9395, 8992])).
% 36.18/24.00 tff(10697,plain,
% 36.18/24.00 (xuntil7(s90)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10696, 10689])).
% 36.18/24.00 tff(10698,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s90, s91)) | (~xuntil7(s90)) | until6(s91))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s90, s91)) | (~xuntil7(s90)) | until6(s91))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10699,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s90, s91)) | (~xuntil7(s90)) | until6(s91))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10700,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s90, s91)) | (~xuntil7(s90)) | until6(s91)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10699, 10698])).
% 36.18/24.00 tff(10701,plain,
% 36.18/24.00 ((~xuntil7(s90)) | until6(s91)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10700, 2767, 9413])).
% 36.18/24.00 tff(10702,plain,
% 36.18/24.00 (until6(s91)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10701, 10697])).
% 36.18/24.00 tff(10703,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s91) | always5(s91) | (~until6(s91)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s91) | always5(s91) | (~until6(s91)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10704,plain,
% 36.18/24.00 ((always5(s91) | (~until6(s91)) | xuntil7(s91)) <=> (xuntil7(s91) | always5(s91) | (~until6(s91)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10705,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s91) | (~until6(s91)) | xuntil7(s91))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s91) | always5(s91) | (~until6(s91))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10704])).
% 36.18/24.00 tff(10706,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s91) | (~until6(s91)) | xuntil7(s91))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s91) | always5(s91) | (~until6(s91)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10705, 10703])).
% 36.18/24.00 tff(10707,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s91) | (~until6(s91)) | xuntil7(s91))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10708,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s91) | always5(s91) | (~until6(s91))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10707, 10706])).
% 36.18/24.00 tff(10709,plain,
% 36.18/24.00 (xuntil7(s91) | (~until6(s91))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10708, 9395, 8991])).
% 36.18/24.00 tff(10710,plain,
% 36.18/24.00 (xuntil7(s91)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10709, 10702])).
% 36.18/24.00 tff(10711,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s91, s92)) | (~xuntil7(s91)) | until6(s92))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s91, s92)) | (~xuntil7(s91)) | until6(s92))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10712,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s91, s92)) | (~xuntil7(s91)) | until6(s92))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10713,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s91, s92)) | (~xuntil7(s91)) | until6(s92)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10712, 10711])).
% 36.18/24.00 tff(10714,plain,
% 36.18/24.00 ((~xuntil7(s91)) | until6(s92)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10713, 2793, 9413])).
% 36.18/24.00 tff(10715,plain,
% 36.18/24.00 (until6(s92)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10714, 10710])).
% 36.18/24.00 tff(10716,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s92) | always5(s92) | (~until6(s92)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s92) | always5(s92) | (~until6(s92)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10717,plain,
% 36.18/24.00 ((always5(s92) | (~until6(s92)) | xuntil7(s92)) <=> (xuntil7(s92) | always5(s92) | (~until6(s92)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10718,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s92) | (~until6(s92)) | xuntil7(s92))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s92) | always5(s92) | (~until6(s92))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10717])).
% 36.18/24.00 tff(10719,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s92) | (~until6(s92)) | xuntil7(s92))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s92) | always5(s92) | (~until6(s92)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10718, 10716])).
% 36.18/24.00 tff(10720,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s92) | (~until6(s92)) | xuntil7(s92))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10721,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s92) | always5(s92) | (~until6(s92))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10720, 10719])).
% 36.18/24.00 tff(10722,plain,
% 36.18/24.00 (xuntil7(s92) | (~until6(s92))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10721, 9395, 8990])).
% 36.18/24.00 tff(10723,plain,
% 36.18/24.00 (xuntil7(s92)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10722, 10715])).
% 36.18/24.00 tff(10724,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s92, s93)) | (~xuntil7(s92)) | until6(s93))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s92, s93)) | (~xuntil7(s92)) | until6(s93))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10725,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s92, s93)) | (~xuntil7(s92)) | until6(s93))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10726,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s92, s93)) | (~xuntil7(s92)) | until6(s93)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10725, 10724])).
% 36.18/24.00 tff(10727,plain,
% 36.18/24.00 ((~xuntil7(s92)) | until6(s93)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10726, 2824, 9413])).
% 36.18/24.00 tff(10728,plain,
% 36.18/24.00 (until6(s93)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10727, 10723])).
% 36.18/24.00 tff(10729,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s93) | always5(s93) | (~until6(s93)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s93) | always5(s93) | (~until6(s93)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10730,plain,
% 36.18/24.00 ((always5(s93) | (~until6(s93)) | xuntil7(s93)) <=> (xuntil7(s93) | always5(s93) | (~until6(s93)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10731,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s93) | (~until6(s93)) | xuntil7(s93))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s93) | always5(s93) | (~until6(s93))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10730])).
% 36.18/24.00 tff(10732,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s93) | (~until6(s93)) | xuntil7(s93))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s93) | always5(s93) | (~until6(s93)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10731, 10729])).
% 36.18/24.00 tff(10733,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s93) | (~until6(s93)) | xuntil7(s93))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10734,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s93) | always5(s93) | (~until6(s93))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10733, 10732])).
% 36.18/24.00 tff(10735,plain,
% 36.18/24.00 (xuntil7(s93) | (~until6(s93))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10734, 9395, 8989])).
% 36.18/24.00 tff(10736,plain,
% 36.18/24.00 (xuntil7(s93)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10735, 10728])).
% 36.18/24.00 tff(10737,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s93, s94)) | (~xuntil7(s93)) | until6(s94))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s93, s94)) | (~xuntil7(s93)) | until6(s94))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10738,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s93, s94)) | (~xuntil7(s93)) | until6(s94))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10739,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s93, s94)) | (~xuntil7(s93)) | until6(s94)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10738, 10737])).
% 36.18/24.00 tff(10740,plain,
% 36.18/24.00 ((~xuntil7(s93)) | until6(s94)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10739, 2852, 9413])).
% 36.18/24.00 tff(10741,plain,
% 36.18/24.00 (until6(s94)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10740, 10736])).
% 36.18/24.00 tff(10742,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s94) | always5(s94) | (~until6(s94)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s94) | always5(s94) | (~until6(s94)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10743,plain,
% 36.18/24.00 ((always5(s94) | (~until6(s94)) | xuntil7(s94)) <=> (xuntil7(s94) | always5(s94) | (~until6(s94)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10744,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s94) | (~until6(s94)) | xuntil7(s94))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s94) | always5(s94) | (~until6(s94))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10743])).
% 36.18/24.00 tff(10745,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s94) | (~until6(s94)) | xuntil7(s94))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s94) | always5(s94) | (~until6(s94)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10744, 10742])).
% 36.18/24.00 tff(10746,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s94) | (~until6(s94)) | xuntil7(s94))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10747,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s94) | always5(s94) | (~until6(s94))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10746, 10745])).
% 36.18/24.00 tff(10748,plain,
% 36.18/24.00 (xuntil7(s94) | (~until6(s94))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10747, 9395, 8988])).
% 36.18/24.00 tff(10749,plain,
% 36.18/24.00 (xuntil7(s94)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10748, 10741])).
% 36.18/24.00 tff(10750,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s94, s95)) | (~xuntil7(s94)) | until6(s95))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s94, s95)) | (~xuntil7(s94)) | until6(s95))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10751,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s94, s95)) | (~xuntil7(s94)) | until6(s95))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10752,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s94, s95)) | (~xuntil7(s94)) | until6(s95)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10751, 10750])).
% 36.18/24.00 tff(10753,plain,
% 36.18/24.00 ((~xuntil7(s94)) | until6(s95)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10752, 8238, 9413])).
% 36.18/24.00 tff(10754,plain,
% 36.18/24.00 (until6(s95)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10753, 10749])).
% 36.18/24.00 tff(10755,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s95) | always5(s95) | (~until6(s95)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s95) | always5(s95) | (~until6(s95)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10756,plain,
% 36.18/24.00 ((always5(s95) | (~until6(s95)) | xuntil7(s95)) <=> (xuntil7(s95) | always5(s95) | (~until6(s95)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10757,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s95) | (~until6(s95)) | xuntil7(s95))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s95) | always5(s95) | (~until6(s95))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10756])).
% 36.18/24.00 tff(10758,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s95) | (~until6(s95)) | xuntil7(s95))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s95) | always5(s95) | (~until6(s95)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10757, 10755])).
% 36.18/24.00 tff(10759,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s95) | (~until6(s95)) | xuntil7(s95))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10760,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s95) | always5(s95) | (~until6(s95))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10759, 10758])).
% 36.18/24.00 tff(10761,plain,
% 36.18/24.00 (xuntil7(s95) | (~until6(s95))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10760, 9395, 8987])).
% 36.18/24.00 tff(10762,plain,
% 36.18/24.00 (xuntil7(s95)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10761, 10754])).
% 36.18/24.00 tff(10763,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s95, s96)) | (~xuntil7(s95)) | until6(s96))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s95, s96)) | (~xuntil7(s95)) | until6(s96))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10764,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s95, s96)) | (~xuntil7(s95)) | until6(s96))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10765,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s95, s96)) | (~xuntil7(s95)) | until6(s96)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10764, 10763])).
% 36.18/24.00 tff(10766,plain,
% 36.18/24.00 ((~xuntil7(s95)) | until6(s96)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10765, 11, 9413])).
% 36.18/24.00 tff(10767,plain,
% 36.18/24.00 (until6(s96)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10766, 10762])).
% 36.18/24.00 tff(10768,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s96) | always5(s96) | (~until6(s96)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s96) | always5(s96) | (~until6(s96)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10769,plain,
% 36.18/24.00 ((always5(s96) | (~until6(s96)) | xuntil7(s96)) <=> (xuntil7(s96) | always5(s96) | (~until6(s96)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10770,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s96) | (~until6(s96)) | xuntil7(s96))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s96) | always5(s96) | (~until6(s96))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10769])).
% 36.18/24.00 tff(10771,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s96) | (~until6(s96)) | xuntil7(s96))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s96) | always5(s96) | (~until6(s96)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10770, 10768])).
% 36.18/24.00 tff(10772,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s96) | (~until6(s96)) | xuntil7(s96))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10773,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s96) | always5(s96) | (~until6(s96))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10772, 10771])).
% 36.18/24.00 tff(10774,plain,
% 36.18/24.00 (xuntil7(s96) | (~until6(s96))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10773, 9395, 8986])).
% 36.18/24.00 tff(10775,plain,
% 36.18/24.00 (xuntil7(s96)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10774, 10767])).
% 36.18/24.00 tff(10776,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s96, s97)) | (~xuntil7(s96)) | until6(s97))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s96, s97)) | (~xuntil7(s96)) | until6(s97))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10777,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s96, s97)) | (~xuntil7(s96)) | until6(s97))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10778,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s96, s97)) | (~xuntil7(s96)) | until6(s97)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10777, 10776])).
% 36.18/24.00 tff(10779,plain,
% 36.18/24.00 ((~xuntil7(s96)) | until6(s97)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10778, 36, 9413])).
% 36.18/24.00 tff(10780,plain,
% 36.18/24.00 (until6(s97)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10779, 10775])).
% 36.18/24.00 tff(10781,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s97) | always5(s97) | (~until6(s97)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s97) | always5(s97) | (~until6(s97)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10782,plain,
% 36.18/24.00 ((always5(s97) | (~until6(s97)) | xuntil7(s97)) <=> (xuntil7(s97) | always5(s97) | (~until6(s97)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10783,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s97) | (~until6(s97)) | xuntil7(s97))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s97) | always5(s97) | (~until6(s97))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10782])).
% 36.18/24.00 tff(10784,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s97) | (~until6(s97)) | xuntil7(s97))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s97) | always5(s97) | (~until6(s97)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10783, 10781])).
% 36.18/24.00 tff(10785,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s97) | (~until6(s97)) | xuntil7(s97))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10786,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s97) | always5(s97) | (~until6(s97))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10785, 10784])).
% 36.18/24.00 tff(10787,plain,
% 36.18/24.00 (xuntil7(s97) | (~until6(s97))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10786, 9395, 8985])).
% 36.18/24.00 tff(10788,plain,
% 36.18/24.00 (xuntil7(s97)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10787, 10780])).
% 36.18/24.00 tff(10789,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s97, s98)) | (~xuntil7(s97)) | until6(s98))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s97, s98)) | (~xuntil7(s97)) | until6(s98))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10790,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s97, s98)) | (~xuntil7(s97)) | until6(s98))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10791,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s97, s98)) | (~xuntil7(s97)) | until6(s98)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10790, 10789])).
% 36.18/24.00 tff(10792,plain,
% 36.18/24.00 ((~xuntil7(s97)) | until6(s98)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10791, 8561, 9413])).
% 36.18/24.00 tff(10793,plain,
% 36.18/24.00 (until6(s98)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10792, 10788])).
% 36.18/24.00 tff(10794,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s98) | always5(s98) | (~until6(s98)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s98) | always5(s98) | (~until6(s98)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10795,plain,
% 36.18/24.00 ((always5(s98) | (~until6(s98)) | xuntil7(s98)) <=> (xuntil7(s98) | always5(s98) | (~until6(s98)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10796,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s98) | (~until6(s98)) | xuntil7(s98))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (xuntil7(s98) | always5(s98) | (~until6(s98))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10795])).
% 36.18/24.00 tff(10797,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s98) | (~until6(s98)) | xuntil7(s98))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s98) | always5(s98) | (~until6(s98)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10796, 10794])).
% 36.18/24.00 tff(10798,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s98) | (~until6(s98)) | xuntil7(s98))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10799,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | xuntil7(s98) | always5(s98) | (~until6(s98))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10798, 10797])).
% 36.18/24.00 tff(10800,plain,
% 36.18/24.00 (xuntil7(s98) | (~until6(s98))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10799, 9395, 8977])).
% 36.18/24.00 tff(10801,plain,
% 36.18/24.00 (xuntil7(s98)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10800, 10793])).
% 36.18/24.00 tff(10802,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s98, s99)) | (~xuntil7(s98)) | until6(s99))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s98, s99)) | (~xuntil7(s98)) | until6(s99))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10803,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | ((~succ(s98, s99)) | (~xuntil7(s98)) | until6(s99))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10804,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | (~xuntil7(X)) | until6(Y))) | (~succ(s98, s99)) | (~xuntil7(s98)) | until6(s99)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10803, 10802])).
% 36.18/24.00 tff(10805,plain,
% 36.18/24.00 ((~xuntil7(s98)) | until6(s99)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10804, 8625, 9413])).
% 36.18/24.00 tff(10806,plain,
% 36.18/24.00 (until6(s99)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10805, 10801])).
% 36.18/24.00 tff(10807,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | xuntil7(s99) | (~until6(s99)))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s99) | xuntil7(s99) | (~until6(s99)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10808,plain,
% 36.18/24.00 ((always5(s99) | (~until6(s99)) | xuntil7(s99)) <=> (always5(s99) | xuntil7(s99) | (~until6(s99)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10809,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | (~until6(s99)) | xuntil7(s99))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | xuntil7(s99) | (~until6(s99))))),
% 36.18/24.00 inference(monotonicity,[status(thm)],[10808])).
% 36.18/24.00 tff(10810,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | (~until6(s99)) | xuntil7(s99))) <=> ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s99) | xuntil7(s99) | (~until6(s99)))),
% 36.18/24.00 inference(transitivity,[status(thm)],[10809, 10807])).
% 36.18/24.00 tff(10811,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | (always5(s99) | (~until6(s99)) | xuntil7(s99))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10812,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | (~until6(X)) | xuntil7(X))) | always5(s99) | xuntil7(s99) | (~until6(s99))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10811, 10810])).
% 36.18/24.00 tff(10813,plain,
% 36.18/24.00 (xuntil7(s99)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10812, 9395, 10806, 8969])).
% 36.18/24.00 tff(10814,plain,
% 36.18/24.00 (^[X: $i] : refl(((~last(X)) | (~xuntil2p9(X))) <=> ((~last(X)) | (~xuntil2p9(X))))),
% 36.18/24.00 inference(bind,[status(th)],[])).
% 36.18/24.00 tff(10815,plain,
% 36.18/24.00 (![X: $i] : ((~last(X)) | (~xuntil2p9(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(quant_intro,[status(thm)],[10814])).
% 36.18/24.00 tff(10816,plain,
% 36.18/24.00 (![X: $i] : ((~last(X)) | (~xuntil2p9(X))) <=> ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10817,axiom,(![X: $i] : ((~last(X)) | (~xuntil2p9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty10')).
% 36.18/24.00 tff(10818,plain,
% 36.18/24.00 (![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10817, 10816])).
% 36.18/24.00 tff(10819,plain,(
% 36.18/24.00 ![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(skolemize,[status(sab)],[10818])).
% 36.18/24.00 tff(10820,plain,
% 36.18/24.00 (![X: $i] : ((~last(X)) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10819, 10815])).
% 36.18/24.00 tff(10821,plain,
% 36.18/24.00 (last(s99) <=> last(s99)),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10822,axiom,(last(s99)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound100')).
% 36.18/24.00 tff(10823,plain,
% 36.18/24.00 (last(s99)),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10822, 10821])).
% 36.18/24.00 tff(10824,plain,
% 36.18/24.00 (((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | ((~last(s99)) | (~xuntil2p9(s99)))) <=> ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | (~last(s99)) | (~xuntil2p9(s99)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10825,plain,
% 36.18/24.00 ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | ((~last(s99)) | (~xuntil2p9(s99)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10826,plain,
% 36.18/24.00 ((~![X: $i] : ((~last(X)) | (~xuntil2p9(X)))) | (~last(s99)) | (~xuntil2p9(s99))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10825, 10824])).
% 36.18/24.00 tff(10827,plain,
% 36.18/24.00 (~xuntil2p9(s99)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10826, 10823, 10820])).
% 36.18/24.00 tff(10828,plain,
% 36.18/24.00 (^[X: $i] : refl((always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> (always5(X) | xuntil2p9(X) | (~until2p8(X))))),
% 36.18/24.00 inference(bind,[status(th)],[])).
% 36.18/24.00 tff(10829,plain,
% 36.18/24.00 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 36.18/24.00 inference(quant_intro,[status(thm)],[10828])).
% 36.18/24.00 tff(10830,plain,
% 36.18/24.00 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10831,plain,
% 36.18/24.00 (^[X: $i] : rewrite(((always5(X) | xuntil2p9(X)) | (~until2p8(X))) <=> (always5(X) | xuntil2p9(X) | (~until2p8(X))))),
% 36.18/24.00 inference(bind,[status(th)],[])).
% 36.18/24.00 tff(10832,plain,
% 36.18/24.00 (![X: $i] : ((always5(X) | xuntil2p9(X)) | (~until2p8(X))) <=> ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 36.18/24.00 inference(quant_intro,[status(thm)],[10831])).
% 36.18/24.00 tff(10833,axiom,(![X: $i] : ((always5(X) | xuntil2p9(X)) | (~until2p8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty8')).
% 36.18/24.00 tff(10834,plain,
% 36.18/24.00 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10833, 10832])).
% 36.18/24.00 tff(10835,plain,
% 36.18/24.00 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10834, 10830])).
% 36.18/24.00 tff(10836,plain,(
% 36.18/24.00 ![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 36.18/24.00 inference(skolemize,[status(sab)],[10835])).
% 36.18/24.00 tff(10837,plain,
% 36.18/24.00 (![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10836, 10829])).
% 36.18/24.00 tff(10838,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s99) | xuntil2p9(s99) | (~until2p8(s99)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s99) | xuntil2p9(s99) | (~until2p8(s99)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10839,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s99) | xuntil2p9(s99) | (~until2p8(s99)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10840,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s99) | xuntil2p9(s99) | (~until2p8(s99))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10839, 10838])).
% 36.18/24.00 tff(10841,plain,
% 36.18/24.00 (always5(s99) | (~until2p8(s99))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10840, 10837, 10827])).
% 36.18/24.00 tff(10842,plain,
% 36.18/24.00 (~until2p8(s99)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10841, 8969])).
% 36.18/24.00 tff(10843,plain,
% 36.18/24.00 (^[Y: $i, X: $i] : refl(((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))))),
% 36.18/24.00 inference(bind,[status(th)],[])).
% 36.18/24.00 tff(10844,plain,
% 36.18/24.00 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(quant_intro,[status(thm)],[10843])).
% 36.18/24.00 tff(10845,plain,
% 36.18/24.00 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10846,plain,
% 36.18/24.00 (^[Y: $i, X: $i] : rewrite(((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X))) <=> ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X))))),
% 36.18/24.00 inference(bind,[status(th)],[])).
% 36.18/24.00 tff(10847,plain,
% 36.18/24.00 (![Y: $i, X: $i] : ((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X))) <=> ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(quant_intro,[status(thm)],[10846])).
% 36.18/24.00 tff(10848,axiom,(![Y: $i, X: $i] : ((until2p8(Y) | (~succ(X, Y))) | (~xuntil2p9(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty9')).
% 36.18/24.00 tff(10849,plain,
% 36.18/24.00 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10848, 10847])).
% 36.18/24.00 tff(10850,plain,
% 36.18/24.00 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10849, 10845])).
% 36.18/24.00 tff(10851,plain,(
% 36.18/24.00 ![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(skolemize,[status(sab)],[10850])).
% 36.18/24.00 tff(10852,plain,
% 36.18/24.00 (![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10851, 10844])).
% 36.18/24.00 tff(10853,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s98, s99)) | until2p8(s99) | (~xuntil2p9(s98)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s98, s99)) | until2p8(s99) | (~xuntil2p9(s98)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10854,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s98, s99)) | until2p8(s99) | (~xuntil2p9(s98)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10855,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s98, s99)) | until2p8(s99) | (~xuntil2p9(s98))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10854, 10853])).
% 36.18/24.00 tff(10856,plain,
% 36.18/24.00 (until2p8(s99) | (~xuntil2p9(s98))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10855, 8625, 10852])).
% 36.18/24.00 tff(10857,plain,
% 36.18/24.00 (~xuntil2p9(s98)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10856, 10842])).
% 36.18/24.00 tff(10858,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s98) | xuntil2p9(s98) | (~until2p8(s98)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s98) | xuntil2p9(s98) | (~until2p8(s98)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10859,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s98) | xuntil2p9(s98) | (~until2p8(s98)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10860,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s98) | xuntil2p9(s98) | (~until2p8(s98))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10859, 10858])).
% 36.18/24.00 tff(10861,plain,
% 36.18/24.00 (~until2p8(s98)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10860, 10837, 10857, 8977])).
% 36.18/24.00 tff(10862,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s97, s98)) | until2p8(s98) | (~xuntil2p9(s97)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s97, s98)) | until2p8(s98) | (~xuntil2p9(s97)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10863,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s97, s98)) | until2p8(s98) | (~xuntil2p9(s97)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10864,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s97, s98)) | until2p8(s98) | (~xuntil2p9(s97))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10863, 10862])).
% 36.18/24.00 tff(10865,plain,
% 36.18/24.00 (until2p8(s98) | (~xuntil2p9(s97))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10864, 8561, 10852])).
% 36.18/24.00 tff(10866,plain,
% 36.18/24.00 (~xuntil2p9(s97)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10865, 10861])).
% 36.18/24.00 tff(10867,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s97) | xuntil2p9(s97) | (~until2p8(s97)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s97) | xuntil2p9(s97) | (~until2p8(s97)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10868,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s97) | xuntil2p9(s97) | (~until2p8(s97)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10869,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s97) | xuntil2p9(s97) | (~until2p8(s97))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10868, 10867])).
% 36.18/24.00 tff(10870,plain,
% 36.18/24.00 (xuntil2p9(s97) | (~until2p8(s97))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10869, 10837, 8985])).
% 36.18/24.00 tff(10871,plain,
% 36.18/24.00 (~until2p8(s97)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10870, 10866])).
% 36.18/24.00 tff(10872,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s96, s97)) | until2p8(s97) | (~xuntil2p9(s96)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s96, s97)) | until2p8(s97) | (~xuntil2p9(s96)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10873,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s96, s97)) | until2p8(s97) | (~xuntil2p9(s96)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10874,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s96, s97)) | until2p8(s97) | (~xuntil2p9(s96))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10873, 10872])).
% 36.18/24.00 tff(10875,plain,
% 36.18/24.00 (until2p8(s97) | (~xuntil2p9(s96))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10874, 36, 10852])).
% 36.18/24.00 tff(10876,plain,
% 36.18/24.00 (~xuntil2p9(s96)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10875, 10871])).
% 36.18/24.00 tff(10877,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s96) | xuntil2p9(s96) | (~until2p8(s96)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s96) | xuntil2p9(s96) | (~until2p8(s96)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10878,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s96) | xuntil2p9(s96) | (~until2p8(s96)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10879,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s96) | xuntil2p9(s96) | (~until2p8(s96))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10878, 10877])).
% 36.18/24.00 tff(10880,plain,
% 36.18/24.00 (xuntil2p9(s96) | (~until2p8(s96))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10879, 10837, 8986])).
% 36.18/24.00 tff(10881,plain,
% 36.18/24.00 (~until2p8(s96)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10880, 10876])).
% 36.18/24.00 tff(10882,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s95, s96)) | until2p8(s96) | (~xuntil2p9(s95)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s95, s96)) | until2p8(s96) | (~xuntil2p9(s95)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10883,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s95, s96)) | until2p8(s96) | (~xuntil2p9(s95)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10884,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s95, s96)) | until2p8(s96) | (~xuntil2p9(s95))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10883, 10882])).
% 36.18/24.00 tff(10885,plain,
% 36.18/24.00 (until2p8(s96) | (~xuntil2p9(s95))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10884, 11, 10852])).
% 36.18/24.00 tff(10886,plain,
% 36.18/24.00 (~xuntil2p9(s95)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10885, 10881])).
% 36.18/24.00 tff(10887,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s95) | xuntil2p9(s95) | (~until2p8(s95)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s95) | xuntil2p9(s95) | (~until2p8(s95)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10888,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s95) | xuntil2p9(s95) | (~until2p8(s95)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10889,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s95) | xuntil2p9(s95) | (~until2p8(s95))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10888, 10887])).
% 36.18/24.00 tff(10890,plain,
% 36.18/24.00 (xuntil2p9(s95) | (~until2p8(s95))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10889, 10837, 8987])).
% 36.18/24.00 tff(10891,plain,
% 36.18/24.00 (~until2p8(s95)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10890, 10886])).
% 36.18/24.00 tff(10892,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s94, s95)) | until2p8(s95) | (~xuntil2p9(s94)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s94, s95)) | until2p8(s95) | (~xuntil2p9(s94)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10893,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s94, s95)) | until2p8(s95) | (~xuntil2p9(s94)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10894,plain,
% 36.18/24.00 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s94, s95)) | until2p8(s95) | (~xuntil2p9(s94))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10893, 10892])).
% 36.18/24.00 tff(10895,plain,
% 36.18/24.00 (until2p8(s95) | (~xuntil2p9(s94))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10894, 8238, 10852])).
% 36.18/24.00 tff(10896,plain,
% 36.18/24.00 (~xuntil2p9(s94)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10895, 10891])).
% 36.18/24.00 tff(10897,plain,
% 36.18/24.00 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s94) | xuntil2p9(s94) | (~until2p8(s94)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s94) | xuntil2p9(s94) | (~until2p8(s94)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10898,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s94) | xuntil2p9(s94) | (~until2p8(s94)))),
% 36.18/24.00 inference(quant_inst,[status(thm)],[])).
% 36.18/24.00 tff(10899,plain,
% 36.18/24.00 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s94) | xuntil2p9(s94) | (~until2p8(s94))),
% 36.18/24.00 inference(modus_ponens,[status(thm)],[10898, 10897])).
% 36.18/24.00 tff(10900,plain,
% 36.18/24.00 (xuntil2p9(s94) | (~until2p8(s94))),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10899, 10837, 8988])).
% 36.18/24.00 tff(10901,plain,
% 36.18/24.00 (~until2p8(s94)),
% 36.18/24.00 inference(unit_resolution,[status(thm)],[10900, 10896])).
% 36.18/24.00 tff(10902,plain,
% 36.18/24.00 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s93, s94)) | until2p8(s94) | (~xuntil2p9(s93)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s93, s94)) | until2p8(s94) | (~xuntil2p9(s93)))),
% 36.18/24.00 inference(rewrite,[status(thm)],[])).
% 36.18/24.00 tff(10903,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s93, s94)) | until2p8(s94) | (~xuntil2p9(s93)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10904,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s93, s94)) | until2p8(s94) | (~xuntil2p9(s93))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10903, 10902])).
% 36.18/24.01 tff(10905,plain,
% 36.18/24.01 (until2p8(s94) | (~xuntil2p9(s93))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10904, 2852, 10852])).
% 36.18/24.01 tff(10906,plain,
% 36.18/24.01 (~xuntil2p9(s93)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10905, 10901])).
% 36.18/24.01 tff(10907,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s93) | xuntil2p9(s93) | (~until2p8(s93)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s93) | xuntil2p9(s93) | (~until2p8(s93)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10908,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s93) | xuntil2p9(s93) | (~until2p8(s93)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10909,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s93) | xuntil2p9(s93) | (~until2p8(s93))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10908, 10907])).
% 36.18/24.01 tff(10910,plain,
% 36.18/24.01 (xuntil2p9(s93) | (~until2p8(s93))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10909, 10837, 8989])).
% 36.18/24.01 tff(10911,plain,
% 36.18/24.01 (~until2p8(s93)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10910, 10906])).
% 36.18/24.01 tff(10912,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s92, s93)) | until2p8(s93) | (~xuntil2p9(s92)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s92, s93)) | until2p8(s93) | (~xuntil2p9(s92)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10913,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s92, s93)) | until2p8(s93) | (~xuntil2p9(s92)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10914,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s92, s93)) | until2p8(s93) | (~xuntil2p9(s92))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10913, 10912])).
% 36.18/24.01 tff(10915,plain,
% 36.18/24.01 (until2p8(s93) | (~xuntil2p9(s92))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10914, 2824, 10852])).
% 36.18/24.01 tff(10916,plain,
% 36.18/24.01 (~xuntil2p9(s92)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10915, 10911])).
% 36.18/24.01 tff(10917,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s92) | xuntil2p9(s92) | (~until2p8(s92)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s92) | xuntil2p9(s92) | (~until2p8(s92)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10918,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s92) | xuntil2p9(s92) | (~until2p8(s92)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10919,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s92) | xuntil2p9(s92) | (~until2p8(s92))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10918, 10917])).
% 36.18/24.01 tff(10920,plain,
% 36.18/24.01 (xuntil2p9(s92) | (~until2p8(s92))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10919, 10837, 8990])).
% 36.18/24.01 tff(10921,plain,
% 36.18/24.01 (~until2p8(s92)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10920, 10916])).
% 36.18/24.01 tff(10922,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s91, s92)) | until2p8(s92) | (~xuntil2p9(s91)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s91, s92)) | until2p8(s92) | (~xuntil2p9(s91)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10923,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s91, s92)) | until2p8(s92) | (~xuntil2p9(s91)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10924,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s91, s92)) | until2p8(s92) | (~xuntil2p9(s91))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10923, 10922])).
% 36.18/24.01 tff(10925,plain,
% 36.18/24.01 (until2p8(s92) | (~xuntil2p9(s91))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10924, 2793, 10852])).
% 36.18/24.01 tff(10926,plain,
% 36.18/24.01 (~xuntil2p9(s91)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10925, 10921])).
% 36.18/24.01 tff(10927,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s91) | xuntil2p9(s91) | (~until2p8(s91)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s91) | xuntil2p9(s91) | (~until2p8(s91)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10928,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s91) | xuntil2p9(s91) | (~until2p8(s91)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10929,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s91) | xuntil2p9(s91) | (~until2p8(s91))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10928, 10927])).
% 36.18/24.01 tff(10930,plain,
% 36.18/24.01 (xuntil2p9(s91) | (~until2p8(s91))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10929, 10837, 8991])).
% 36.18/24.01 tff(10931,plain,
% 36.18/24.01 (~until2p8(s91)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10930, 10926])).
% 36.18/24.01 tff(10932,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s90, s91)) | until2p8(s91) | (~xuntil2p9(s90)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s90, s91)) | until2p8(s91) | (~xuntil2p9(s90)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10933,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s90, s91)) | until2p8(s91) | (~xuntil2p9(s90)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10934,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s90, s91)) | until2p8(s91) | (~xuntil2p9(s90))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10933, 10932])).
% 36.18/24.01 tff(10935,plain,
% 36.18/24.01 (until2p8(s91) | (~xuntil2p9(s90))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10934, 2767, 10852])).
% 36.18/24.01 tff(10936,plain,
% 36.18/24.01 (~xuntil2p9(s90)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10935, 10931])).
% 36.18/24.01 tff(10937,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s90) | xuntil2p9(s90) | (~until2p8(s90)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s90) | xuntil2p9(s90) | (~until2p8(s90)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10938,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s90) | xuntil2p9(s90) | (~until2p8(s90)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10939,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s90) | xuntil2p9(s90) | (~until2p8(s90))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10938, 10937])).
% 36.18/24.01 tff(10940,plain,
% 36.18/24.01 (xuntil2p9(s90) | (~until2p8(s90))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10939, 10837, 8992])).
% 36.18/24.01 tff(10941,plain,
% 36.18/24.01 (~until2p8(s90)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10940, 10936])).
% 36.18/24.01 tff(10942,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s89, s90)) | until2p8(s90) | (~xuntil2p9(s89)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s89, s90)) | until2p8(s90) | (~xuntil2p9(s89)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10943,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s89, s90)) | until2p8(s90) | (~xuntil2p9(s89)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10944,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s89, s90)) | until2p8(s90) | (~xuntil2p9(s89))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10943, 10942])).
% 36.18/24.01 tff(10945,plain,
% 36.18/24.01 (until2p8(s90) | (~xuntil2p9(s89))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10944, 2738, 10852])).
% 36.18/24.01 tff(10946,plain,
% 36.18/24.01 (~xuntil2p9(s89)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10945, 10941])).
% 36.18/24.01 tff(10947,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s89) | xuntil2p9(s89) | (~until2p8(s89)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s89) | xuntil2p9(s89) | (~until2p8(s89)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10948,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s89) | xuntil2p9(s89) | (~until2p8(s89)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10949,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s89) | xuntil2p9(s89) | (~until2p8(s89))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10948, 10947])).
% 36.18/24.01 tff(10950,plain,
% 36.18/24.01 (xuntil2p9(s89) | (~until2p8(s89))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10949, 10837, 8993])).
% 36.18/24.01 tff(10951,plain,
% 36.18/24.01 (~until2p8(s89)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10950, 10946])).
% 36.18/24.01 tff(10952,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s88, s89)) | until2p8(s89) | (~xuntil2p9(s88)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s88, s89)) | until2p8(s89) | (~xuntil2p9(s88)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10953,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s88, s89)) | until2p8(s89) | (~xuntil2p9(s88)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10954,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s88, s89)) | until2p8(s89) | (~xuntil2p9(s88))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10953, 10952])).
% 36.18/24.01 tff(10955,plain,
% 36.18/24.01 (until2p8(s89) | (~xuntil2p9(s88))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10954, 2710, 10852])).
% 36.18/24.01 tff(10956,plain,
% 36.18/24.01 (~xuntil2p9(s88)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10955, 10951])).
% 36.18/24.01 tff(10957,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s88) | xuntil2p9(s88) | (~until2p8(s88)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s88) | xuntil2p9(s88) | (~until2p8(s88)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10958,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s88) | xuntil2p9(s88) | (~until2p8(s88)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10959,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s88) | xuntil2p9(s88) | (~until2p8(s88))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10958, 10957])).
% 36.18/24.01 tff(10960,plain,
% 36.18/24.01 (xuntil2p9(s88) | (~until2p8(s88))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10959, 10837, 8994])).
% 36.18/24.01 tff(10961,plain,
% 36.18/24.01 (~until2p8(s88)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10960, 10956])).
% 36.18/24.01 tff(10962,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s87, s88)) | until2p8(s88) | (~xuntil2p9(s87)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s87, s88)) | until2p8(s88) | (~xuntil2p9(s87)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10963,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s87, s88)) | until2p8(s88) | (~xuntil2p9(s87)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10964,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s87, s88)) | until2p8(s88) | (~xuntil2p9(s87))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10963, 10962])).
% 36.18/24.01 tff(10965,plain,
% 36.18/24.01 (until2p8(s88) | (~xuntil2p9(s87))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10964, 2679, 10852])).
% 36.18/24.01 tff(10966,plain,
% 36.18/24.01 (~xuntil2p9(s87)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10965, 10961])).
% 36.18/24.01 tff(10967,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s87) | xuntil2p9(s87) | (~until2p8(s87)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s87) | xuntil2p9(s87) | (~until2p8(s87)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10968,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s87) | xuntil2p9(s87) | (~until2p8(s87)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10969,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s87) | xuntil2p9(s87) | (~until2p8(s87))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10968, 10967])).
% 36.18/24.01 tff(10970,plain,
% 36.18/24.01 (xuntil2p9(s87) | (~until2p8(s87))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10969, 10837, 8995])).
% 36.18/24.01 tff(10971,plain,
% 36.18/24.01 (~until2p8(s87)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10970, 10966])).
% 36.18/24.01 tff(10972,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s86, s87)) | until2p8(s87) | (~xuntil2p9(s86)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s86, s87)) | until2p8(s87) | (~xuntil2p9(s86)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10973,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s86, s87)) | until2p8(s87) | (~xuntil2p9(s86)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10974,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s86, s87)) | until2p8(s87) | (~xuntil2p9(s86))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10973, 10972])).
% 36.18/24.01 tff(10975,plain,
% 36.18/24.01 (until2p8(s87) | (~xuntil2p9(s86))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10974, 2651, 10852])).
% 36.18/24.01 tff(10976,plain,
% 36.18/24.01 (~xuntil2p9(s86)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10975, 10971])).
% 36.18/24.01 tff(10977,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s86) | xuntil2p9(s86) | (~until2p8(s86)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s86) | xuntil2p9(s86) | (~until2p8(s86)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10978,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s86) | xuntil2p9(s86) | (~until2p8(s86)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10979,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s86) | xuntil2p9(s86) | (~until2p8(s86))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10978, 10977])).
% 36.18/24.01 tff(10980,plain,
% 36.18/24.01 (xuntil2p9(s86) | (~until2p8(s86))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10979, 10837, 8996])).
% 36.18/24.01 tff(10981,plain,
% 36.18/24.01 (~until2p8(s86)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10980, 10976])).
% 36.18/24.01 tff(10982,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s85, s86)) | until2p8(s86) | (~xuntil2p9(s85)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s85, s86)) | until2p8(s86) | (~xuntil2p9(s85)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10983,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s85, s86)) | until2p8(s86) | (~xuntil2p9(s85)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10984,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s85, s86)) | until2p8(s86) | (~xuntil2p9(s85))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10983, 10982])).
% 36.18/24.01 tff(10985,plain,
% 36.18/24.01 (until2p8(s86) | (~xuntil2p9(s85))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10984, 2620, 10852])).
% 36.18/24.01 tff(10986,plain,
% 36.18/24.01 (~xuntil2p9(s85)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10985, 10981])).
% 36.18/24.01 tff(10987,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s85) | xuntil2p9(s85) | (~until2p8(s85)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s85) | xuntil2p9(s85) | (~until2p8(s85)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10988,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s85) | xuntil2p9(s85) | (~until2p8(s85)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10989,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s85) | xuntil2p9(s85) | (~until2p8(s85))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10988, 10987])).
% 36.18/24.01 tff(10990,plain,
% 36.18/24.01 (xuntil2p9(s85) | (~until2p8(s85))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10989, 10837, 8997])).
% 36.18/24.01 tff(10991,plain,
% 36.18/24.01 (~until2p8(s85)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10990, 10986])).
% 36.18/24.01 tff(10992,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s84, s85)) | until2p8(s85) | (~xuntil2p9(s84)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s84, s85)) | until2p8(s85) | (~xuntil2p9(s84)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10993,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s84, s85)) | until2p8(s85) | (~xuntil2p9(s84)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10994,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s84, s85)) | until2p8(s85) | (~xuntil2p9(s84))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10993, 10992])).
% 36.18/24.01 tff(10995,plain,
% 36.18/24.01 (until2p8(s85) | (~xuntil2p9(s84))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10994, 2592, 10852])).
% 36.18/24.01 tff(10996,plain,
% 36.18/24.01 (~xuntil2p9(s84)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10995, 10991])).
% 36.18/24.01 tff(10997,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s84) | xuntil2p9(s84) | (~until2p8(s84)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s84) | xuntil2p9(s84) | (~until2p8(s84)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(10998,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s84) | xuntil2p9(s84) | (~until2p8(s84)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(10999,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s84) | xuntil2p9(s84) | (~until2p8(s84))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[10998, 10997])).
% 36.18/24.01 tff(11000,plain,
% 36.18/24.01 (xuntil2p9(s84) | (~until2p8(s84))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[10999, 10837, 8998])).
% 36.18/24.01 tff(11001,plain,
% 36.18/24.01 (~until2p8(s84)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11000, 10996])).
% 36.18/24.01 tff(11002,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s83, s84)) | until2p8(s84) | (~xuntil2p9(s83)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s83, s84)) | until2p8(s84) | (~xuntil2p9(s83)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11003,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s83, s84)) | until2p8(s84) | (~xuntil2p9(s83)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11004,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s83, s84)) | until2p8(s84) | (~xuntil2p9(s83))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11003, 11002])).
% 36.18/24.01 tff(11005,plain,
% 36.18/24.01 (until2p8(s84) | (~xuntil2p9(s83))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11004, 2561, 10852])).
% 36.18/24.01 tff(11006,plain,
% 36.18/24.01 (~xuntil2p9(s83)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11005, 11001])).
% 36.18/24.01 tff(11007,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s83) | xuntil2p9(s83) | (~until2p8(s83)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s83) | xuntil2p9(s83) | (~until2p8(s83)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11008,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s83) | xuntil2p9(s83) | (~until2p8(s83)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11009,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s83) | xuntil2p9(s83) | (~until2p8(s83))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11008, 11007])).
% 36.18/24.01 tff(11010,plain,
% 36.18/24.01 (xuntil2p9(s83) | (~until2p8(s83))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11009, 10837, 8999])).
% 36.18/24.01 tff(11011,plain,
% 36.18/24.01 (~until2p8(s83)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11010, 11006])).
% 36.18/24.01 tff(11012,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s82, s83)) | until2p8(s83) | (~xuntil2p9(s82)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s82, s83)) | until2p8(s83) | (~xuntil2p9(s82)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11013,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s82, s83)) | until2p8(s83) | (~xuntil2p9(s82)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11014,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s82, s83)) | until2p8(s83) | (~xuntil2p9(s82))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11013, 11012])).
% 36.18/24.01 tff(11015,plain,
% 36.18/24.01 (until2p8(s83) | (~xuntil2p9(s82))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11014, 2533, 10852])).
% 36.18/24.01 tff(11016,plain,
% 36.18/24.01 (~xuntil2p9(s82)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11015, 11011])).
% 36.18/24.01 tff(11017,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s82) | xuntil2p9(s82) | (~until2p8(s82)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s82) | xuntil2p9(s82) | (~until2p8(s82)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11018,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s82) | xuntil2p9(s82) | (~until2p8(s82)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11019,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s82) | xuntil2p9(s82) | (~until2p8(s82))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11018, 11017])).
% 36.18/24.01 tff(11020,plain,
% 36.18/24.01 (xuntil2p9(s82) | (~until2p8(s82))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11019, 10837, 9000])).
% 36.18/24.01 tff(11021,plain,
% 36.18/24.01 (~until2p8(s82)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11020, 11016])).
% 36.18/24.01 tff(11022,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s81, s82)) | until2p8(s82) | (~xuntil2p9(s81)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s81, s82)) | until2p8(s82) | (~xuntil2p9(s81)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11023,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s81, s82)) | until2p8(s82) | (~xuntil2p9(s81)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11024,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s81, s82)) | until2p8(s82) | (~xuntil2p9(s81))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11023, 11022])).
% 36.18/24.01 tff(11025,plain,
% 36.18/24.01 (until2p8(s82) | (~xuntil2p9(s81))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11024, 2502, 10852])).
% 36.18/24.01 tff(11026,plain,
% 36.18/24.01 (~xuntil2p9(s81)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11025, 11021])).
% 36.18/24.01 tff(11027,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s81) | xuntil2p9(s81) | (~until2p8(s81)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s81) | xuntil2p9(s81) | (~until2p8(s81)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11028,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s81) | xuntil2p9(s81) | (~until2p8(s81)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11029,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s81) | xuntil2p9(s81) | (~until2p8(s81))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11028, 11027])).
% 36.18/24.01 tff(11030,plain,
% 36.18/24.01 (xuntil2p9(s81) | (~until2p8(s81))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11029, 10837, 9001])).
% 36.18/24.01 tff(11031,plain,
% 36.18/24.01 (~until2p8(s81)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11030, 11026])).
% 36.18/24.01 tff(11032,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s80, s81)) | until2p8(s81) | (~xuntil2p9(s80)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s80, s81)) | until2p8(s81) | (~xuntil2p9(s80)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11033,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s80, s81)) | until2p8(s81) | (~xuntil2p9(s80)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11034,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s80, s81)) | until2p8(s81) | (~xuntil2p9(s80))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11033, 11032])).
% 36.18/24.01 tff(11035,plain,
% 36.18/24.01 (until2p8(s81) | (~xuntil2p9(s80))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11034, 2474, 10852])).
% 36.18/24.01 tff(11036,plain,
% 36.18/24.01 (~xuntil2p9(s80)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11035, 11031])).
% 36.18/24.01 tff(11037,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s80) | xuntil2p9(s80) | (~until2p8(s80)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s80) | xuntil2p9(s80) | (~until2p8(s80)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11038,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s80) | xuntil2p9(s80) | (~until2p8(s80)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11039,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s80) | xuntil2p9(s80) | (~until2p8(s80))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11038, 11037])).
% 36.18/24.01 tff(11040,plain,
% 36.18/24.01 (xuntil2p9(s80) | (~until2p8(s80))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11039, 10837, 9002])).
% 36.18/24.01 tff(11041,plain,
% 36.18/24.01 (~until2p8(s80)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11040, 11036])).
% 36.18/24.01 tff(11042,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s79, s80)) | until2p8(s80) | (~xuntil2p9(s79)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s79, s80)) | until2p8(s80) | (~xuntil2p9(s79)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11043,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s79, s80)) | until2p8(s80) | (~xuntil2p9(s79)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11044,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s79, s80)) | until2p8(s80) | (~xuntil2p9(s79))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11043, 11042])).
% 36.18/24.01 tff(11045,plain,
% 36.18/24.01 (until2p8(s80) | (~xuntil2p9(s79))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11044, 2443, 10852])).
% 36.18/24.01 tff(11046,plain,
% 36.18/24.01 (~xuntil2p9(s79)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11045, 11041])).
% 36.18/24.01 tff(11047,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s79) | xuntil2p9(s79) | (~until2p8(s79)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s79) | xuntil2p9(s79) | (~until2p8(s79)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11048,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s79) | xuntil2p9(s79) | (~until2p8(s79)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11049,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s79) | xuntil2p9(s79) | (~until2p8(s79))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11048, 11047])).
% 36.18/24.01 tff(11050,plain,
% 36.18/24.01 (xuntil2p9(s79) | (~until2p8(s79))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11049, 10837, 9003])).
% 36.18/24.01 tff(11051,plain,
% 36.18/24.01 (~until2p8(s79)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11050, 11046])).
% 36.18/24.01 tff(11052,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s78, s79)) | until2p8(s79) | (~xuntil2p9(s78)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s78, s79)) | until2p8(s79) | (~xuntil2p9(s78)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11053,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s78, s79)) | until2p8(s79) | (~xuntil2p9(s78)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11054,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s78, s79)) | until2p8(s79) | (~xuntil2p9(s78))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11053, 11052])).
% 36.18/24.01 tff(11055,plain,
% 36.18/24.01 (until2p8(s79) | (~xuntil2p9(s78))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11054, 2415, 10852])).
% 36.18/24.01 tff(11056,plain,
% 36.18/24.01 (~xuntil2p9(s78)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11055, 11051])).
% 36.18/24.01 tff(11057,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s78) | xuntil2p9(s78) | (~until2p8(s78)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s78) | xuntil2p9(s78) | (~until2p8(s78)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11058,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s78) | xuntil2p9(s78) | (~until2p8(s78)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11059,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s78) | xuntil2p9(s78) | (~until2p8(s78))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11058, 11057])).
% 36.18/24.01 tff(11060,plain,
% 36.18/24.01 (xuntil2p9(s78) | (~until2p8(s78))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11059, 10837, 9004])).
% 36.18/24.01 tff(11061,plain,
% 36.18/24.01 (~until2p8(s78)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11060, 11056])).
% 36.18/24.01 tff(11062,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s77, s78)) | until2p8(s78) | (~xuntil2p9(s77)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s77, s78)) | until2p8(s78) | (~xuntil2p9(s77)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11063,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s77, s78)) | until2p8(s78) | (~xuntil2p9(s77)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11064,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s77, s78)) | until2p8(s78) | (~xuntil2p9(s77))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11063, 11062])).
% 36.18/24.01 tff(11065,plain,
% 36.18/24.01 (until2p8(s78) | (~xuntil2p9(s77))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11064, 2384, 10852])).
% 36.18/24.01 tff(11066,plain,
% 36.18/24.01 (~xuntil2p9(s77)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11065, 11061])).
% 36.18/24.01 tff(11067,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s77) | xuntil2p9(s77) | (~until2p8(s77)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s77) | xuntil2p9(s77) | (~until2p8(s77)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11068,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s77) | xuntil2p9(s77) | (~until2p8(s77)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11069,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s77) | xuntil2p9(s77) | (~until2p8(s77))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11068, 11067])).
% 36.18/24.01 tff(11070,plain,
% 36.18/24.01 (xuntil2p9(s77) | (~until2p8(s77))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11069, 10837, 9005])).
% 36.18/24.01 tff(11071,plain,
% 36.18/24.01 (~until2p8(s77)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11070, 11066])).
% 36.18/24.01 tff(11072,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s76, s77)) | until2p8(s77) | (~xuntil2p9(s76)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s76, s77)) | until2p8(s77) | (~xuntil2p9(s76)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11073,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s76, s77)) | until2p8(s77) | (~xuntil2p9(s76)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11074,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s76, s77)) | until2p8(s77) | (~xuntil2p9(s76))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11073, 11072])).
% 36.18/24.01 tff(11075,plain,
% 36.18/24.01 (until2p8(s77) | (~xuntil2p9(s76))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11074, 2356, 10852])).
% 36.18/24.01 tff(11076,plain,
% 36.18/24.01 (~xuntil2p9(s76)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11075, 11071])).
% 36.18/24.01 tff(11077,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s76) | xuntil2p9(s76) | (~until2p8(s76)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s76) | xuntil2p9(s76) | (~until2p8(s76)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11078,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s76) | xuntil2p9(s76) | (~until2p8(s76)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11079,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s76) | xuntil2p9(s76) | (~until2p8(s76))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11078, 11077])).
% 36.18/24.01 tff(11080,plain,
% 36.18/24.01 (xuntil2p9(s76) | (~until2p8(s76))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11079, 10837, 9006])).
% 36.18/24.01 tff(11081,plain,
% 36.18/24.01 (~until2p8(s76)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11080, 11076])).
% 36.18/24.01 tff(11082,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s75, s76)) | until2p8(s76) | (~xuntil2p9(s75)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s75, s76)) | until2p8(s76) | (~xuntil2p9(s75)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11083,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s75, s76)) | until2p8(s76) | (~xuntil2p9(s75)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11084,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s75, s76)) | until2p8(s76) | (~xuntil2p9(s75))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11083, 11082])).
% 36.18/24.01 tff(11085,plain,
% 36.18/24.01 (until2p8(s76) | (~xuntil2p9(s75))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11084, 2325, 10852])).
% 36.18/24.01 tff(11086,plain,
% 36.18/24.01 (~xuntil2p9(s75)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11085, 11081])).
% 36.18/24.01 tff(11087,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s75) | xuntil2p9(s75) | (~until2p8(s75)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s75) | xuntil2p9(s75) | (~until2p8(s75)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11088,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s75) | xuntil2p9(s75) | (~until2p8(s75)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11089,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s75) | xuntil2p9(s75) | (~until2p8(s75))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11088, 11087])).
% 36.18/24.01 tff(11090,plain,
% 36.18/24.01 (xuntil2p9(s75) | (~until2p8(s75))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11089, 10837, 9007])).
% 36.18/24.01 tff(11091,plain,
% 36.18/24.01 (~until2p8(s75)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11090, 11086])).
% 36.18/24.01 tff(11092,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s74, s75)) | until2p8(s75) | (~xuntil2p9(s74)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s74, s75)) | until2p8(s75) | (~xuntil2p9(s74)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11093,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s74, s75)) | until2p8(s75) | (~xuntil2p9(s74)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11094,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s74, s75)) | until2p8(s75) | (~xuntil2p9(s74))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11093, 11092])).
% 36.18/24.01 tff(11095,plain,
% 36.18/24.01 (until2p8(s75) | (~xuntil2p9(s74))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11094, 2297, 10852])).
% 36.18/24.01 tff(11096,plain,
% 36.18/24.01 (~xuntil2p9(s74)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11095, 11091])).
% 36.18/24.01 tff(11097,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s74) | xuntil2p9(s74) | (~until2p8(s74)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s74) | xuntil2p9(s74) | (~until2p8(s74)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11098,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s74) | xuntil2p9(s74) | (~until2p8(s74)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11099,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s74) | xuntil2p9(s74) | (~until2p8(s74))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11098, 11097])).
% 36.18/24.01 tff(11100,plain,
% 36.18/24.01 (xuntil2p9(s74) | (~until2p8(s74))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11099, 10837, 9008])).
% 36.18/24.01 tff(11101,plain,
% 36.18/24.01 (~until2p8(s74)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11100, 11096])).
% 36.18/24.01 tff(11102,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s73, s74)) | until2p8(s74) | (~xuntil2p9(s73)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s73, s74)) | until2p8(s74) | (~xuntil2p9(s73)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11103,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s73, s74)) | until2p8(s74) | (~xuntil2p9(s73)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11104,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s73, s74)) | until2p8(s74) | (~xuntil2p9(s73))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11103, 11102])).
% 36.18/24.01 tff(11105,plain,
% 36.18/24.01 (until2p8(s74) | (~xuntil2p9(s73))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11104, 2266, 10852])).
% 36.18/24.01 tff(11106,plain,
% 36.18/24.01 (~xuntil2p9(s73)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11105, 11101])).
% 36.18/24.01 tff(11107,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s73) | xuntil2p9(s73) | (~until2p8(s73)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s73) | xuntil2p9(s73) | (~until2p8(s73)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11108,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s73) | xuntil2p9(s73) | (~until2p8(s73)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11109,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s73) | xuntil2p9(s73) | (~until2p8(s73))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11108, 11107])).
% 36.18/24.01 tff(11110,plain,
% 36.18/24.01 (xuntil2p9(s73) | (~until2p8(s73))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11109, 10837, 9009])).
% 36.18/24.01 tff(11111,plain,
% 36.18/24.01 (~until2p8(s73)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11110, 11106])).
% 36.18/24.01 tff(11112,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s72, s73)) | until2p8(s73) | (~xuntil2p9(s72)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s72, s73)) | until2p8(s73) | (~xuntil2p9(s72)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11113,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s72, s73)) | until2p8(s73) | (~xuntil2p9(s72)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11114,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s72, s73)) | until2p8(s73) | (~xuntil2p9(s72))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11113, 11112])).
% 36.18/24.01 tff(11115,plain,
% 36.18/24.01 (until2p8(s73) | (~xuntil2p9(s72))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11114, 2238, 10852])).
% 36.18/24.01 tff(11116,plain,
% 36.18/24.01 (~xuntil2p9(s72)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11115, 11111])).
% 36.18/24.01 tff(11117,plain,
% 36.18/24.01 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s72) | xuntil2p9(s72) | (~until2p8(s72)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s72) | xuntil2p9(s72) | (~until2p8(s72)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11118,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s72) | xuntil2p9(s72) | (~until2p8(s72)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.01 tff(11119,plain,
% 36.18/24.01 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s72) | xuntil2p9(s72) | (~until2p8(s72))),
% 36.18/24.01 inference(modus_ponens,[status(thm)],[11118, 11117])).
% 36.18/24.01 tff(11120,plain,
% 36.18/24.01 (xuntil2p9(s72) | (~until2p8(s72))),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11119, 10837, 9010])).
% 36.18/24.01 tff(11121,plain,
% 36.18/24.01 (~until2p8(s72)),
% 36.18/24.01 inference(unit_resolution,[status(thm)],[11120, 11116])).
% 36.18/24.01 tff(11122,plain,
% 36.18/24.01 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s71, s72)) | until2p8(s72) | (~xuntil2p9(s71)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s71, s72)) | until2p8(s72) | (~xuntil2p9(s71)))),
% 36.18/24.01 inference(rewrite,[status(thm)],[])).
% 36.18/24.01 tff(11123,plain,
% 36.18/24.01 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s71, s72)) | until2p8(s72) | (~xuntil2p9(s71)))),
% 36.18/24.01 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11124,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s71, s72)) | until2p8(s72) | (~xuntil2p9(s71))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11123, 11122])).
% 36.18/24.02 tff(11125,plain,
% 36.18/24.02 (until2p8(s72) | (~xuntil2p9(s71))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11124, 2207, 10852])).
% 36.18/24.02 tff(11126,plain,
% 36.18/24.02 (~xuntil2p9(s71)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11125, 11121])).
% 36.18/24.02 tff(11127,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s71) | xuntil2p9(s71) | (~until2p8(s71)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s71) | xuntil2p9(s71) | (~until2p8(s71)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11128,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s71) | xuntil2p9(s71) | (~until2p8(s71)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11129,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s71) | xuntil2p9(s71) | (~until2p8(s71))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11128, 11127])).
% 36.18/24.02 tff(11130,plain,
% 36.18/24.02 (xuntil2p9(s71) | (~until2p8(s71))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11129, 10837, 9011])).
% 36.18/24.02 tff(11131,plain,
% 36.18/24.02 (~until2p8(s71)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11130, 11126])).
% 36.18/24.02 tff(11132,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s70, s71)) | until2p8(s71) | (~xuntil2p9(s70)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s70, s71)) | until2p8(s71) | (~xuntil2p9(s70)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11133,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s70, s71)) | until2p8(s71) | (~xuntil2p9(s70)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11134,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s70, s71)) | until2p8(s71) | (~xuntil2p9(s70))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11133, 11132])).
% 36.18/24.02 tff(11135,plain,
% 36.18/24.02 (until2p8(s71) | (~xuntil2p9(s70))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11134, 2179, 10852])).
% 36.18/24.02 tff(11136,plain,
% 36.18/24.02 (~xuntil2p9(s70)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11135, 11131])).
% 36.18/24.02 tff(11137,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s70) | xuntil2p9(s70) | (~until2p8(s70)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s70) | xuntil2p9(s70) | (~until2p8(s70)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11138,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s70) | xuntil2p9(s70) | (~until2p8(s70)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11139,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s70) | xuntil2p9(s70) | (~until2p8(s70))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11138, 11137])).
% 36.18/24.02 tff(11140,plain,
% 36.18/24.02 (xuntil2p9(s70) | (~until2p8(s70))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11139, 10837, 9012])).
% 36.18/24.02 tff(11141,plain,
% 36.18/24.02 (~until2p8(s70)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11140, 11136])).
% 36.18/24.02 tff(11142,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s69, s70)) | until2p8(s70) | (~xuntil2p9(s69)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s69, s70)) | until2p8(s70) | (~xuntil2p9(s69)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11143,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s69, s70)) | until2p8(s70) | (~xuntil2p9(s69)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11144,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s69, s70)) | until2p8(s70) | (~xuntil2p9(s69))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11143, 11142])).
% 36.18/24.02 tff(11145,plain,
% 36.18/24.02 (until2p8(s70) | (~xuntil2p9(s69))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11144, 2148, 10852])).
% 36.18/24.02 tff(11146,plain,
% 36.18/24.02 (~xuntil2p9(s69)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11145, 11141])).
% 36.18/24.02 tff(11147,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s69) | xuntil2p9(s69) | (~until2p8(s69)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s69) | xuntil2p9(s69) | (~until2p8(s69)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11148,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s69) | xuntil2p9(s69) | (~until2p8(s69)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11149,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s69) | xuntil2p9(s69) | (~until2p8(s69))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11148, 11147])).
% 36.18/24.02 tff(11150,plain,
% 36.18/24.02 (xuntil2p9(s69) | (~until2p8(s69))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11149, 10837, 9013])).
% 36.18/24.02 tff(11151,plain,
% 36.18/24.02 (~until2p8(s69)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11150, 11146])).
% 36.18/24.02 tff(11152,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s68, s69)) | until2p8(s69) | (~xuntil2p9(s68)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s68, s69)) | until2p8(s69) | (~xuntil2p9(s68)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11153,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s68, s69)) | until2p8(s69) | (~xuntil2p9(s68)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11154,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s68, s69)) | until2p8(s69) | (~xuntil2p9(s68))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11153, 11152])).
% 36.18/24.02 tff(11155,plain,
% 36.18/24.02 (until2p8(s69) | (~xuntil2p9(s68))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11154, 2120, 10852])).
% 36.18/24.02 tff(11156,plain,
% 36.18/24.02 (~xuntil2p9(s68)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11155, 11151])).
% 36.18/24.02 tff(11157,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s68) | xuntil2p9(s68) | (~until2p8(s68)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s68) | xuntil2p9(s68) | (~until2p8(s68)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11158,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s68) | xuntil2p9(s68) | (~until2p8(s68)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11159,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s68) | xuntil2p9(s68) | (~until2p8(s68))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11158, 11157])).
% 36.18/24.02 tff(11160,plain,
% 36.18/24.02 (xuntil2p9(s68) | (~until2p8(s68))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11159, 10837, 9014])).
% 36.18/24.02 tff(11161,plain,
% 36.18/24.02 (~until2p8(s68)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11160, 11156])).
% 36.18/24.02 tff(11162,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s67, s68)) | until2p8(s68) | (~xuntil2p9(s67)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s67, s68)) | until2p8(s68) | (~xuntil2p9(s67)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11163,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s67, s68)) | until2p8(s68) | (~xuntil2p9(s67)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11164,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s67, s68)) | until2p8(s68) | (~xuntil2p9(s67))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11163, 11162])).
% 36.18/24.02 tff(11165,plain,
% 36.18/24.02 (until2p8(s68) | (~xuntil2p9(s67))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11164, 2089, 10852])).
% 36.18/24.02 tff(11166,plain,
% 36.18/24.02 (~xuntil2p9(s67)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11165, 11161])).
% 36.18/24.02 tff(11167,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s67) | xuntil2p9(s67) | (~until2p8(s67)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s67) | xuntil2p9(s67) | (~until2p8(s67)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11168,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s67) | xuntil2p9(s67) | (~until2p8(s67)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11169,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s67) | xuntil2p9(s67) | (~until2p8(s67))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11168, 11167])).
% 36.18/24.02 tff(11170,plain,
% 36.18/24.02 (xuntil2p9(s67) | (~until2p8(s67))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11169, 10837, 9015])).
% 36.18/24.02 tff(11171,plain,
% 36.18/24.02 (~until2p8(s67)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11170, 11166])).
% 36.18/24.02 tff(11172,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s66, s67)) | until2p8(s67) | (~xuntil2p9(s66)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s66, s67)) | until2p8(s67) | (~xuntil2p9(s66)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11173,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s66, s67)) | until2p8(s67) | (~xuntil2p9(s66)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11174,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s66, s67)) | until2p8(s67) | (~xuntil2p9(s66))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11173, 11172])).
% 36.18/24.02 tff(11175,plain,
% 36.18/24.02 (until2p8(s67) | (~xuntil2p9(s66))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11174, 2061, 10852])).
% 36.18/24.02 tff(11176,plain,
% 36.18/24.02 (~xuntil2p9(s66)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11175, 11171])).
% 36.18/24.02 tff(11177,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s66) | xuntil2p9(s66) | (~until2p8(s66)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s66) | xuntil2p9(s66) | (~until2p8(s66)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11178,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s66) | xuntil2p9(s66) | (~until2p8(s66)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11179,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s66) | xuntil2p9(s66) | (~until2p8(s66))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11178, 11177])).
% 36.18/24.02 tff(11180,plain,
% 36.18/24.02 (xuntil2p9(s66) | (~until2p8(s66))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11179, 10837, 9016])).
% 36.18/24.02 tff(11181,plain,
% 36.18/24.02 (~until2p8(s66)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11180, 11176])).
% 36.18/24.02 tff(11182,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s65, s66)) | until2p8(s66) | (~xuntil2p9(s65)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s65, s66)) | until2p8(s66) | (~xuntil2p9(s65)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11183,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s65, s66)) | until2p8(s66) | (~xuntil2p9(s65)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11184,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s65, s66)) | until2p8(s66) | (~xuntil2p9(s65))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11183, 11182])).
% 36.18/24.02 tff(11185,plain,
% 36.18/24.02 (until2p8(s66) | (~xuntil2p9(s65))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11184, 2030, 10852])).
% 36.18/24.02 tff(11186,plain,
% 36.18/24.02 (~xuntil2p9(s65)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11185, 11181])).
% 36.18/24.02 tff(11187,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s65) | xuntil2p9(s65) | (~until2p8(s65)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s65) | xuntil2p9(s65) | (~until2p8(s65)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11188,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s65) | xuntil2p9(s65) | (~until2p8(s65)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11189,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s65) | xuntil2p9(s65) | (~until2p8(s65))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11188, 11187])).
% 36.18/24.02 tff(11190,plain,
% 36.18/24.02 (xuntil2p9(s65) | (~until2p8(s65))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11189, 10837, 9017])).
% 36.18/24.02 tff(11191,plain,
% 36.18/24.02 (~until2p8(s65)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11190, 11186])).
% 36.18/24.02 tff(11192,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s64, s65)) | until2p8(s65) | (~xuntil2p9(s64)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s64, s65)) | until2p8(s65) | (~xuntil2p9(s64)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11193,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s64, s65)) | until2p8(s65) | (~xuntil2p9(s64)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11194,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s64, s65)) | until2p8(s65) | (~xuntil2p9(s64))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11193, 11192])).
% 36.18/24.02 tff(11195,plain,
% 36.18/24.02 (until2p8(s65) | (~xuntil2p9(s64))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11194, 2002, 10852])).
% 36.18/24.02 tff(11196,plain,
% 36.18/24.02 (~xuntil2p9(s64)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11195, 11191])).
% 36.18/24.02 tff(11197,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s64) | xuntil2p9(s64) | (~until2p8(s64)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s64) | xuntil2p9(s64) | (~until2p8(s64)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11198,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s64) | xuntil2p9(s64) | (~until2p8(s64)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11199,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s64) | xuntil2p9(s64) | (~until2p8(s64))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11198, 11197])).
% 36.18/24.02 tff(11200,plain,
% 36.18/24.02 (xuntil2p9(s64) | (~until2p8(s64))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11199, 10837, 9018])).
% 36.18/24.02 tff(11201,plain,
% 36.18/24.02 (~until2p8(s64)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11200, 11196])).
% 36.18/24.02 tff(11202,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s63, s64)) | until2p8(s64) | (~xuntil2p9(s63)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s63, s64)) | until2p8(s64) | (~xuntil2p9(s63)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11203,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s63, s64)) | until2p8(s64) | (~xuntil2p9(s63)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11204,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s63, s64)) | until2p8(s64) | (~xuntil2p9(s63))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11203, 11202])).
% 36.18/24.02 tff(11205,plain,
% 36.18/24.02 (until2p8(s64) | (~xuntil2p9(s63))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11204, 1971, 10852])).
% 36.18/24.02 tff(11206,plain,
% 36.18/24.02 (~xuntil2p9(s63)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11205, 11201])).
% 36.18/24.02 tff(11207,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s63) | xuntil2p9(s63) | (~until2p8(s63)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s63) | xuntil2p9(s63) | (~until2p8(s63)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11208,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s63) | xuntil2p9(s63) | (~until2p8(s63)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11209,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s63) | xuntil2p9(s63) | (~until2p8(s63))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11208, 11207])).
% 36.18/24.02 tff(11210,plain,
% 36.18/24.02 (xuntil2p9(s63) | (~until2p8(s63))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11209, 10837, 9019])).
% 36.18/24.02 tff(11211,plain,
% 36.18/24.02 (~until2p8(s63)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11210, 11206])).
% 36.18/24.02 tff(11212,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s62, s63)) | until2p8(s63) | (~xuntil2p9(s62)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s62, s63)) | until2p8(s63) | (~xuntil2p9(s62)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11213,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s62, s63)) | until2p8(s63) | (~xuntil2p9(s62)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11214,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s62, s63)) | until2p8(s63) | (~xuntil2p9(s62))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11213, 11212])).
% 36.18/24.02 tff(11215,plain,
% 36.18/24.02 (until2p8(s63) | (~xuntil2p9(s62))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11214, 1943, 10852])).
% 36.18/24.02 tff(11216,plain,
% 36.18/24.02 (~xuntil2p9(s62)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11215, 11211])).
% 36.18/24.02 tff(11217,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s62) | xuntil2p9(s62) | (~until2p8(s62)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s62) | xuntil2p9(s62) | (~until2p8(s62)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11218,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s62) | xuntil2p9(s62) | (~until2p8(s62)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11219,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s62) | xuntil2p9(s62) | (~until2p8(s62))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11218, 11217])).
% 36.18/24.02 tff(11220,plain,
% 36.18/24.02 (xuntil2p9(s62) | (~until2p8(s62))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11219, 10837, 9020])).
% 36.18/24.02 tff(11221,plain,
% 36.18/24.02 (~until2p8(s62)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11220, 11216])).
% 36.18/24.02 tff(11222,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s61, s62)) | until2p8(s62) | (~xuntil2p9(s61)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s61, s62)) | until2p8(s62) | (~xuntil2p9(s61)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11223,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s61, s62)) | until2p8(s62) | (~xuntil2p9(s61)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11224,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s61, s62)) | until2p8(s62) | (~xuntil2p9(s61))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11223, 11222])).
% 36.18/24.02 tff(11225,plain,
% 36.18/24.02 (until2p8(s62) | (~xuntil2p9(s61))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11224, 1912, 10852])).
% 36.18/24.02 tff(11226,plain,
% 36.18/24.02 (~xuntil2p9(s61)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11225, 11221])).
% 36.18/24.02 tff(11227,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s61) | xuntil2p9(s61) | (~until2p8(s61)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s61) | xuntil2p9(s61) | (~until2p8(s61)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11228,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s61) | xuntil2p9(s61) | (~until2p8(s61)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11229,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s61) | xuntil2p9(s61) | (~until2p8(s61))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11228, 11227])).
% 36.18/24.02 tff(11230,plain,
% 36.18/24.02 (xuntil2p9(s61) | (~until2p8(s61))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11229, 10837, 9021])).
% 36.18/24.02 tff(11231,plain,
% 36.18/24.02 (~until2p8(s61)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11230, 11226])).
% 36.18/24.02 tff(11232,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s60, s61)) | until2p8(s61) | (~xuntil2p9(s60)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s60, s61)) | until2p8(s61) | (~xuntil2p9(s60)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11233,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s60, s61)) | until2p8(s61) | (~xuntil2p9(s60)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11234,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s60, s61)) | until2p8(s61) | (~xuntil2p9(s60))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11233, 11232])).
% 36.18/24.02 tff(11235,plain,
% 36.18/24.02 (until2p8(s61) | (~xuntil2p9(s60))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11234, 1884, 10852])).
% 36.18/24.02 tff(11236,plain,
% 36.18/24.02 (~xuntil2p9(s60)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11235, 11231])).
% 36.18/24.02 tff(11237,plain,
% 36.18/24.02 (((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s60) | xuntil2p9(s60) | (~until2p8(s60)))) <=> ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s60) | xuntil2p9(s60) | (~until2p8(s60)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11238,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s60) | xuntil2p9(s60) | (~until2p8(s60)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11239,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s60) | xuntil2p9(s60) | (~until2p8(s60))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11238, 11237])).
% 36.18/24.02 tff(11240,plain,
% 36.18/24.02 (xuntil2p9(s60) | (~until2p8(s60))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11239, 10837, 9022])).
% 36.18/24.02 tff(11241,plain,
% 36.18/24.02 (~until2p8(s60)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11240, 11236])).
% 36.18/24.02 tff(11242,plain,
% 36.18/24.02 (((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s59, s60)) | until2p8(s60) | (~xuntil2p9(s59)))) <=> ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s59, s60)) | until2p8(s60) | (~xuntil2p9(s59)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11243,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s59, s60)) | until2p8(s60) | (~xuntil2p9(s59)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11244,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s59, s60)) | until2p8(s60) | (~xuntil2p9(s59))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11243, 11242])).
% 36.18/24.02 tff(11245,plain,
% 36.18/24.02 (until2p8(s60) | (~xuntil2p9(s59))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11244, 70, 10852])).
% 36.18/24.02 tff(11246,plain,
% 36.18/24.02 (~xuntil2p9(s59)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11245, 11241])).
% 36.18/24.02 tff(11247,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11248,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s59) | xuntil2p9(s59) | (~until2p8(s59)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11249,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s59) | xuntil2p9(s59) | (~until2p8(s59))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11248, 11247])).
% 36.18/24.02 tff(11250,plain,
% 36.18/24.02 (xuntil2p9(s59) | (~until2p8(s59))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11249, 10837, 9023])).
% 36.18/24.02 tff(11251,plain,
% 36.18/24.02 (~until2p8(s59)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11250, 11246])).
% 36.18/24.02 tff(11252,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11253,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11254,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s58, s59)) | until2p8(s59) | (~xuntil2p9(s58))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11253, 11252])).
% 36.18/24.02 tff(11255,plain,
% 36.18/24.02 (until2p8(s59) | (~xuntil2p9(s58))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11254, 1837, 10852])).
% 36.18/24.02 tff(11256,plain,
% 36.18/24.02 (~xuntil2p9(s58)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11255, 11251])).
% 36.18/24.02 tff(11257,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11258,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s58) | xuntil2p9(s58) | (~until2p8(s58)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11259,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s58) | xuntil2p9(s58) | (~until2p8(s58))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11258, 11257])).
% 36.18/24.02 tff(11260,plain,
% 36.18/24.02 (xuntil2p9(s58) | (~until2p8(s58))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11259, 10837, 9031])).
% 36.18/24.02 tff(11261,plain,
% 36.18/24.02 (~until2p8(s58)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11260, 11256])).
% 36.18/24.02 tff(11262,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11263,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11264,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s57, s58)) | until2p8(s58) | (~xuntil2p9(s57))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11263, 11262])).
% 36.18/24.02 tff(11265,plain,
% 36.18/24.02 (until2p8(s58) | (~xuntil2p9(s57))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11264, 1806, 10852])).
% 36.18/24.02 tff(11266,plain,
% 36.18/24.02 (~xuntil2p9(s57)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11265, 11261])).
% 36.18/24.02 tff(11267,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11268,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s57) | xuntil2p9(s57) | (~until2p8(s57)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11269,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s57) | xuntil2p9(s57) | (~until2p8(s57))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11268, 11267])).
% 36.18/24.02 tff(11270,plain,
% 36.18/24.02 (xuntil2p9(s57) | (~until2p8(s57))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11269, 10837, 9039])).
% 36.18/24.02 tff(11271,plain,
% 36.18/24.02 (~until2p8(s57)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11270, 11266])).
% 36.18/24.02 tff(11272,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11273,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11274,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s56, s57)) | until2p8(s57) | (~xuntil2p9(s56))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11273, 11272])).
% 36.18/24.02 tff(11275,plain,
% 36.18/24.02 (until2p8(s57) | (~xuntil2p9(s56))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11274, 1778, 10852])).
% 36.18/24.02 tff(11276,plain,
% 36.18/24.02 (~xuntil2p9(s56)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11275, 11271])).
% 36.18/24.02 tff(11277,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11278,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s56) | xuntil2p9(s56) | (~until2p8(s56)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11279,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s56) | xuntil2p9(s56) | (~until2p8(s56))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11278, 11277])).
% 36.18/24.02 tff(11280,plain,
% 36.18/24.02 (xuntil2p9(s56) | (~until2p8(s56))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11279, 10837, 9047])).
% 36.18/24.02 tff(11281,plain,
% 36.18/24.02 (~until2p8(s56)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11280, 11276])).
% 36.18/24.02 tff(11282,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11283,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11284,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s55, s56)) | until2p8(s56) | (~xuntil2p9(s55))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11283, 11282])).
% 36.18/24.02 tff(11285,plain,
% 36.18/24.02 (until2p8(s56) | (~xuntil2p9(s55))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11284, 1747, 10852])).
% 36.18/24.02 tff(11286,plain,
% 36.18/24.02 (~xuntil2p9(s55)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11285, 11281])).
% 36.18/24.02 tff(11287,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11288,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s55) | xuntil2p9(s55) | (~until2p8(s55)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11289,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s55) | xuntil2p9(s55) | (~until2p8(s55))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11288, 11287])).
% 36.18/24.02 tff(11290,plain,
% 36.18/24.02 (xuntil2p9(s55) | (~until2p8(s55))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11289, 10837, 9055])).
% 36.18/24.02 tff(11291,plain,
% 36.18/24.02 (~until2p8(s55)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11290, 11286])).
% 36.18/24.02 tff(11292,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11293,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11294,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s54, s55)) | until2p8(s55) | (~xuntil2p9(s54))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11293, 11292])).
% 36.18/24.02 tff(11295,plain,
% 36.18/24.02 (until2p8(s55) | (~xuntil2p9(s54))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11294, 1719, 10852])).
% 36.18/24.02 tff(11296,plain,
% 36.18/24.02 (~xuntil2p9(s54)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11295, 11291])).
% 36.18/24.02 tff(11297,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11298,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s54) | xuntil2p9(s54) | (~until2p8(s54)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11299,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s54) | xuntil2p9(s54) | (~until2p8(s54))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11298, 11297])).
% 36.18/24.02 tff(11300,plain,
% 36.18/24.02 (xuntil2p9(s54) | (~until2p8(s54))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11299, 10837, 9063])).
% 36.18/24.02 tff(11301,plain,
% 36.18/24.02 (~until2p8(s54)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11300, 11296])).
% 36.18/24.02 tff(11302,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11303,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11304,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s53, s54)) | until2p8(s54) | (~xuntil2p9(s53))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11303, 11302])).
% 36.18/24.02 tff(11305,plain,
% 36.18/24.02 (until2p8(s54) | (~xuntil2p9(s53))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11304, 1688, 10852])).
% 36.18/24.02 tff(11306,plain,
% 36.18/24.02 (~xuntil2p9(s53)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11305, 11301])).
% 36.18/24.02 tff(11307,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11308,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s53) | xuntil2p9(s53) | (~until2p8(s53)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11309,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s53) | xuntil2p9(s53) | (~until2p8(s53))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11308, 11307])).
% 36.18/24.02 tff(11310,plain,
% 36.18/24.02 (xuntil2p9(s53) | (~until2p8(s53))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11309, 10837, 9071])).
% 36.18/24.02 tff(11311,plain,
% 36.18/24.02 (~until2p8(s53)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11310, 11306])).
% 36.18/24.02 tff(11312,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11313,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11314,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s52, s53)) | until2p8(s53) | (~xuntil2p9(s52))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11313, 11312])).
% 36.18/24.02 tff(11315,plain,
% 36.18/24.02 (until2p8(s53) | (~xuntil2p9(s52))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11314, 1660, 10852])).
% 36.18/24.02 tff(11316,plain,
% 36.18/24.02 (~xuntil2p9(s52)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11315, 11311])).
% 36.18/24.02 tff(11317,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11318,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s52) | xuntil2p9(s52) | (~until2p8(s52)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11319,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s52) | xuntil2p9(s52) | (~until2p8(s52))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11318, 11317])).
% 36.18/24.02 tff(11320,plain,
% 36.18/24.02 (xuntil2p9(s52) | (~until2p8(s52))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11319, 10837, 9079])).
% 36.18/24.02 tff(11321,plain,
% 36.18/24.02 (~until2p8(s52)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11320, 11316])).
% 36.18/24.02 tff(11322,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11323,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11324,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s51, s52)) | until2p8(s52) | (~xuntil2p9(s51))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11323, 11322])).
% 36.18/24.02 tff(11325,plain,
% 36.18/24.02 (until2p8(s52) | (~xuntil2p9(s51))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11324, 1629, 10852])).
% 36.18/24.02 tff(11326,plain,
% 36.18/24.02 (~xuntil2p9(s51)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11325, 11321])).
% 36.18/24.02 tff(11327,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11328,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s51) | xuntil2p9(s51) | (~until2p8(s51)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11329,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s51) | xuntil2p9(s51) | (~until2p8(s51))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11328, 11327])).
% 36.18/24.02 tff(11330,plain,
% 36.18/24.02 (xuntil2p9(s51) | (~until2p8(s51))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11329, 10837, 9087])).
% 36.18/24.02 tff(11331,plain,
% 36.18/24.02 (~until2p8(s51)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11330, 11326])).
% 36.18/24.02 tff(11332,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11333,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11334,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s50, s51)) | until2p8(s51) | (~xuntil2p9(s50))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11333, 11332])).
% 36.18/24.02 tff(11335,plain,
% 36.18/24.02 (until2p8(s51) | (~xuntil2p9(s50))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11334, 1601, 10852])).
% 36.18/24.02 tff(11336,plain,
% 36.18/24.02 (~xuntil2p9(s50)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11335, 11331])).
% 36.18/24.02 tff(11337,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11338,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s50) | xuntil2p9(s50) | (~until2p8(s50)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11339,plain,
% 36.18/24.02 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s50) | xuntil2p9(s50) | (~until2p8(s50))),
% 36.18/24.02 inference(modus_ponens,[status(thm)],[11338, 11337])).
% 36.18/24.02 tff(11340,plain,
% 36.18/24.02 (xuntil2p9(s50) | (~until2p8(s50))),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11339, 10837, 9095])).
% 36.18/24.02 tff(11341,plain,
% 36.18/24.02 (~until2p8(s50)),
% 36.18/24.02 inference(unit_resolution,[status(thm)],[11340, 11336])).
% 36.18/24.02 tff(11342,plain,
% 36.18/24.02 (((~![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)))),
% 36.18/24.02 inference(rewrite,[status(thm)],[])).
% 36.18/24.02 tff(11343,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49)))),
% 36.18/24.02 inference(quant_inst,[status(thm)],[])).
% 36.18/24.02 tff(11344,plain,
% 36.18/24.02 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s49, s50)) | until2p8(s50) | (~xuntil2p9(s49))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11343, 11342])).
% 36.18/24.03 tff(11345,plain,
% 36.18/24.03 (until2p8(s50) | (~xuntil2p9(s49))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11344, 1570, 10852])).
% 36.18/24.03 tff(11346,plain,
% 36.18/24.03 (~xuntil2p9(s49)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11345, 11341])).
% 36.18/24.03 tff(11347,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11348,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s49) | xuntil2p9(s49) | (~until2p8(s49)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11349,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s49) | xuntil2p9(s49) | (~until2p8(s49))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11348, 11347])).
% 36.18/24.03 tff(11350,plain,
% 36.18/24.03 (xuntil2p9(s49) | (~until2p8(s49))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11349, 10837, 9103])).
% 36.18/24.03 tff(11351,plain,
% 36.18/24.03 (~until2p8(s49)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11350, 11346])).
% 36.18/24.03 tff(11352,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11353,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11354,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s48, s49)) | until2p8(s49) | (~xuntil2p9(s48))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11353, 11352])).
% 36.18/24.03 tff(11355,plain,
% 36.18/24.03 (until2p8(s49) | (~xuntil2p9(s48))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11354, 1542, 10852])).
% 36.18/24.03 tff(11356,plain,
% 36.18/24.03 (~xuntil2p9(s48)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11355, 11351])).
% 36.18/24.03 tff(11357,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11358,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s48) | xuntil2p9(s48) | (~until2p8(s48)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11359,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s48) | xuntil2p9(s48) | (~until2p8(s48))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11358, 11357])).
% 36.18/24.03 tff(11360,plain,
% 36.18/24.03 (xuntil2p9(s48) | (~until2p8(s48))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11359, 10837, 9111])).
% 36.18/24.03 tff(11361,plain,
% 36.18/24.03 (~until2p8(s48)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11360, 11356])).
% 36.18/24.03 tff(11362,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11363,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11364,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s47, s48)) | until2p8(s48) | (~xuntil2p9(s47))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11363, 11362])).
% 36.18/24.03 tff(11365,plain,
% 36.18/24.03 (until2p8(s48) | (~xuntil2p9(s47))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11364, 1511, 10852])).
% 36.18/24.03 tff(11366,plain,
% 36.18/24.03 (~xuntil2p9(s47)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11365, 11361])).
% 36.18/24.03 tff(11367,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11368,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s47) | xuntil2p9(s47) | (~until2p8(s47)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11369,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s47) | xuntil2p9(s47) | (~until2p8(s47))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11368, 11367])).
% 36.18/24.03 tff(11370,plain,
% 36.18/24.03 (xuntil2p9(s47) | (~until2p8(s47))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11369, 10837, 9119])).
% 36.18/24.03 tff(11371,plain,
% 36.18/24.03 (~until2p8(s47)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11370, 11366])).
% 36.18/24.03 tff(11372,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11373,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11374,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s46, s47)) | until2p8(s47) | (~xuntil2p9(s46))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11373, 11372])).
% 36.18/24.03 tff(11375,plain,
% 36.18/24.03 (until2p8(s47) | (~xuntil2p9(s46))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11374, 1483, 10852])).
% 36.18/24.03 tff(11376,plain,
% 36.18/24.03 (~xuntil2p9(s46)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11375, 11371])).
% 36.18/24.03 tff(11377,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11378,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s46) | xuntil2p9(s46) | (~until2p8(s46)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11379,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s46) | xuntil2p9(s46) | (~until2p8(s46))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11378, 11377])).
% 36.18/24.03 tff(11380,plain,
% 36.18/24.03 (xuntil2p9(s46) | (~until2p8(s46))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11379, 10837, 9127])).
% 36.18/24.03 tff(11381,plain,
% 36.18/24.03 (~until2p8(s46)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11380, 11376])).
% 36.18/24.03 tff(11382,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11383,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11384,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s45, s46)) | until2p8(s46) | (~xuntil2p9(s45))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11383, 11382])).
% 36.18/24.03 tff(11385,plain,
% 36.18/24.03 (until2p8(s46) | (~xuntil2p9(s45))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11384, 1452, 10852])).
% 36.18/24.03 tff(11386,plain,
% 36.18/24.03 (~xuntil2p9(s45)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11385, 11381])).
% 36.18/24.03 tff(11387,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11388,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s45) | xuntil2p9(s45) | (~until2p8(s45)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11389,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s45) | xuntil2p9(s45) | (~until2p8(s45))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11388, 11387])).
% 36.18/24.03 tff(11390,plain,
% 36.18/24.03 (xuntil2p9(s45) | (~until2p8(s45))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11389, 10837, 9135])).
% 36.18/24.03 tff(11391,plain,
% 36.18/24.03 (~until2p8(s45)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11390, 11386])).
% 36.18/24.03 tff(11392,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11393,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11394,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s44, s45)) | until2p8(s45) | (~xuntil2p9(s44))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11393, 11392])).
% 36.18/24.03 tff(11395,plain,
% 36.18/24.03 (until2p8(s45) | (~xuntil2p9(s44))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11394, 1426, 10852])).
% 36.18/24.03 tff(11396,plain,
% 36.18/24.03 (~xuntil2p9(s44)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11395, 11391])).
% 36.18/24.03 tff(11397,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11398,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s44) | xuntil2p9(s44) | (~until2p8(s44)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11399,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s44) | xuntil2p9(s44) | (~until2p8(s44))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11398, 11397])).
% 36.18/24.03 tff(11400,plain,
% 36.18/24.03 (xuntil2p9(s44) | (~until2p8(s44))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11399, 10837, 9143])).
% 36.18/24.03 tff(11401,plain,
% 36.18/24.03 (~until2p8(s44)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11400, 11396])).
% 36.18/24.03 tff(11402,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11403,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11404,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s43, s44)) | until2p8(s44) | (~xuntil2p9(s43))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11403, 11402])).
% 36.18/24.03 tff(11405,plain,
% 36.18/24.03 (until2p8(s44) | (~xuntil2p9(s43))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11404, 1395, 10852])).
% 36.18/24.03 tff(11406,plain,
% 36.18/24.03 (~xuntil2p9(s43)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11405, 11401])).
% 36.18/24.03 tff(11407,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11408,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s43) | xuntil2p9(s43) | (~until2p8(s43)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11409,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s43) | xuntil2p9(s43) | (~until2p8(s43))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11408, 11407])).
% 36.18/24.03 tff(11410,plain,
% 36.18/24.03 (xuntil2p9(s43) | (~until2p8(s43))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11409, 10837, 9151])).
% 36.18/24.03 tff(11411,plain,
% 36.18/24.03 (~until2p8(s43)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11410, 11406])).
% 36.18/24.03 tff(11412,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11413,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11414,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s42, s43)) | until2p8(s43) | (~xuntil2p9(s42))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11413, 11412])).
% 36.18/24.03 tff(11415,plain,
% 36.18/24.03 (until2p8(s43) | (~xuntil2p9(s42))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11414, 1367, 10852])).
% 36.18/24.03 tff(11416,plain,
% 36.18/24.03 (~xuntil2p9(s42)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11415, 11411])).
% 36.18/24.03 tff(11417,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11418,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s42) | xuntil2p9(s42) | (~until2p8(s42)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11419,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s42) | xuntil2p9(s42) | (~until2p8(s42))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11418, 11417])).
% 36.18/24.03 tff(11420,plain,
% 36.18/24.03 (xuntil2p9(s42) | (~until2p8(s42))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11419, 10837, 9159])).
% 36.18/24.03 tff(11421,plain,
% 36.18/24.03 (~until2p8(s42)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11420, 11416])).
% 36.18/24.03 tff(11422,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11423,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11424,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s41, s42)) | until2p8(s42) | (~xuntil2p9(s41))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11423, 11422])).
% 36.18/24.03 tff(11425,plain,
% 36.18/24.03 (until2p8(s42) | (~xuntil2p9(s41))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11424, 1336, 10852])).
% 36.18/24.03 tff(11426,plain,
% 36.18/24.03 (~xuntil2p9(s41)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11425, 11421])).
% 36.18/24.03 tff(11427,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11428,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s41) | xuntil2p9(s41) | (~until2p8(s41)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11429,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s41) | xuntil2p9(s41) | (~until2p8(s41))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11428, 11427])).
% 36.18/24.03 tff(11430,plain,
% 36.18/24.03 (xuntil2p9(s41) | (~until2p8(s41))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11429, 10837, 9167])).
% 36.18/24.03 tff(11431,plain,
% 36.18/24.03 (~until2p8(s41)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11430, 11426])).
% 36.18/24.03 tff(11432,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11433,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11434,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s40, s41)) | until2p8(s41) | (~xuntil2p9(s40))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11433, 11432])).
% 36.18/24.03 tff(11435,plain,
% 36.18/24.03 (until2p8(s41) | (~xuntil2p9(s40))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11434, 1308, 10852])).
% 36.18/24.03 tff(11436,plain,
% 36.18/24.03 (~xuntil2p9(s40)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11435, 11431])).
% 36.18/24.03 tff(11437,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11438,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s40) | xuntil2p9(s40) | (~until2p8(s40)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11439,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s40) | xuntil2p9(s40) | (~until2p8(s40))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11438, 11437])).
% 36.18/24.03 tff(11440,plain,
% 36.18/24.03 (xuntil2p9(s40) | (~until2p8(s40))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11439, 10837, 9175])).
% 36.18/24.03 tff(11441,plain,
% 36.18/24.03 (~until2p8(s40)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11440, 11436])).
% 36.18/24.03 tff(11442,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11443,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11444,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s39, s40)) | until2p8(s40) | (~xuntil2p9(s39))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11443, 11442])).
% 36.18/24.03 tff(11445,plain,
% 36.18/24.03 (until2p8(s40) | (~xuntil2p9(s39))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11444, 1277, 10852])).
% 36.18/24.03 tff(11446,plain,
% 36.18/24.03 (~xuntil2p9(s39)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11445, 11441])).
% 36.18/24.03 tff(11447,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11448,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s39) | xuntil2p9(s39) | (~until2p8(s39)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11449,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s39) | xuntil2p9(s39) | (~until2p8(s39))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11448, 11447])).
% 36.18/24.03 tff(11450,plain,
% 36.18/24.03 (xuntil2p9(s39) | (~until2p8(s39))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11449, 10837, 9183])).
% 36.18/24.03 tff(11451,plain,
% 36.18/24.03 (~until2p8(s39)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11450, 11446])).
% 36.18/24.03 tff(11452,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11453,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11454,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s38, s39)) | until2p8(s39) | (~xuntil2p9(s38))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11453, 11452])).
% 36.18/24.03 tff(11455,plain,
% 36.18/24.03 (until2p8(s39) | (~xuntil2p9(s38))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11454, 1249, 10852])).
% 36.18/24.03 tff(11456,plain,
% 36.18/24.03 (~xuntil2p9(s38)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11455, 11451])).
% 36.18/24.03 tff(11457,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11458,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s38) | xuntil2p9(s38) | (~until2p8(s38)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11459,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s38) | xuntil2p9(s38) | (~until2p8(s38))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11458, 11457])).
% 36.18/24.03 tff(11460,plain,
% 36.18/24.03 (xuntil2p9(s38) | (~until2p8(s38))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11459, 10837, 9191])).
% 36.18/24.03 tff(11461,plain,
% 36.18/24.03 (~until2p8(s38)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11460, 11456])).
% 36.18/24.03 tff(11462,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11463,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11464,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s37, s38)) | until2p8(s38) | (~xuntil2p9(s37))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11463, 11462])).
% 36.18/24.03 tff(11465,plain,
% 36.18/24.03 (until2p8(s38) | (~xuntil2p9(s37))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11464, 1218, 10852])).
% 36.18/24.03 tff(11466,plain,
% 36.18/24.03 (~xuntil2p9(s37)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11465, 11461])).
% 36.18/24.03 tff(11467,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11468,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s37) | xuntil2p9(s37) | (~until2p8(s37)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11469,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s37) | xuntil2p9(s37) | (~until2p8(s37))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11468, 11467])).
% 36.18/24.03 tff(11470,plain,
% 36.18/24.03 (xuntil2p9(s37) | (~until2p8(s37))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11469, 10837, 9199])).
% 36.18/24.03 tff(11471,plain,
% 36.18/24.03 (~until2p8(s37)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11470, 11466])).
% 36.18/24.03 tff(11472,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11473,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11474,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s36, s37)) | until2p8(s37) | (~xuntil2p9(s36))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11473, 11472])).
% 36.18/24.03 tff(11475,plain,
% 36.18/24.03 (until2p8(s37) | (~xuntil2p9(s36))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11474, 1190, 10852])).
% 36.18/24.03 tff(11476,plain,
% 36.18/24.03 (~xuntil2p9(s36)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11475, 11471])).
% 36.18/24.03 tff(11477,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11478,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s36) | xuntil2p9(s36) | (~until2p8(s36)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11479,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s36) | xuntil2p9(s36) | (~until2p8(s36))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11478, 11477])).
% 36.18/24.03 tff(11480,plain,
% 36.18/24.03 (xuntil2p9(s36) | (~until2p8(s36))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11479, 10837, 9207])).
% 36.18/24.03 tff(11481,plain,
% 36.18/24.03 (~until2p8(s36)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11480, 11476])).
% 36.18/24.03 tff(11482,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11483,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11484,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s35, s36)) | until2p8(s36) | (~xuntil2p9(s35))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11483, 11482])).
% 36.18/24.03 tff(11485,plain,
% 36.18/24.03 (until2p8(s36) | (~xuntil2p9(s35))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11484, 1159, 10852])).
% 36.18/24.03 tff(11486,plain,
% 36.18/24.03 (~xuntil2p9(s35)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11485, 11481])).
% 36.18/24.03 tff(11487,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11488,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s35) | xuntil2p9(s35) | (~until2p8(s35)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11489,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s35) | xuntil2p9(s35) | (~until2p8(s35))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11488, 11487])).
% 36.18/24.03 tff(11490,plain,
% 36.18/24.03 (xuntil2p9(s35) | (~until2p8(s35))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11489, 10837, 9215])).
% 36.18/24.03 tff(11491,plain,
% 36.18/24.03 (~until2p8(s35)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11490, 11486])).
% 36.18/24.03 tff(11492,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11493,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11494,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s34, s35)) | until2p8(s35) | (~xuntil2p9(s34))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11493, 11492])).
% 36.18/24.03 tff(11495,plain,
% 36.18/24.03 (until2p8(s35) | (~xuntil2p9(s34))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11494, 1131, 10852])).
% 36.18/24.03 tff(11496,plain,
% 36.18/24.03 (~xuntil2p9(s34)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11495, 11491])).
% 36.18/24.03 tff(11497,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11498,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s34) | xuntil2p9(s34) | (~until2p8(s34)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11499,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s34) | xuntil2p9(s34) | (~until2p8(s34))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11498, 11497])).
% 36.18/24.03 tff(11500,plain,
% 36.18/24.03 (xuntil2p9(s34) | (~until2p8(s34))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11499, 10837, 9223])).
% 36.18/24.03 tff(11501,plain,
% 36.18/24.03 (~until2p8(s34)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11500, 11496])).
% 36.18/24.03 tff(11502,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11503,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11504,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s33, s34)) | until2p8(s34) | (~xuntil2p9(s33))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11503, 11502])).
% 36.18/24.03 tff(11505,plain,
% 36.18/24.03 (until2p8(s34) | (~xuntil2p9(s33))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11504, 1100, 10852])).
% 36.18/24.03 tff(11506,plain,
% 36.18/24.03 (~xuntil2p9(s33)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11505, 11501])).
% 36.18/24.03 tff(11507,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11508,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s33) | xuntil2p9(s33) | (~until2p8(s33)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11509,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s33) | xuntil2p9(s33) | (~until2p8(s33))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11508, 11507])).
% 36.18/24.03 tff(11510,plain,
% 36.18/24.03 (xuntil2p9(s33) | (~until2p8(s33))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11509, 10837, 9231])).
% 36.18/24.03 tff(11511,plain,
% 36.18/24.03 (~until2p8(s33)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11510, 11506])).
% 36.18/24.03 tff(11512,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11513,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11514,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s32, s33)) | until2p8(s33) | (~xuntil2p9(s32))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11513, 11512])).
% 36.18/24.03 tff(11515,plain,
% 36.18/24.03 (until2p8(s33) | (~xuntil2p9(s32))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11514, 1072, 10852])).
% 36.18/24.03 tff(11516,plain,
% 36.18/24.03 (~xuntil2p9(s32)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11515, 11511])).
% 36.18/24.03 tff(11517,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11518,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s32) | xuntil2p9(s32) | (~until2p8(s32)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11519,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s32) | xuntil2p9(s32) | (~until2p8(s32))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11518, 11517])).
% 36.18/24.03 tff(11520,plain,
% 36.18/24.03 (xuntil2p9(s32) | (~until2p8(s32))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11519, 10837, 9239])).
% 36.18/24.03 tff(11521,plain,
% 36.18/24.03 (~until2p8(s32)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11520, 11516])).
% 36.18/24.03 tff(11522,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11523,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11524,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s31, s32)) | until2p8(s32) | (~xuntil2p9(s31))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11523, 11522])).
% 36.18/24.03 tff(11525,plain,
% 36.18/24.03 (until2p8(s32) | (~xuntil2p9(s31))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11524, 1041, 10852])).
% 36.18/24.03 tff(11526,plain,
% 36.18/24.03 (~xuntil2p9(s31)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11525, 11521])).
% 36.18/24.03 tff(11527,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11528,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s31) | xuntil2p9(s31) | (~until2p8(s31)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11529,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s31) | xuntil2p9(s31) | (~until2p8(s31))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11528, 11527])).
% 36.18/24.03 tff(11530,plain,
% 36.18/24.03 (xuntil2p9(s31) | (~until2p8(s31))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11529, 10837, 9247])).
% 36.18/24.03 tff(11531,plain,
% 36.18/24.03 (~until2p8(s31)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11530, 11526])).
% 36.18/24.03 tff(11532,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11533,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11534,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s30, s31)) | until2p8(s31) | (~xuntil2p9(s30))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11533, 11532])).
% 36.18/24.03 tff(11535,plain,
% 36.18/24.03 (until2p8(s31) | (~xuntil2p9(s30))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11534, 1013, 10852])).
% 36.18/24.03 tff(11536,plain,
% 36.18/24.03 (~xuntil2p9(s30)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11535, 11531])).
% 36.18/24.03 tff(11537,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11538,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s30) | xuntil2p9(s30) | (~until2p8(s30)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11539,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s30) | xuntil2p9(s30) | (~until2p8(s30))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11538, 11537])).
% 36.18/24.03 tff(11540,plain,
% 36.18/24.03 (xuntil2p9(s30) | (~until2p8(s30))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11539, 10837, 9255])).
% 36.18/24.03 tff(11541,plain,
% 36.18/24.03 (~until2p8(s30)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11540, 11536])).
% 36.18/24.03 tff(11542,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11543,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11544,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s29, s30)) | until2p8(s30) | (~xuntil2p9(s29))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11543, 11542])).
% 36.18/24.03 tff(11545,plain,
% 36.18/24.03 (until2p8(s30) | (~xuntil2p9(s29))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11544, 982, 10852])).
% 36.18/24.03 tff(11546,plain,
% 36.18/24.03 (~xuntil2p9(s29)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11545, 11541])).
% 36.18/24.03 tff(11547,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11548,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s29) | xuntil2p9(s29) | (~until2p8(s29)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11549,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s29) | xuntil2p9(s29) | (~until2p8(s29))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11548, 11547])).
% 36.18/24.03 tff(11550,plain,
% 36.18/24.03 (xuntil2p9(s29) | (~until2p8(s29))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11549, 10837, 9263])).
% 36.18/24.03 tff(11551,plain,
% 36.18/24.03 (~until2p8(s29)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11550, 11546])).
% 36.18/24.03 tff(11552,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11553,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11554,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s28, s29)) | until2p8(s29) | (~xuntil2p9(s28))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11553, 11552])).
% 36.18/24.03 tff(11555,plain,
% 36.18/24.03 (until2p8(s29) | (~xuntil2p9(s28))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11554, 954, 10852])).
% 36.18/24.03 tff(11556,plain,
% 36.18/24.03 (~xuntil2p9(s28)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11555, 11551])).
% 36.18/24.03 tff(11557,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11558,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s28) | xuntil2p9(s28) | (~until2p8(s28)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11559,plain,
% 36.18/24.03 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s28) | xuntil2p9(s28) | (~until2p8(s28))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11558, 11557])).
% 36.18/24.03 tff(11560,plain,
% 36.18/24.03 (xuntil2p9(s28) | (~until2p8(s28))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11559, 10837, 9271])).
% 36.18/24.03 tff(11561,plain,
% 36.18/24.03 (~until2p8(s28)),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11560, 11556])).
% 36.18/24.03 tff(11562,plain,
% 36.18/24.03 (((~![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)))),
% 36.18/24.03 inference(rewrite,[status(thm)],[])).
% 36.18/24.03 tff(11563,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27)))),
% 36.18/24.03 inference(quant_inst,[status(thm)],[])).
% 36.18/24.03 tff(11564,plain,
% 36.18/24.03 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s27, s28)) | until2p8(s28) | (~xuntil2p9(s27))),
% 36.18/24.03 inference(modus_ponens,[status(thm)],[11563, 11562])).
% 36.18/24.03 tff(11565,plain,
% 36.18/24.03 (until2p8(s28) | (~xuntil2p9(s27))),
% 36.18/24.03 inference(unit_resolution,[status(thm)],[11564, 925, 10852])).
% 36.18/24.04 tff(11566,plain,
% 36.18/24.04 (~xuntil2p9(s27)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11565, 11561])).
% 36.18/24.04 tff(11567,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11568,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s27) | xuntil2p9(s27) | (~until2p8(s27)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11569,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s27) | xuntil2p9(s27) | (~until2p8(s27))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11568, 11567])).
% 36.18/24.04 tff(11570,plain,
% 36.18/24.04 (xuntil2p9(s27) | (~until2p8(s27))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11569, 10837, 9279])).
% 36.18/24.04 tff(11571,plain,
% 36.18/24.04 (~until2p8(s27)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11570, 11566])).
% 36.18/24.04 tff(11572,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11573,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11574,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s26, s27)) | until2p8(s27) | (~xuntil2p9(s26))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11573, 11572])).
% 36.18/24.04 tff(11575,plain,
% 36.18/24.04 (until2p8(s27) | (~xuntil2p9(s26))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11574, 897, 10852])).
% 36.18/24.04 tff(11576,plain,
% 36.18/24.04 (~xuntil2p9(s26)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11575, 11571])).
% 36.18/24.04 tff(11577,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11578,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s26) | xuntil2p9(s26) | (~until2p8(s26)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11579,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s26) | xuntil2p9(s26) | (~until2p8(s26))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11578, 11577])).
% 36.18/24.04 tff(11580,plain,
% 36.18/24.04 (xuntil2p9(s26) | (~until2p8(s26))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11579, 10837, 9287])).
% 36.18/24.04 tff(11581,plain,
% 36.18/24.04 (~until2p8(s26)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11580, 11576])).
% 36.18/24.04 tff(11582,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11583,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11584,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s25, s26)) | until2p8(s26) | (~xuntil2p9(s25))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11583, 11582])).
% 36.18/24.04 tff(11585,plain,
% 36.18/24.04 (until2p8(s26) | (~xuntil2p9(s25))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11584, 866, 10852])).
% 36.18/24.04 tff(11586,plain,
% 36.18/24.04 (~xuntil2p9(s25)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11585, 11581])).
% 36.18/24.04 tff(11587,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11588,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s25) | xuntil2p9(s25) | (~until2p8(s25)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11589,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s25) | xuntil2p9(s25) | (~until2p8(s25))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11588, 11587])).
% 36.18/24.04 tff(11590,plain,
% 36.18/24.04 (xuntil2p9(s25) | (~until2p8(s25))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11589, 10837, 9295])).
% 36.18/24.04 tff(11591,plain,
% 36.18/24.04 (~until2p8(s25)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11590, 11586])).
% 36.18/24.04 tff(11592,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11593,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11594,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s24, s25)) | until2p8(s25) | (~xuntil2p9(s24))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11593, 11592])).
% 36.18/24.04 tff(11595,plain,
% 36.18/24.04 (until2p8(s25) | (~xuntil2p9(s24))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11594, 840, 10852])).
% 36.18/24.04 tff(11596,plain,
% 36.18/24.04 (~xuntil2p9(s24)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11595, 11591])).
% 36.18/24.04 tff(11597,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11598,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s24) | xuntil2p9(s24) | (~until2p8(s24)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11599,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s24) | xuntil2p9(s24) | (~until2p8(s24))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11598, 11597])).
% 36.18/24.04 tff(11600,plain,
% 36.18/24.04 (xuntil2p9(s24) | (~until2p8(s24))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11599, 10837, 9303])).
% 36.18/24.04 tff(11601,plain,
% 36.18/24.04 (~until2p8(s24)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11600, 11596])).
% 36.18/24.04 tff(11602,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11603,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11604,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s23, s24)) | until2p8(s24) | (~xuntil2p9(s23))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11603, 11602])).
% 36.18/24.04 tff(11605,plain,
% 36.18/24.04 (until2p8(s24) | (~xuntil2p9(s23))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11604, 809, 10852])).
% 36.18/24.04 tff(11606,plain,
% 36.18/24.04 (~xuntil2p9(s23)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11605, 11601])).
% 36.18/24.04 tff(11607,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11608,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s23) | xuntil2p9(s23) | (~until2p8(s23)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11609,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s23) | xuntil2p9(s23) | (~until2p8(s23))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11608, 11607])).
% 36.18/24.04 tff(11610,plain,
% 36.18/24.04 (xuntil2p9(s23) | (~until2p8(s23))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11609, 10837, 9311])).
% 36.18/24.04 tff(11611,plain,
% 36.18/24.04 (~until2p8(s23)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11610, 11606])).
% 36.18/24.04 tff(11612,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11613,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11614,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s22, s23)) | until2p8(s23) | (~xuntil2p9(s22))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11613, 11612])).
% 36.18/24.04 tff(11615,plain,
% 36.18/24.04 (until2p8(s23) | (~xuntil2p9(s22))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11614, 781, 10852])).
% 36.18/24.04 tff(11616,plain,
% 36.18/24.04 (~xuntil2p9(s22)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11615, 11611])).
% 36.18/24.04 tff(11617,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11618,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s22) | xuntil2p9(s22) | (~until2p8(s22)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11619,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s22) | xuntil2p9(s22) | (~until2p8(s22))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11618, 11617])).
% 36.18/24.04 tff(11620,plain,
% 36.18/24.04 (xuntil2p9(s22) | (~until2p8(s22))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11619, 10837, 9319])).
% 36.18/24.04 tff(11621,plain,
% 36.18/24.04 (~until2p8(s22)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11620, 11616])).
% 36.18/24.04 tff(11622,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11623,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11624,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s21, s22)) | until2p8(s22) | (~xuntil2p9(s21))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11623, 11622])).
% 36.18/24.04 tff(11625,plain,
% 36.18/24.04 (until2p8(s22) | (~xuntil2p9(s21))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11624, 750, 10852])).
% 36.18/24.04 tff(11626,plain,
% 36.18/24.04 (~xuntil2p9(s21)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11625, 11621])).
% 36.18/24.04 tff(11627,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11628,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s21) | xuntil2p9(s21) | (~until2p8(s21)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11629,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s21) | xuntil2p9(s21) | (~until2p8(s21))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11628, 11627])).
% 36.18/24.04 tff(11630,plain,
% 36.18/24.04 (xuntil2p9(s21) | (~until2p8(s21))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11629, 10837, 9327])).
% 36.18/24.04 tff(11631,plain,
% 36.18/24.04 (~until2p8(s21)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11630, 11626])).
% 36.18/24.04 tff(11632,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11633,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11634,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s20, s21)) | until2p8(s21) | (~xuntil2p9(s20))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11633, 11632])).
% 36.18/24.04 tff(11635,plain,
% 36.18/24.04 (until2p8(s21) | (~xuntil2p9(s20))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11634, 722, 10852])).
% 36.18/24.04 tff(11636,plain,
% 36.18/24.04 (~xuntil2p9(s20)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11635, 11631])).
% 36.18/24.04 tff(11637,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11638,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s20) | xuntil2p9(s20) | (~until2p8(s20)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11639,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s20) | xuntil2p9(s20) | (~until2p8(s20))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11638, 11637])).
% 36.18/24.04 tff(11640,plain,
% 36.18/24.04 (xuntil2p9(s20) | (~until2p8(s20))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11639, 10837, 9335])).
% 36.18/24.04 tff(11641,plain,
% 36.18/24.04 (~until2p8(s20)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11640, 11636])).
% 36.18/24.04 tff(11642,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11643,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11644,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s19, s20)) | until2p8(s20) | (~xuntil2p9(s19))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11643, 11642])).
% 36.18/24.04 tff(11645,plain,
% 36.18/24.04 (until2p8(s20) | (~xuntil2p9(s19))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11644, 693, 10852])).
% 36.18/24.04 tff(11646,plain,
% 36.18/24.04 (~xuntil2p9(s19)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11645, 11641])).
% 36.18/24.04 tff(11647,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11648,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s19) | xuntil2p9(s19) | (~until2p8(s19)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11649,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s19) | xuntil2p9(s19) | (~until2p8(s19))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11648, 11647])).
% 36.18/24.04 tff(11650,plain,
% 36.18/24.04 (xuntil2p9(s19) | (~until2p8(s19))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11649, 10837, 9343])).
% 36.18/24.04 tff(11651,plain,
% 36.18/24.04 (~until2p8(s19)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11650, 11646])).
% 36.18/24.04 tff(11652,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11653,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11654,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s18, s19)) | until2p8(s19) | (~xuntil2p9(s18))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11653, 11652])).
% 36.18/24.04 tff(11655,plain,
% 36.18/24.04 (until2p8(s19) | (~xuntil2p9(s18))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11654, 665, 10852])).
% 36.18/24.04 tff(11656,plain,
% 36.18/24.04 (~xuntil2p9(s18)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11655, 11651])).
% 36.18/24.04 tff(11657,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11658,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s18) | xuntil2p9(s18) | (~until2p8(s18)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11659,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s18) | xuntil2p9(s18) | (~until2p8(s18))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11658, 11657])).
% 36.18/24.04 tff(11660,plain,
% 36.18/24.04 (xuntil2p9(s18) | (~until2p8(s18))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11659, 10837, 9351])).
% 36.18/24.04 tff(11661,plain,
% 36.18/24.04 (~until2p8(s18)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11660, 11656])).
% 36.18/24.04 tff(11662,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11663,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11664,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s17, s18)) | until2p8(s18) | (~xuntil2p9(s17))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11663, 11662])).
% 36.18/24.04 tff(11665,plain,
% 36.18/24.04 (until2p8(s18) | (~xuntil2p9(s17))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11664, 634, 10852])).
% 36.18/24.04 tff(11666,plain,
% 36.18/24.04 (~xuntil2p9(s17)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11665, 11661])).
% 36.18/24.04 tff(11667,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11668,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s17) | xuntil2p9(s17) | (~until2p8(s17)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11669,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s17) | xuntil2p9(s17) | (~until2p8(s17))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11668, 11667])).
% 36.18/24.04 tff(11670,plain,
% 36.18/24.04 (xuntil2p9(s17) | (~until2p8(s17))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11669, 10837, 9359])).
% 36.18/24.04 tff(11671,plain,
% 36.18/24.04 (~until2p8(s17)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11670, 11666])).
% 36.18/24.04 tff(11672,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11673,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11674,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s16, s17)) | until2p8(s17) | (~xuntil2p9(s16))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11673, 11672])).
% 36.18/24.04 tff(11675,plain,
% 36.18/24.04 (until2p8(s17) | (~xuntil2p9(s16))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11674, 606, 10852])).
% 36.18/24.04 tff(11676,plain,
% 36.18/24.04 (~xuntil2p9(s16)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11675, 11671])).
% 36.18/24.04 tff(11677,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11678,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s16) | xuntil2p9(s16) | (~until2p8(s16)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11679,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s16) | xuntil2p9(s16) | (~until2p8(s16))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11678, 11677])).
% 36.18/24.04 tff(11680,plain,
% 36.18/24.04 (xuntil2p9(s16) | (~until2p8(s16))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11679, 10837, 9367])).
% 36.18/24.04 tff(11681,plain,
% 36.18/24.04 (~until2p8(s16)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11680, 11676])).
% 36.18/24.04 tff(11682,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11683,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11684,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s15, s16)) | until2p8(s16) | (~xuntil2p9(s15))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11683, 11682])).
% 36.18/24.04 tff(11685,plain,
% 36.18/24.04 (until2p8(s16) | (~xuntil2p9(s15))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11684, 577, 10852])).
% 36.18/24.04 tff(11686,plain,
% 36.18/24.04 (~xuntil2p9(s15)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11685, 11681])).
% 36.18/24.04 tff(11687,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11688,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s15) | xuntil2p9(s15) | (~until2p8(s15)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11689,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s15) | xuntil2p9(s15) | (~until2p8(s15))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11688, 11687])).
% 36.18/24.04 tff(11690,plain,
% 36.18/24.04 (xuntil2p9(s15) | (~until2p8(s15))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11689, 10837, 9375])).
% 36.18/24.04 tff(11691,plain,
% 36.18/24.04 (~until2p8(s15)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11690, 11686])).
% 36.18/24.04 tff(11692,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11693,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11694,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s14, s15)) | until2p8(s15) | (~xuntil2p9(s14))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11693, 11692])).
% 36.18/24.04 tff(11695,plain,
% 36.18/24.04 (until2p8(s15) | (~xuntil2p9(s14))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11694, 549, 10852])).
% 36.18/24.04 tff(11696,plain,
% 36.18/24.04 (~xuntil2p9(s14)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11695, 11691])).
% 36.18/24.04 tff(11697,plain,
% 36.18/24.04 (~always5(s14)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9383, 9375])).
% 36.18/24.04 tff(11698,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11699,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s14) | xuntil2p9(s14) | (~until2p8(s14)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11700,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s14) | xuntil2p9(s14) | (~until2p8(s14))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11699, 11698])).
% 36.18/24.04 tff(11701,plain,
% 36.18/24.04 (xuntil2p9(s14) | (~until2p8(s14))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11700, 10837, 11697])).
% 36.18/24.04 tff(11702,plain,
% 36.18/24.04 (~until2p8(s14)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11701, 11696])).
% 36.18/24.04 tff(11703,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11704,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11705,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s13, s14)) | until2p8(s14) | (~xuntil2p9(s13))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11704, 11703])).
% 36.18/24.04 tff(11706,plain,
% 36.18/24.04 (until2p8(s14) | (~xuntil2p9(s13))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11705, 518, 10852])).
% 36.18/24.04 tff(11707,plain,
% 36.18/24.04 (~xuntil2p9(s13)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11706, 11702])).
% 36.18/24.04 tff(11708,plain,
% 36.18/24.04 (~always5(s13)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9437, 11697])).
% 36.18/24.04 tff(11709,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11710,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s13) | xuntil2p9(s13) | (~until2p8(s13)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11711,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s13) | xuntil2p9(s13) | (~until2p8(s13))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11710, 11709])).
% 36.18/24.04 tff(11712,plain,
% 36.18/24.04 (xuntil2p9(s13) | (~until2p8(s13))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11711, 10837, 11708])).
% 36.18/24.04 tff(11713,plain,
% 36.18/24.04 (~until2p8(s13)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11712, 11707])).
% 36.18/24.04 tff(11714,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11715,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11716,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s12, s13)) | until2p8(s13) | (~xuntil2p9(s12))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11715, 11714])).
% 36.18/24.04 tff(11717,plain,
% 36.18/24.04 (until2p8(s13) | (~xuntil2p9(s12))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11716, 490, 10852])).
% 36.18/24.04 tff(11718,plain,
% 36.18/24.04 (~xuntil2p9(s12)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11717, 11713])).
% 36.18/24.04 tff(11719,plain,
% 36.18/24.04 (~always5(s12)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9458, 11708])).
% 36.18/24.04 tff(11720,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11721,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s12) | xuntil2p9(s12) | (~until2p8(s12)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11722,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s12) | xuntil2p9(s12) | (~until2p8(s12))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11721, 11720])).
% 36.18/24.04 tff(11723,plain,
% 36.18/24.04 (xuntil2p9(s12) | (~until2p8(s12))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11722, 10837, 11719])).
% 36.18/24.04 tff(11724,plain,
% 36.18/24.04 (~until2p8(s12)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11723, 11718])).
% 36.18/24.04 tff(11725,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11726,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11727,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s11, s12)) | until2p8(s12) | (~xuntil2p9(s11))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11726, 11725])).
% 36.18/24.04 tff(11728,plain,
% 36.18/24.04 (until2p8(s12) | (~xuntil2p9(s11))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11727, 459, 10852])).
% 36.18/24.04 tff(11729,plain,
% 36.18/24.04 (~xuntil2p9(s11)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11728, 11724])).
% 36.18/24.04 tff(11730,plain,
% 36.18/24.04 (~always5(s11)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9479, 11719])).
% 36.18/24.04 tff(11731,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11732,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s11) | xuntil2p9(s11) | (~until2p8(s11)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11733,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s11) | xuntil2p9(s11) | (~until2p8(s11))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11732, 11731])).
% 36.18/24.04 tff(11734,plain,
% 36.18/24.04 (xuntil2p9(s11) | (~until2p8(s11))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11733, 10837, 11730])).
% 36.18/24.04 tff(11735,plain,
% 36.18/24.04 (~until2p8(s11)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11734, 11729])).
% 36.18/24.04 tff(11736,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11737,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11738,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s10, s11)) | until2p8(s11) | (~xuntil2p9(s10))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11737, 11736])).
% 36.18/24.04 tff(11739,plain,
% 36.18/24.04 (until2p8(s11) | (~xuntil2p9(s10))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11738, 431, 10852])).
% 36.18/24.04 tff(11740,plain,
% 36.18/24.04 (~xuntil2p9(s10)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11739, 11735])).
% 36.18/24.04 tff(11741,plain,
% 36.18/24.04 (~always5(s10)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9500, 11730])).
% 36.18/24.04 tff(11742,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11743,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s10) | xuntil2p9(s10) | (~until2p8(s10)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11744,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s10) | xuntil2p9(s10) | (~until2p8(s10))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11743, 11742])).
% 36.18/24.04 tff(11745,plain,
% 36.18/24.04 (xuntil2p9(s10) | (~until2p8(s10))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11744, 10837, 11741])).
% 36.18/24.04 tff(11746,plain,
% 36.18/24.04 (~until2p8(s10)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11745, 11740])).
% 36.18/24.04 tff(11747,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11748,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11749,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s9, s10)) | until2p8(s10) | (~xuntil2p9(s9))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11748, 11747])).
% 36.18/24.04 tff(11750,plain,
% 36.18/24.04 (until2p8(s10) | (~xuntil2p9(s9))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11749, 400, 10852])).
% 36.18/24.04 tff(11751,plain,
% 36.18/24.04 (~xuntil2p9(s9)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11750, 11746])).
% 36.18/24.04 tff(11752,plain,
% 36.18/24.04 (~always5(s9)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9521, 11741])).
% 36.18/24.04 tff(11753,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11754,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s9) | xuntil2p9(s9) | (~until2p8(s9)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11755,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s9) | xuntil2p9(s9) | (~until2p8(s9))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11754, 11753])).
% 36.18/24.04 tff(11756,plain,
% 36.18/24.04 (xuntil2p9(s9) | (~until2p8(s9))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11755, 10837, 11752])).
% 36.18/24.04 tff(11757,plain,
% 36.18/24.04 (~until2p8(s9)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11756, 11751])).
% 36.18/24.04 tff(11758,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11759,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11760,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s8, s9)) | until2p8(s9) | (~xuntil2p9(s8))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11759, 11758])).
% 36.18/24.04 tff(11761,plain,
% 36.18/24.04 (until2p8(s9) | (~xuntil2p9(s8))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11760, 374, 10852])).
% 36.18/24.04 tff(11762,plain,
% 36.18/24.04 (~xuntil2p9(s8)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11761, 11757])).
% 36.18/24.04 tff(11763,plain,
% 36.18/24.04 (~always5(s8)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9542, 11752])).
% 36.18/24.04 tff(11764,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11765,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s8) | xuntil2p9(s8) | (~until2p8(s8)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11766,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s8) | xuntil2p9(s8) | (~until2p8(s8))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11765, 11764])).
% 36.18/24.04 tff(11767,plain,
% 36.18/24.04 (xuntil2p9(s8) | (~until2p8(s8))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11766, 10837, 11763])).
% 36.18/24.04 tff(11768,plain,
% 36.18/24.04 (~until2p8(s8)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11767, 11762])).
% 36.18/24.04 tff(11769,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11770,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11771,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s7, s8)) | until2p8(s8) | (~xuntil2p9(s7))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11770, 11769])).
% 36.18/24.04 tff(11772,plain,
% 36.18/24.04 (until2p8(s8) | (~xuntil2p9(s7))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11771, 345, 10852])).
% 36.18/24.04 tff(11773,plain,
% 36.18/24.04 (~xuntil2p9(s7)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11772, 11768])).
% 36.18/24.04 tff(11774,plain,
% 36.18/24.04 (~always5(s7)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9558, 11763])).
% 36.18/24.04 tff(11775,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11776,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s7) | xuntil2p9(s7) | (~until2p8(s7)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11777,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s7) | xuntil2p9(s7) | (~until2p8(s7))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11776, 11775])).
% 36.18/24.04 tff(11778,plain,
% 36.18/24.04 (xuntil2p9(s7) | (~until2p8(s7))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11777, 10837, 11774])).
% 36.18/24.04 tff(11779,plain,
% 36.18/24.04 (~until2p8(s7)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11778, 11773])).
% 36.18/24.04 tff(11780,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11781,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11782,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s6, s7)) | until2p8(s7) | (~xuntil2p9(s6))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11781, 11780])).
% 36.18/24.04 tff(11783,plain,
% 36.18/24.04 (until2p8(s7) | (~xuntil2p9(s6))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11782, 317, 10852])).
% 36.18/24.04 tff(11784,plain,
% 36.18/24.04 (~xuntil2p9(s6)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11783, 11779])).
% 36.18/24.04 tff(11785,plain,
% 36.18/24.04 (~always5(s6)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9566, 11774])).
% 36.18/24.04 tff(11786,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11787,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s6) | xuntil2p9(s6) | (~until2p8(s6)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11788,plain,
% 36.18/24.04 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s6) | xuntil2p9(s6) | (~until2p8(s6))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11787, 11786])).
% 36.18/24.04 tff(11789,plain,
% 36.18/24.04 (xuntil2p9(s6) | (~until2p8(s6))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11788, 10837, 11785])).
% 36.18/24.04 tff(11790,plain,
% 36.18/24.04 (~until2p8(s6)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11789, 11784])).
% 36.18/24.04 tff(11791,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.04 inference(rewrite,[status(thm)],[])).
% 36.18/24.04 tff(11792,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5)))),
% 36.18/24.04 inference(quant_inst,[status(thm)],[])).
% 36.18/24.04 tff(11793,plain,
% 36.18/24.04 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s5, s6)) | until2p8(s6) | (~xuntil2p9(s5))),
% 36.18/24.04 inference(modus_ponens,[status(thm)],[11792, 11791])).
% 36.18/24.04 tff(11794,plain,
% 36.18/24.04 (until2p8(s6) | (~xuntil2p9(s5))),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11793, 88, 10852])).
% 36.18/24.04 tff(11795,plain,
% 36.18/24.04 (~xuntil2p9(s5)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[11794, 11790])).
% 36.18/24.04 tff(11796,plain,
% 36.18/24.04 (~always5(s5)),
% 36.18/24.04 inference(unit_resolution,[status(thm)],[9574, 11785])).
% 36.18/24.04 tff(11797,plain,
% 36.18/24.04 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11798,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s5) | xuntil2p9(s5) | (~until2p8(s5)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11799,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s5) | xuntil2p9(s5) | (~until2p8(s5))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11798, 11797])).
% 36.18/24.05 tff(11800,plain,
% 36.18/24.05 (xuntil2p9(s5) | (~until2p8(s5))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11799, 10837, 11796])).
% 36.18/24.05 tff(11801,plain,
% 36.18/24.05 (~until2p8(s5)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11800, 11795])).
% 36.18/24.05 tff(11802,plain,
% 36.18/24.05 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11803,plain,
% 36.18/24.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11804,plain,
% 36.18/24.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s4, s5)) | until2p8(s5) | (~xuntil2p9(s4))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11803, 11802])).
% 36.18/24.05 tff(11805,plain,
% 36.18/24.05 (until2p8(s5) | (~xuntil2p9(s4))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11804, 99, 10852])).
% 36.18/24.05 tff(11806,plain,
% 36.18/24.05 (~xuntil2p9(s4)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11805, 11801])).
% 36.18/24.05 tff(11807,plain,
% 36.18/24.05 (~always5(s4)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[9582, 11796])).
% 36.18/24.05 tff(11808,plain,
% 36.18/24.05 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11809,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s4) | xuntil2p9(s4) | (~until2p8(s4)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11810,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s4) | xuntil2p9(s4) | (~until2p8(s4))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11809, 11808])).
% 36.18/24.05 tff(11811,plain,
% 36.18/24.05 (xuntil2p9(s4) | (~until2p8(s4))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11810, 10837, 11807])).
% 36.18/24.05 tff(11812,plain,
% 36.18/24.05 (~until2p8(s4)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11811, 11806])).
% 36.18/24.05 tff(11813,plain,
% 36.18/24.05 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11814,plain,
% 36.18/24.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11815,plain,
% 36.18/24.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s3, s4)) | until2p8(s4) | (~xuntil2p9(s3))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11814, 11813])).
% 36.18/24.05 tff(11816,plain,
% 36.18/24.05 (until2p8(s4) | (~xuntil2p9(s3))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11815, 110, 10852])).
% 36.18/24.05 tff(11817,plain,
% 36.18/24.05 (~xuntil2p9(s3)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11816, 11812])).
% 36.18/24.05 tff(11818,plain,
% 36.18/24.05 (~always5(s3)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[9590, 11807])).
% 36.18/24.05 tff(11819,plain,
% 36.18/24.05 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11820,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s3) | xuntil2p9(s3) | (~until2p8(s3)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11821,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s3) | xuntil2p9(s3) | (~until2p8(s3))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11820, 11819])).
% 36.18/24.05 tff(11822,plain,
% 36.18/24.05 (xuntil2p9(s3) | (~until2p8(s3))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11821, 10837, 11818])).
% 36.18/24.05 tff(11823,plain,
% 36.18/24.05 (~until2p8(s3)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11822, 11817])).
% 36.18/24.05 tff(11824,plain,
% 36.18/24.05 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11825,plain,
% 36.18/24.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11826,plain,
% 36.18/24.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s2, s3)) | until2p8(s3) | (~xuntil2p9(s2))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11825, 11824])).
% 36.18/24.05 tff(11827,plain,
% 36.18/24.05 (until2p8(s3) | (~xuntil2p9(s2))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11826, 121, 10852])).
% 36.18/24.05 tff(11828,plain,
% 36.18/24.05 (~xuntil2p9(s2)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11827, 11823])).
% 36.18/24.05 tff(11829,plain,
% 36.18/24.05 (~always5(s2)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[9598, 11818])).
% 36.18/24.05 tff(11830,plain,
% 36.18/24.05 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11831,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s2) | xuntil2p9(s2) | (~until2p8(s2)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11832,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s2) | xuntil2p9(s2) | (~until2p8(s2))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11831, 11830])).
% 36.18/24.05 tff(11833,plain,
% 36.18/24.05 (xuntil2p9(s2) | (~until2p8(s2))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11832, 10837, 11829])).
% 36.18/24.05 tff(11834,plain,
% 36.18/24.05 (~until2p8(s2)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11833, 11828])).
% 36.18/24.05 tff(11835,plain,
% 36.18/24.05 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11836,plain,
% 36.18/24.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11837,plain,
% 36.18/24.05 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s1, s2)) | until2p8(s2) | (~xuntil2p9(s1))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11836, 11835])).
% 36.18/24.05 tff(11838,plain,
% 36.18/24.05 (until2p8(s2) | (~xuntil2p9(s1))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11837, 132, 10852])).
% 36.18/24.05 tff(11839,plain,
% 36.18/24.05 (~xuntil2p9(s1)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11838, 11834])).
% 36.18/24.05 tff(11840,assumption,(~always5(s1)), introduced(assumption)).
% 36.18/24.05 tff(11841,plain,
% 36.18/24.05 (((~![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)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11842,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s1) | xuntil2p9(s1) | (~until2p8(s1)))),
% 36.18/24.05 inference(quant_inst,[status(thm)],[])).
% 36.18/24.05 tff(11843,plain,
% 36.18/24.05 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s1) | xuntil2p9(s1) | (~until2p8(s1))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11842, 11841])).
% 36.18/24.05 tff(11844,plain,
% 36.18/24.05 (xuntil2p9(s1) | (~until2p8(s1))),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11843, 10837, 11840])).
% 36.18/24.05 tff(11845,plain,
% 36.18/24.05 (~until2p8(s1)),
% 36.18/24.05 inference(unit_resolution,[status(thm)],[11844, 11839])).
% 36.18/24.05 tff(11846,plain,
% 36.18/24.05 (^[Y: $i, X: $i] : refl(((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)) <=> ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y)))),
% 36.18/24.05 inference(bind,[status(th)],[])).
% 36.18/24.05 tff(11847,plain,
% 36.18/24.05 (![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))),
% 36.18/24.05 inference(quant_intro,[status(thm)],[11846])).
% 36.18/24.05 tff(11848,plain,
% 36.18/24.05 (![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))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11849,plain,
% 36.18/24.05 (^[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))))),
% 36.18/24.05 inference(bind,[status(th)],[])).
% 36.18/24.05 tff(11850,plain,
% 36.18/24.05 (![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))),
% 36.18/24.05 inference(quant_intro,[status(thm)],[11849])).
% 36.18/24.05 tff(11851,axiom,(![Y: $i, X: $i] : (((until2p8(Y) | (~trans(X, Y))) | (~last(X))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty7')).
% 36.18/24.05 tff(11852,plain,
% 36.18/24.05 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11851, 11850])).
% 36.18/24.05 tff(11853,plain,
% 36.18/24.05 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11852, 11848])).
% 36.18/24.05 tff(11854,plain,(
% 36.18/24.05 ![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 36.18/24.05 inference(skolemize,[status(sab)],[11853])).
% 36.18/24.05 tff(11855,plain,
% 36.18/24.05 (![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))),
% 36.18/24.05 inference(modus_ponens,[status(thm)],[11854, 11847])).
% 36.18/24.05 tff(11856,assumption,(xuntil7(s99)), introduced(assumption)).
% 36.18/24.05 tff(11857,assumption,(~until2p8(s38)), introduced(assumption)).
% 36.18/24.05 tff(11858,assumption,(trans(s99, s38)), introduced(assumption)).
% 36.18/24.05 tff(11859,plain,
% 36.18/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38)))),
% 36.18/24.05 inference(rewrite,[status(thm)],[])).
% 36.18/24.05 tff(11860,plain,
% 36.18/24.05 (((~last(s99)) | (~trans(s99, s38)) | (~xuntil7(s99)) | until2p8(s38)) <=> (until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11861,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s38)) | (~xuntil7(s99)) | until2p8(s38))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11860])).
% 36.24/24.05 tff(11862,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s38)) | (~xuntil7(s99)) | until2p8(s38))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11861, 11859])).
% 36.24/24.05 tff(11863,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s38)) | (~xuntil7(s99)) | until2p8(s38))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11864,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s38) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s38))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11863, 11862])).
% 36.24/24.05 tff(11865,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11864, 10823, 11858, 11855, 11857, 11856])).
% 36.24/24.05 tff(11866,plain,((~trans(s99, s38)) | until2p8(s38) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11867,plain,
% 36.24/24.05 (~trans(s99, s38)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11866, 11461, 10813])).
% 36.24/24.05 tff(11868,assumption,(~until2p8(s86)), introduced(assumption)).
% 36.24/24.05 tff(11869,assumption,(trans(s99, s86)), introduced(assumption)).
% 36.24/24.05 tff(11870,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11871,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s86)) | (~xuntil7(s99)) | until2p8(s86)) <=> (until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11872,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s86)) | (~xuntil7(s99)) | until2p8(s86))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11871])).
% 36.24/24.05 tff(11873,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s86)) | (~xuntil7(s99)) | until2p8(s86))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11872, 11870])).
% 36.24/24.05 tff(11874,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s86)) | (~xuntil7(s99)) | until2p8(s86))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11875,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s86) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s86))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11874, 11873])).
% 36.24/24.05 tff(11876,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11875, 10823, 11869, 11855, 11868, 11856])).
% 36.24/24.05 tff(11877,plain,((~trans(s99, s86)) | until2p8(s86) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11878,plain,
% 36.24/24.05 (~trans(s99, s86)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11877, 10981, 10813])).
% 36.24/24.05 tff(11879,assumption,(~until2p8(s63)), introduced(assumption)).
% 36.24/24.05 tff(11880,assumption,(trans(s99, s63)), introduced(assumption)).
% 36.24/24.05 tff(11881,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11882,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s63)) | (~xuntil7(s99)) | until2p8(s63)) <=> (until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11883,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s63)) | (~xuntil7(s99)) | until2p8(s63))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11882])).
% 36.24/24.05 tff(11884,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s63)) | (~xuntil7(s99)) | until2p8(s63))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11883, 11881])).
% 36.24/24.05 tff(11885,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s63)) | (~xuntil7(s99)) | until2p8(s63))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11886,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s63) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s63))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11885, 11884])).
% 36.24/24.05 tff(11887,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11886, 10823, 11880, 11855, 11879, 11856])).
% 36.24/24.05 tff(11888,plain,((~trans(s99, s63)) | until2p8(s63) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11889,plain,
% 36.24/24.05 (~trans(s99, s63)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11888, 11211, 10813])).
% 36.24/24.05 tff(11890,assumption,(~until2p8(s36)), introduced(assumption)).
% 36.24/24.05 tff(11891,assumption,(trans(s99, s36)), introduced(assumption)).
% 36.24/24.05 tff(11892,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11893,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s36)) | (~xuntil7(s99)) | until2p8(s36)) <=> (until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11894,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s36)) | (~xuntil7(s99)) | until2p8(s36))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11893])).
% 36.24/24.05 tff(11895,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s36)) | (~xuntil7(s99)) | until2p8(s36))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11894, 11892])).
% 36.24/24.05 tff(11896,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s36)) | (~xuntil7(s99)) | until2p8(s36))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11897,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s36) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s36))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11896, 11895])).
% 36.24/24.05 tff(11898,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11897, 10823, 11891, 11855, 11890, 11856])).
% 36.24/24.05 tff(11899,plain,((~trans(s99, s36)) | until2p8(s36) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11900,plain,
% 36.24/24.05 (~trans(s99, s36)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11899, 11481, 10813])).
% 36.24/24.05 tff(11901,assumption,(~until2p8(s42)), introduced(assumption)).
% 36.24/24.05 tff(11902,assumption,(trans(s99, s42)), introduced(assumption)).
% 36.24/24.05 tff(11903,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11904,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s42)) | (~xuntil7(s99)) | until2p8(s42)) <=> (until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11905,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s42)) | (~xuntil7(s99)) | until2p8(s42))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11904])).
% 36.24/24.05 tff(11906,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s42)) | (~xuntil7(s99)) | until2p8(s42))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11905, 11903])).
% 36.24/24.05 tff(11907,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s42)) | (~xuntil7(s99)) | until2p8(s42))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11908,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s42) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s42))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11907, 11906])).
% 36.24/24.05 tff(11909,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11908, 10823, 11902, 11855, 11901, 11856])).
% 36.24/24.05 tff(11910,plain,((~trans(s99, s42)) | until2p8(s42) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11911,plain,
% 36.24/24.05 (~trans(s99, s42)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11910, 11421, 10813])).
% 36.24/24.05 tff(11912,assumption,(~until2p8(s57)), introduced(assumption)).
% 36.24/24.05 tff(11913,assumption,(trans(s99, s57)), introduced(assumption)).
% 36.24/24.05 tff(11914,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11915,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s57)) | (~xuntil7(s99)) | until2p8(s57)) <=> (until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11916,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s57)) | (~xuntil7(s99)) | until2p8(s57))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11915])).
% 36.24/24.05 tff(11917,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s57)) | (~xuntil7(s99)) | until2p8(s57))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11916, 11914])).
% 36.24/24.05 tff(11918,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s57)) | (~xuntil7(s99)) | until2p8(s57))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11919,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s57) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s57))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11918, 11917])).
% 36.24/24.05 tff(11920,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11919, 10823, 11913, 11855, 11912, 11856])).
% 36.24/24.05 tff(11921,plain,((~trans(s99, s57)) | until2p8(s57) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11922,plain,
% 36.24/24.05 (~trans(s99, s57)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11921, 11271, 10813])).
% 36.24/24.05 tff(11923,assumption,(~until2p8(s49)), introduced(assumption)).
% 36.24/24.05 tff(11924,assumption,(trans(s99, s49)), introduced(assumption)).
% 36.24/24.05 tff(11925,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11926,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s49)) | (~xuntil7(s99)) | until2p8(s49)) <=> (until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11927,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s49)) | (~xuntil7(s99)) | until2p8(s49))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11926])).
% 36.24/24.05 tff(11928,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s49)) | (~xuntil7(s99)) | until2p8(s49))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11927, 11925])).
% 36.24/24.05 tff(11929,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s49)) | (~xuntil7(s99)) | until2p8(s49))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11930,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s49) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s49))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11929, 11928])).
% 36.24/24.05 tff(11931,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11930, 10823, 11924, 11855, 11923, 11856])).
% 36.24/24.05 tff(11932,plain,((~trans(s99, s49)) | until2p8(s49) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11933,plain,
% 36.24/24.05 (~trans(s99, s49)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11932, 11351, 10813])).
% 36.24/24.05 tff(11934,assumption,(~until2p8(s8)), introduced(assumption)).
% 36.24/24.05 tff(11935,assumption,(trans(s99, s8)), introduced(assumption)).
% 36.24/24.05 tff(11936,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11937,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s8)) | (~xuntil7(s99)) | until2p8(s8)) <=> (until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11938,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s8)) | (~xuntil7(s99)) | until2p8(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11937])).
% 36.24/24.05 tff(11939,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s8)) | (~xuntil7(s99)) | until2p8(s8))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11938, 11936])).
% 36.24/24.05 tff(11940,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s8)) | (~xuntil7(s99)) | until2p8(s8))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11941,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s8) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s8))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11940, 11939])).
% 36.24/24.05 tff(11942,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11941, 10823, 11935, 11855, 11934, 11856])).
% 36.24/24.05 tff(11943,plain,((~trans(s99, s8)) | until2p8(s8) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11944,plain,
% 36.24/24.05 (~trans(s99, s8)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11943, 11768, 10813])).
% 36.24/24.05 tff(11945,assumption,(~until2p8(s9)), introduced(assumption)).
% 36.24/24.05 tff(11946,assumption,(trans(s99, s9)), introduced(assumption)).
% 36.24/24.05 tff(11947,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11948,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s9)) | (~xuntil7(s99)) | until2p8(s9)) <=> (until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11949,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s9)) | (~xuntil7(s99)) | until2p8(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11948])).
% 36.24/24.05 tff(11950,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s9)) | (~xuntil7(s99)) | until2p8(s9))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11949, 11947])).
% 36.24/24.05 tff(11951,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s9)) | (~xuntil7(s99)) | until2p8(s9))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11952,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s9) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s9))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11951, 11950])).
% 36.24/24.05 tff(11953,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11952, 10823, 11946, 11855, 11945, 11856])).
% 36.24/24.05 tff(11954,plain,((~trans(s99, s9)) | until2p8(s9) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11955,plain,
% 36.24/24.05 (~trans(s99, s9)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11954, 11757, 10813])).
% 36.24/24.05 tff(11956,assumption,(~until2p8(s10)), introduced(assumption)).
% 36.24/24.05 tff(11957,assumption,(trans(s99, s10)), introduced(assumption)).
% 36.24/24.05 tff(11958,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11959,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s10)) | (~xuntil7(s99)) | until2p8(s10)) <=> (until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11960,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s10)) | (~xuntil7(s99)) | until2p8(s10))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11959])).
% 36.24/24.05 tff(11961,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s10)) | (~xuntil7(s99)) | until2p8(s10))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11960, 11958])).
% 36.24/24.05 tff(11962,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s10)) | (~xuntil7(s99)) | until2p8(s10))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11963,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s10) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s10))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11962, 11961])).
% 36.24/24.05 tff(11964,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11963, 10823, 11957, 11855, 11956, 11856])).
% 36.24/24.05 tff(11965,plain,((~trans(s99, s10)) | until2p8(s10) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11966,plain,
% 36.24/24.05 (~trans(s99, s10)),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11965, 11746, 10813])).
% 36.24/24.05 tff(11967,assumption,(~until2p8(s5)), introduced(assumption)).
% 36.24/24.05 tff(11968,assumption,(trans(s99, s5)), introduced(assumption)).
% 36.24/24.05 tff(11969,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11970,plain,
% 36.24/24.05 (((~last(s99)) | (~trans(s99, s5)) | (~xuntil7(s99)) | until2p8(s5)) <=> (until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5)))),
% 36.24/24.05 inference(rewrite,[status(thm)],[])).
% 36.24/24.05 tff(11971,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s5)) | (~xuntil7(s99)) | until2p8(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5))))),
% 36.24/24.05 inference(monotonicity,[status(thm)],[11970])).
% 36.24/24.05 tff(11972,plain,
% 36.24/24.05 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s5)) | (~xuntil7(s99)) | until2p8(s5))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5)))),
% 36.24/24.05 inference(transitivity,[status(thm)],[11971, 11969])).
% 36.24/24.05 tff(11973,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s5)) | (~xuntil7(s99)) | until2p8(s5))),
% 36.24/24.05 inference(quant_inst,[status(thm)],[])).
% 36.24/24.05 tff(11974,plain,
% 36.24/24.05 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s5) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s5))),
% 36.24/24.05 inference(modus_ponens,[status(thm)],[11973, 11972])).
% 36.24/24.05 tff(11975,plain,
% 36.24/24.05 ($false),
% 36.24/24.05 inference(unit_resolution,[status(thm)],[11974, 10823, 11968, 11855, 11967, 11856])).
% 36.24/24.05 tff(11976,plain,((~trans(s99, s5)) | until2p8(s5) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.05 tff(11977,plain,
% 36.24/24.06 (~trans(s99, s5)),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[11976, 11801, 10813])).
% 36.24/24.06 tff(11978,assumption,(~until2p8(s15)), introduced(assumption)).
% 36.24/24.06 tff(11979,assumption,(trans(s99, s15)), introduced(assumption)).
% 36.24/24.06 tff(11980,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(11981,plain,
% 36.24/24.06 (((~last(s99)) | (~trans(s99, s15)) | (~xuntil7(s99)) | until2p8(s15)) <=> (until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(11982,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s15)) | (~xuntil7(s99)) | until2p8(s15))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15))))),
% 36.24/24.06 inference(monotonicity,[status(thm)],[11981])).
% 36.24/24.06 tff(11983,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s15)) | (~xuntil7(s99)) | until2p8(s15))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15)))),
% 36.24/24.06 inference(transitivity,[status(thm)],[11982, 11980])).
% 36.24/24.06 tff(11984,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s15)) | (~xuntil7(s99)) | until2p8(s15))),
% 36.24/24.06 inference(quant_inst,[status(thm)],[])).
% 36.24/24.06 tff(11985,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s15) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s15))),
% 36.24/24.06 inference(modus_ponens,[status(thm)],[11984, 11983])).
% 36.24/24.06 tff(11986,plain,
% 36.24/24.06 ($false),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[11985, 10823, 11979, 11855, 11978, 11856])).
% 36.24/24.06 tff(11987,plain,((~trans(s99, s15)) | until2p8(s15) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.06 tff(11988,plain,
% 36.24/24.06 (~trans(s99, s15)),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[11987, 11691, 10813])).
% 36.24/24.06 tff(11989,assumption,(~until2p8(s43)), introduced(assumption)).
% 36.24/24.06 tff(11990,assumption,(trans(s99, s43)), introduced(assumption)).
% 36.24/24.06 tff(11991,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(11992,plain,
% 36.24/24.06 (((~last(s99)) | (~trans(s99, s43)) | (~xuntil7(s99)) | until2p8(s43)) <=> (until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(11993,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s43)) | (~xuntil7(s99)) | until2p8(s43))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43))))),
% 36.24/24.06 inference(monotonicity,[status(thm)],[11992])).
% 36.24/24.06 tff(11994,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s43)) | (~xuntil7(s99)) | until2p8(s43))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43)))),
% 36.24/24.06 inference(transitivity,[status(thm)],[11993, 11991])).
% 36.24/24.06 tff(11995,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s43)) | (~xuntil7(s99)) | until2p8(s43))),
% 36.24/24.06 inference(quant_inst,[status(thm)],[])).
% 36.24/24.06 tff(11996,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s43) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s43))),
% 36.24/24.06 inference(modus_ponens,[status(thm)],[11995, 11994])).
% 36.24/24.06 tff(11997,plain,
% 36.24/24.06 ($false),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[11996, 10823, 11990, 11855, 11989, 11856])).
% 36.24/24.06 tff(11998,plain,((~trans(s99, s43)) | until2p8(s43) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.06 tff(11999,plain,
% 36.24/24.06 (~trans(s99, s43)),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[11998, 11411, 10813])).
% 36.24/24.06 tff(12000,assumption,(~until2p8(s47)), introduced(assumption)).
% 36.24/24.06 tff(12001,assumption,(trans(s99, s47)), introduced(assumption)).
% 36.24/24.06 tff(12002,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(12003,plain,
% 36.24/24.06 (((~last(s99)) | (~trans(s99, s47)) | (~xuntil7(s99)) | until2p8(s47)) <=> (until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(12004,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s47)) | (~xuntil7(s99)) | until2p8(s47))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47))))),
% 36.24/24.06 inference(monotonicity,[status(thm)],[12003])).
% 36.24/24.06 tff(12005,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s47)) | (~xuntil7(s99)) | until2p8(s47))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47)))),
% 36.24/24.06 inference(transitivity,[status(thm)],[12004, 12002])).
% 36.24/24.06 tff(12006,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s47)) | (~xuntil7(s99)) | until2p8(s47))),
% 36.24/24.06 inference(quant_inst,[status(thm)],[])).
% 36.24/24.06 tff(12007,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s47) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s47))),
% 36.24/24.06 inference(modus_ponens,[status(thm)],[12006, 12005])).
% 36.24/24.06 tff(12008,plain,
% 36.24/24.06 ($false),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[12007, 10823, 12001, 11855, 12000, 11856])).
% 36.24/24.06 tff(12009,plain,((~trans(s99, s47)) | until2p8(s47) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.06 tff(12010,plain,
% 36.24/24.06 (~trans(s99, s47)),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[12009, 11371, 10813])).
% 36.24/24.06 tff(12011,assumption,(~until2p8(s17)), introduced(assumption)).
% 36.24/24.06 tff(12012,assumption,(trans(s99, s17)), introduced(assumption)).
% 36.24/24.06 tff(12013,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(12014,plain,
% 36.24/24.06 (((~last(s99)) | (~trans(s99, s17)) | (~xuntil7(s99)) | until2p8(s17)) <=> (until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(12015,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s17)) | (~xuntil7(s99)) | until2p8(s17))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17))))),
% 36.24/24.06 inference(monotonicity,[status(thm)],[12014])).
% 36.24/24.06 tff(12016,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s17)) | (~xuntil7(s99)) | until2p8(s17))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17)))),
% 36.24/24.06 inference(transitivity,[status(thm)],[12015, 12013])).
% 36.24/24.06 tff(12017,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s17)) | (~xuntil7(s99)) | until2p8(s17))),
% 36.24/24.06 inference(quant_inst,[status(thm)],[])).
% 36.24/24.06 tff(12018,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s17) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s17))),
% 36.24/24.06 inference(modus_ponens,[status(thm)],[12017, 12016])).
% 36.24/24.06 tff(12019,plain,
% 36.24/24.06 ($false),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[12018, 10823, 12012, 11855, 12011, 11856])).
% 36.24/24.06 tff(12020,plain,((~trans(s99, s17)) | until2p8(s17) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.06 tff(12021,plain,
% 36.24/24.06 (~trans(s99, s17)),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[12020, 11671, 10813])).
% 36.24/24.06 tff(12022,assumption,(~until2p8(s27)), introduced(assumption)).
% 36.24/24.06 tff(12023,assumption,(trans(s99, s27)), introduced(assumption)).
% 36.24/24.06 tff(12024,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(12025,plain,
% 36.24/24.06 (((~last(s99)) | (~trans(s99, s27)) | (~xuntil7(s99)) | until2p8(s27)) <=> (until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(12026,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s27)) | (~xuntil7(s99)) | until2p8(s27))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27))))),
% 36.24/24.06 inference(monotonicity,[status(thm)],[12025])).
% 36.24/24.06 tff(12027,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s27)) | (~xuntil7(s99)) | until2p8(s27))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27)))),
% 36.24/24.06 inference(transitivity,[status(thm)],[12026, 12024])).
% 36.24/24.06 tff(12028,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s27)) | (~xuntil7(s99)) | until2p8(s27))),
% 36.24/24.06 inference(quant_inst,[status(thm)],[])).
% 36.24/24.06 tff(12029,plain,
% 36.24/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s27) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s27))),
% 36.24/24.06 inference(modus_ponens,[status(thm)],[12028, 12027])).
% 36.24/24.06 tff(12030,plain,
% 36.24/24.06 ($false),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[12029, 10823, 12023, 11855, 12022, 11856])).
% 36.24/24.06 tff(12031,plain,((~trans(s99, s27)) | until2p8(s27) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.24/24.06 tff(12032,plain,
% 36.24/24.06 (~trans(s99, s27)),
% 36.24/24.06 inference(unit_resolution,[status(thm)],[12031, 11571, 10813])).
% 36.24/24.06 tff(12033,assumption,(~until2p8(s76)), introduced(assumption)).
% 36.24/24.06 tff(12034,assumption,(trans(s99, s76)), introduced(assumption)).
% 36.24/24.06 tff(12035,plain,
% 36.24/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.24/24.06 tff(12036,plain,
% 36.24/24.06 (((~last(s99)) | (~trans(s99, s76)) | (~xuntil7(s99)) | until2p8(s76)) <=> (until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76)))),
% 36.24/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12037,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s76)) | (~xuntil7(s99)) | until2p8(s76))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12036])).
% 36.25/24.06 tff(12038,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s76)) | (~xuntil7(s99)) | until2p8(s76))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12037, 12035])).
% 36.25/24.06 tff(12039,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s76)) | (~xuntil7(s99)) | until2p8(s76))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12040,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s76) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s76))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12039, 12038])).
% 36.25/24.06 tff(12041,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12040, 10823, 12034, 11855, 12033, 11856])).
% 36.25/24.06 tff(12042,plain,((~trans(s99, s76)) | until2p8(s76) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12043,plain,
% 36.25/24.06 (~trans(s99, s76)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12042, 11081, 10813])).
% 36.25/24.06 tff(12044,assumption,(~until2p8(s39)), introduced(assumption)).
% 36.25/24.06 tff(12045,assumption,(trans(s99, s39)), introduced(assumption)).
% 36.25/24.06 tff(12046,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12047,plain,
% 36.25/24.06 (((~last(s99)) | (~trans(s99, s39)) | (~xuntil7(s99)) | until2p8(s39)) <=> (until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12048,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s39)) | (~xuntil7(s99)) | until2p8(s39))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12047])).
% 36.25/24.06 tff(12049,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s39)) | (~xuntil7(s99)) | until2p8(s39))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12048, 12046])).
% 36.25/24.06 tff(12050,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s39)) | (~xuntil7(s99)) | until2p8(s39))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12051,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s39) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s39))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12050, 12049])).
% 36.25/24.06 tff(12052,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12051, 10823, 12045, 11855, 12044, 11856])).
% 36.25/24.06 tff(12053,plain,((~trans(s99, s39)) | until2p8(s39) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12054,plain,
% 36.25/24.06 (~trans(s99, s39)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12053, 11451, 10813])).
% 36.25/24.06 tff(12055,assumption,(~until2p8(s87)), introduced(assumption)).
% 36.25/24.06 tff(12056,assumption,(trans(s99, s87)), introduced(assumption)).
% 36.25/24.06 tff(12057,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12058,plain,
% 36.25/24.06 (((~last(s99)) | (~trans(s99, s87)) | (~xuntil7(s99)) | until2p8(s87)) <=> (until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12059,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s87)) | (~xuntil7(s99)) | until2p8(s87))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12058])).
% 36.25/24.06 tff(12060,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s87)) | (~xuntil7(s99)) | until2p8(s87))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12059, 12057])).
% 36.25/24.06 tff(12061,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s87)) | (~xuntil7(s99)) | until2p8(s87))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12062,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s87) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s87))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12061, 12060])).
% 36.25/24.06 tff(12063,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12062, 10823, 12056, 11855, 12055, 11856])).
% 36.25/24.06 tff(12064,plain,((~trans(s99, s87)) | until2p8(s87) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12065,plain,
% 36.25/24.06 (~trans(s99, s87)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12064, 10971, 10813])).
% 36.25/24.06 tff(12066,assumption,(~until2p8(s52)), introduced(assumption)).
% 36.25/24.06 tff(12067,assumption,(trans(s99, s52)), introduced(assumption)).
% 36.25/24.06 tff(12068,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12069,plain,
% 36.25/24.06 (((~last(s99)) | (~trans(s99, s52)) | (~xuntil7(s99)) | until2p8(s52)) <=> (until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12070,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s52)) | (~xuntil7(s99)) | until2p8(s52))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12069])).
% 36.25/24.06 tff(12071,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s52)) | (~xuntil7(s99)) | until2p8(s52))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12070, 12068])).
% 36.25/24.06 tff(12072,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s52)) | (~xuntil7(s99)) | until2p8(s52))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12073,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s52) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s52))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12072, 12071])).
% 36.25/24.06 tff(12074,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12073, 10823, 12067, 11855, 12066, 11856])).
% 36.25/24.06 tff(12075,plain,((~trans(s99, s52)) | until2p8(s52) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12076,plain,
% 36.25/24.06 (~trans(s99, s52)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12075, 11321, 10813])).
% 36.25/24.06 tff(12077,assumption,(~until2p8(s13)), introduced(assumption)).
% 36.25/24.06 tff(12078,assumption,(trans(s99, s13)), introduced(assumption)).
% 36.25/24.06 tff(12079,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12080,plain,
% 36.25/24.06 (((~last(s99)) | (~trans(s99, s13)) | (~xuntil7(s99)) | until2p8(s13)) <=> (until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12081,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s13)) | (~xuntil7(s99)) | until2p8(s13))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12080])).
% 36.25/24.06 tff(12082,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s13)) | (~xuntil7(s99)) | until2p8(s13))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12081, 12079])).
% 36.25/24.06 tff(12083,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s13)) | (~xuntil7(s99)) | until2p8(s13))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12084,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s13) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s13))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12083, 12082])).
% 36.25/24.06 tff(12085,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12084, 10823, 12078, 11855, 12077, 11856])).
% 36.25/24.06 tff(12086,plain,((~trans(s99, s13)) | until2p8(s13) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12087,plain,
% 36.25/24.06 (~trans(s99, s13)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12086, 11713, 10813])).
% 36.25/24.06 tff(12088,assumption,(~until2p8(s68)), introduced(assumption)).
% 36.25/24.06 tff(12089,assumption,(trans(s99, s68)), introduced(assumption)).
% 36.25/24.06 tff(12090,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12091,plain,
% 36.25/24.06 (((~last(s99)) | (~trans(s99, s68)) | (~xuntil7(s99)) | until2p8(s68)) <=> (until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12092,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s68)) | (~xuntil7(s99)) | until2p8(s68))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12091])).
% 36.25/24.06 tff(12093,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s68)) | (~xuntil7(s99)) | until2p8(s68))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12092, 12090])).
% 36.25/24.06 tff(12094,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s68)) | (~xuntil7(s99)) | until2p8(s68))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12095,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s68) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s68))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12094, 12093])).
% 36.25/24.06 tff(12096,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12095, 10823, 12089, 11855, 12088, 11856])).
% 36.25/24.06 tff(12097,plain,((~trans(s99, s68)) | until2p8(s68) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12098,plain,
% 36.25/24.06 (~trans(s99, s68)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12097, 11161, 10813])).
% 36.25/24.06 tff(12099,assumption,(~until2p8(s44)), introduced(assumption)).
% 36.25/24.06 tff(12100,assumption,(trans(s99, s44)), introduced(assumption)).
% 36.25/24.06 tff(12101,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12102,plain,
% 36.25/24.06 (((~last(s99)) | (~trans(s99, s44)) | (~xuntil7(s99)) | until2p8(s44)) <=> (until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12103,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s44)) | (~xuntil7(s99)) | until2p8(s44))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12102])).
% 36.25/24.06 tff(12104,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s44)) | (~xuntil7(s99)) | until2p8(s44))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12103, 12101])).
% 36.25/24.06 tff(12105,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s44)) | (~xuntil7(s99)) | until2p8(s44))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12106,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s44) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s44))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12105, 12104])).
% 36.25/24.06 tff(12107,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12106, 10823, 12100, 11855, 12099, 11856])).
% 36.25/24.06 tff(12108,plain,((~trans(s99, s44)) | until2p8(s44) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12109,plain,
% 36.25/24.06 (~trans(s99, s44)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12108, 11401, 10813])).
% 36.25/24.06 tff(12110,assumption,(~until2p8(s55)), introduced(assumption)).
% 36.25/24.06 tff(12111,assumption,(trans(s99, s55)), introduced(assumption)).
% 36.25/24.06 tff(12112,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12113,plain,
% 36.25/24.06 (((~last(s99)) | (~trans(s99, s55)) | (~xuntil7(s99)) | until2p8(s55)) <=> (until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12114,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s55)) | (~xuntil7(s99)) | until2p8(s55))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12113])).
% 36.25/24.06 tff(12115,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s55)) | (~xuntil7(s99)) | until2p8(s55))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12114, 12112])).
% 36.25/24.06 tff(12116,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s55)) | (~xuntil7(s99)) | until2p8(s55))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12117,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s55) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s55))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12116, 12115])).
% 36.25/24.06 tff(12118,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12117, 10823, 12111, 11855, 12110, 11856])).
% 36.25/24.06 tff(12119,plain,((~trans(s99, s55)) | until2p8(s55) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12120,plain,
% 36.25/24.06 (~trans(s99, s55)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12119, 11291, 10813])).
% 36.25/24.06 tff(12121,assumption,(~until2p8(s46)), introduced(assumption)).
% 36.25/24.06 tff(12122,assumption,(trans(s99, s46)), introduced(assumption)).
% 36.25/24.06 tff(12123,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12124,plain,
% 36.25/24.06 (((~last(s99)) | (~trans(s99, s46)) | (~xuntil7(s99)) | until2p8(s46)) <=> (until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.06 tff(12125,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s46)) | (~xuntil7(s99)) | until2p8(s46))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46))))),
% 36.25/24.06 inference(monotonicity,[status(thm)],[12124])).
% 36.25/24.06 tff(12126,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s46)) | (~xuntil7(s99)) | until2p8(s46))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46)))),
% 36.25/24.06 inference(transitivity,[status(thm)],[12125, 12123])).
% 36.25/24.06 tff(12127,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s46)) | (~xuntil7(s99)) | until2p8(s46))),
% 36.25/24.06 inference(quant_inst,[status(thm)],[])).
% 36.25/24.06 tff(12128,plain,
% 36.25/24.06 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s46) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s46))),
% 36.25/24.06 inference(modus_ponens,[status(thm)],[12127, 12126])).
% 36.25/24.06 tff(12129,plain,
% 36.25/24.06 ($false),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12128, 10823, 12122, 11855, 12121, 11856])).
% 36.25/24.06 tff(12130,plain,((~trans(s99, s46)) | until2p8(s46) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.06 tff(12131,plain,
% 36.25/24.06 (~trans(s99, s46)),
% 36.25/24.06 inference(unit_resolution,[status(thm)],[12130, 11381, 10813])).
% 36.25/24.06 tff(12132,assumption,(~until2p8(s18)), introduced(assumption)).
% 36.25/24.06 tff(12133,assumption,(trans(s99, s18)), introduced(assumption)).
% 36.25/24.06 tff(12134,plain,
% 36.25/24.06 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18)))),
% 36.25/24.06 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12135,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s18)) | (~xuntil7(s99)) | until2p8(s18)) <=> (until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12136,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s18)) | (~xuntil7(s99)) | until2p8(s18))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12135])).
% 36.25/24.07 tff(12137,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s18)) | (~xuntil7(s99)) | until2p8(s18))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12136, 12134])).
% 36.25/24.07 tff(12138,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s18)) | (~xuntil7(s99)) | until2p8(s18))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12139,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s18) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s18))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12138, 12137])).
% 36.25/24.07 tff(12140,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12139, 10823, 12133, 11855, 12132, 11856])).
% 36.25/24.07 tff(12141,plain,((~trans(s99, s18)) | until2p8(s18) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12142,plain,
% 36.25/24.07 (~trans(s99, s18)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12141, 11661, 10813])).
% 36.25/24.07 tff(12143,assumption,(~until2p8(s75)), introduced(assumption)).
% 36.25/24.07 tff(12144,assumption,(trans(s99, s75)), introduced(assumption)).
% 36.25/24.07 tff(12145,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12146,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s75)) | (~xuntil7(s99)) | until2p8(s75)) <=> (until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12147,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s75)) | (~xuntil7(s99)) | until2p8(s75))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12146])).
% 36.25/24.07 tff(12148,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s75)) | (~xuntil7(s99)) | until2p8(s75))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12147, 12145])).
% 36.25/24.07 tff(12149,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s75)) | (~xuntil7(s99)) | until2p8(s75))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12150,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s75) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s75))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12149, 12148])).
% 36.25/24.07 tff(12151,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12150, 10823, 12144, 11855, 12143, 11856])).
% 36.25/24.07 tff(12152,plain,((~trans(s99, s75)) | until2p8(s75) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12153,plain,
% 36.25/24.07 (~trans(s99, s75)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12152, 11091, 10813])).
% 36.25/24.07 tff(12154,assumption,(~until2p8(s91)), introduced(assumption)).
% 36.25/24.07 tff(12155,assumption,(trans(s99, s91)), introduced(assumption)).
% 36.25/24.07 tff(12156,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12157,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s91)) | (~xuntil7(s99)) | until2p8(s91)) <=> (until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12158,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s91)) | (~xuntil7(s99)) | until2p8(s91))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12157])).
% 36.25/24.07 tff(12159,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s91)) | (~xuntil7(s99)) | until2p8(s91))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12158, 12156])).
% 36.25/24.07 tff(12160,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s91)) | (~xuntil7(s99)) | until2p8(s91))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12161,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s91) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s91))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12160, 12159])).
% 36.25/24.07 tff(12162,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12161, 10823, 12155, 11855, 12154, 11856])).
% 36.25/24.07 tff(12163,plain,((~trans(s99, s91)) | until2p8(s91) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12164,plain,
% 36.25/24.07 (~trans(s99, s91)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12163, 10931, 10813])).
% 36.25/24.07 tff(12165,assumption,(~until2p8(s3)), introduced(assumption)).
% 36.25/24.07 tff(12166,assumption,(trans(s99, s3)), introduced(assumption)).
% 36.25/24.07 tff(12167,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12168,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s3)) | (~xuntil7(s99)) | until2p8(s3)) <=> (until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12169,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s3)) | (~xuntil7(s99)) | until2p8(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12168])).
% 36.25/24.07 tff(12170,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s3)) | (~xuntil7(s99)) | until2p8(s3))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12169, 12167])).
% 36.25/24.07 tff(12171,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s3)) | (~xuntil7(s99)) | until2p8(s3))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12172,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s3) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s3))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12171, 12170])).
% 36.25/24.07 tff(12173,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12172, 10823, 12166, 11855, 12165, 11856])).
% 36.25/24.07 tff(12174,plain,((~trans(s99, s3)) | until2p8(s3) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12175,plain,
% 36.25/24.07 (~trans(s99, s3)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12174, 11823, 10813])).
% 36.25/24.07 tff(12176,assumption,(~until2p8(s96)), introduced(assumption)).
% 36.25/24.07 tff(12177,assumption,(trans(s99, s96)), introduced(assumption)).
% 36.25/24.07 tff(12178,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12179,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s96)) | (~xuntil7(s99)) | until2p8(s96)) <=> (until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12180,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s96)) | (~xuntil7(s99)) | until2p8(s96))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12179])).
% 36.25/24.07 tff(12181,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s96)) | (~xuntil7(s99)) | until2p8(s96))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12180, 12178])).
% 36.25/24.07 tff(12182,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s96)) | (~xuntil7(s99)) | until2p8(s96))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12183,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s96) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s96))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12182, 12181])).
% 36.25/24.07 tff(12184,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12183, 10823, 12177, 11855, 12176, 11856])).
% 36.25/24.07 tff(12185,plain,((~trans(s99, s96)) | until2p8(s96) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12186,plain,
% 36.25/24.07 (~trans(s99, s96)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12185, 10881, 10813])).
% 36.25/24.07 tff(12187,assumption,(~until2p8(s41)), introduced(assumption)).
% 36.25/24.07 tff(12188,assumption,(trans(s99, s41)), introduced(assumption)).
% 36.25/24.07 tff(12189,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12190,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s41)) | (~xuntil7(s99)) | until2p8(s41)) <=> (until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12191,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s41)) | (~xuntil7(s99)) | until2p8(s41))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12190])).
% 36.25/24.07 tff(12192,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s41)) | (~xuntil7(s99)) | until2p8(s41))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12191, 12189])).
% 36.25/24.07 tff(12193,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s41)) | (~xuntil7(s99)) | until2p8(s41))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12194,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s41) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s41))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12193, 12192])).
% 36.25/24.07 tff(12195,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12194, 10823, 12188, 11855, 12187, 11856])).
% 36.25/24.07 tff(12196,plain,((~trans(s99, s41)) | until2p8(s41) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12197,plain,
% 36.25/24.07 (~trans(s99, s41)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12196, 11431, 10813])).
% 36.25/24.07 tff(12198,assumption,(~until2p8(s48)), introduced(assumption)).
% 36.25/24.07 tff(12199,assumption,(trans(s99, s48)), introduced(assumption)).
% 36.25/24.07 tff(12200,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12201,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s48)) | (~xuntil7(s99)) | until2p8(s48)) <=> (until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12202,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s48)) | (~xuntil7(s99)) | until2p8(s48))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12201])).
% 36.25/24.07 tff(12203,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s48)) | (~xuntil7(s99)) | until2p8(s48))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12202, 12200])).
% 36.25/24.07 tff(12204,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s48)) | (~xuntil7(s99)) | until2p8(s48))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12205,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s48) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s48))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12204, 12203])).
% 36.25/24.07 tff(12206,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12205, 10823, 12199, 11855, 12198, 11856])).
% 36.25/24.07 tff(12207,plain,((~trans(s99, s48)) | until2p8(s48) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12208,plain,
% 36.25/24.07 (~trans(s99, s48)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12207, 11361, 10813])).
% 36.25/24.07 tff(12209,assumption,(~until2p8(s98)), introduced(assumption)).
% 36.25/24.07 tff(12210,assumption,(trans(s99, s98)), introduced(assumption)).
% 36.25/24.07 tff(12211,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12212,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s98)) | (~xuntil7(s99)) | until2p8(s98)) <=> (until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12213,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s98)) | (~xuntil7(s99)) | until2p8(s98))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12212])).
% 36.25/24.07 tff(12214,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s98)) | (~xuntil7(s99)) | until2p8(s98))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12213, 12211])).
% 36.25/24.07 tff(12215,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s98)) | (~xuntil7(s99)) | until2p8(s98))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12216,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s98) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s98))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12215, 12214])).
% 36.25/24.07 tff(12217,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12216, 10823, 12210, 11855, 12209, 11856])).
% 36.25/24.07 tff(12218,plain,((~trans(s99, s98)) | until2p8(s98) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12219,plain,
% 36.25/24.07 (~trans(s99, s98)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12218, 10861, 10813])).
% 36.25/24.07 tff(12220,assumption,(~until2p8(s30)), introduced(assumption)).
% 36.25/24.07 tff(12221,assumption,(trans(s99, s30)), introduced(assumption)).
% 36.25/24.07 tff(12222,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12223,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s30)) | (~xuntil7(s99)) | until2p8(s30)) <=> (until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12224,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s30)) | (~xuntil7(s99)) | until2p8(s30))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12223])).
% 36.25/24.07 tff(12225,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s30)) | (~xuntil7(s99)) | until2p8(s30))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12224, 12222])).
% 36.25/24.07 tff(12226,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s30)) | (~xuntil7(s99)) | until2p8(s30))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12227,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s30) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s30))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12226, 12225])).
% 36.25/24.07 tff(12228,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12227, 10823, 12221, 11855, 12220, 11856])).
% 36.25/24.07 tff(12229,plain,((~trans(s99, s30)) | until2p8(s30) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12230,plain,
% 36.25/24.07 (~trans(s99, s30)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12229, 11541, 10813])).
% 36.25/24.07 tff(12231,assumption,(~until2p8(s51)), introduced(assumption)).
% 36.25/24.07 tff(12232,assumption,(trans(s99, s51)), introduced(assumption)).
% 36.25/24.07 tff(12233,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12234,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s51)) | (~xuntil7(s99)) | until2p8(s51)) <=> (until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12235,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s51)) | (~xuntil7(s99)) | until2p8(s51))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12234])).
% 36.25/24.07 tff(12236,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s51)) | (~xuntil7(s99)) | until2p8(s51))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12235, 12233])).
% 36.25/24.07 tff(12237,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s51)) | (~xuntil7(s99)) | until2p8(s51))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12238,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s51) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s51))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12237, 12236])).
% 36.25/24.07 tff(12239,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12238, 10823, 12232, 11855, 12231, 11856])).
% 36.25/24.07 tff(12240,plain,((~trans(s99, s51)) | until2p8(s51) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12241,plain,
% 36.25/24.07 (~trans(s99, s51)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12240, 11331, 10813])).
% 36.25/24.07 tff(12242,plain,
% 36.25/24.07 (((~![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)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12243,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | ((~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0)))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12244,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~succ(X, Y)) | until2p8(Y) | (~xuntil2p9(X)))) | (~succ(s0, s1)) | until2p8(s1) | (~xuntil2p9(s0))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12243, 12242])).
% 36.25/24.07 tff(12245,plain,
% 36.25/24.07 (until2p8(s1) | (~xuntil2p9(s0))),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12244, 181, 10852])).
% 36.25/24.07 tff(12246,plain,
% 36.25/24.07 (~xuntil2p9(s0)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12245, 11845])).
% 36.25/24.07 tff(12247,plain,
% 36.25/24.07 (~always5(s0)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[9614, 11840])).
% 36.25/24.07 tff(12248,plain,
% 36.25/24.07 (((~![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)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12249,plain,
% 36.25/24.07 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | (always5(s0) | xuntil2p9(s0) | (~until2p8(s0)))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12250,plain,
% 36.25/24.07 ((~![X: $i] : (always5(X) | xuntil2p9(X) | (~until2p8(X)))) | always5(s0) | xuntil2p9(s0) | (~until2p8(s0))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12249, 12248])).
% 36.25/24.07 tff(12251,plain,
% 36.25/24.07 (xuntil2p9(s0) | (~until2p8(s0))),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12250, 10837, 12247])).
% 36.25/24.07 tff(12252,plain,
% 36.25/24.07 (~until2p8(s0)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12251, 12246])).
% 36.25/24.07 tff(12253,assumption,(~until2p8(s0)), introduced(assumption)).
% 36.25/24.07 tff(12254,assumption,(trans(s99, s0)), introduced(assumption)).
% 36.25/24.07 tff(12255,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12256,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0)) <=> ((~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12257,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12256])).
% 36.25/24.07 tff(12258,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12257, 12255])).
% 36.25/24.07 tff(12259,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12260,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (~last(s99)) | (~xuntil7(s99)) | until2p8(s0) | (~trans(s99, s0))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12259, 12258])).
% 36.25/24.07 tff(12261,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12260, 10823, 12254, 11855, 11856, 12253])).
% 36.25/24.07 tff(12262,plain,((~trans(s99, s0)) | (~xuntil7(s99)) | until2p8(s0)), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12263,plain,
% 36.25/24.07 (~trans(s99, s0)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12262, 10813, 12252])).
% 36.25/24.07 tff(12264,assumption,(~until2p8(s28)), introduced(assumption)).
% 36.25/24.07 tff(12265,assumption,(trans(s99, s28)), introduced(assumption)).
% 36.25/24.07 tff(12266,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12267,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s28)) | (~xuntil7(s99)) | until2p8(s28)) <=> (until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12268,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s28)) | (~xuntil7(s99)) | until2p8(s28))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12267])).
% 36.25/24.07 tff(12269,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s28)) | (~xuntil7(s99)) | until2p8(s28))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12268, 12266])).
% 36.25/24.07 tff(12270,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s28)) | (~xuntil7(s99)) | until2p8(s28))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12271,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s28) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s28))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12270, 12269])).
% 36.25/24.07 tff(12272,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12271, 10823, 12265, 11855, 12264, 11856])).
% 36.25/24.07 tff(12273,plain,((~trans(s99, s28)) | until2p8(s28) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12274,plain,
% 36.25/24.07 (~trans(s99, s28)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12273, 11561, 10813])).
% 36.25/24.07 tff(12275,assumption,(~until2p8(s50)), introduced(assumption)).
% 36.25/24.07 tff(12276,assumption,(trans(s99, s50)), introduced(assumption)).
% 36.25/24.07 tff(12277,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12278,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s50)) | (~xuntil7(s99)) | until2p8(s50)) <=> (until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12279,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s50)) | (~xuntil7(s99)) | until2p8(s50))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12278])).
% 36.25/24.07 tff(12280,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s50)) | (~xuntil7(s99)) | until2p8(s50))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12279, 12277])).
% 36.25/24.07 tff(12281,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s50)) | (~xuntil7(s99)) | until2p8(s50))),
% 36.25/24.07 inference(quant_inst,[status(thm)],[])).
% 36.25/24.07 tff(12282,plain,
% 36.25/24.07 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s50) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s50))),
% 36.25/24.07 inference(modus_ponens,[status(thm)],[12281, 12280])).
% 36.25/24.07 tff(12283,plain,
% 36.25/24.07 ($false),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12282, 10823, 12276, 11855, 12275, 11856])).
% 36.25/24.07 tff(12284,plain,((~trans(s99, s50)) | until2p8(s50) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.07 tff(12285,plain,
% 36.25/24.07 (~trans(s99, s50)),
% 36.25/24.07 inference(unit_resolution,[status(thm)],[12284, 11341, 10813])).
% 36.25/24.07 tff(12286,assumption,(~until2p8(s73)), introduced(assumption)).
% 36.25/24.07 tff(12287,assumption,(trans(s99, s73)), introduced(assumption)).
% 36.25/24.07 tff(12288,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12289,plain,
% 36.25/24.07 (((~last(s99)) | (~trans(s99, s73)) | (~xuntil7(s99)) | until2p8(s73)) <=> (until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73)))),
% 36.25/24.07 inference(rewrite,[status(thm)],[])).
% 36.25/24.07 tff(12290,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s73)) | (~xuntil7(s99)) | until2p8(s73))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73))))),
% 36.25/24.07 inference(monotonicity,[status(thm)],[12289])).
% 36.25/24.07 tff(12291,plain,
% 36.25/24.07 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s73)) | (~xuntil7(s99)) | until2p8(s73))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73)))),
% 36.25/24.07 inference(transitivity,[status(thm)],[12290, 12288])).
% 36.25/24.08 tff(12292,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s73)) | (~xuntil7(s99)) | until2p8(s73))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12293,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s73) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s73))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12292, 12291])).
% 36.25/24.08 tff(12294,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12293, 10823, 12287, 11855, 12286, 11856])).
% 36.25/24.08 tff(12295,plain,((~trans(s99, s73)) | until2p8(s73) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12296,plain,
% 36.25/24.08 (~trans(s99, s73)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12295, 11111, 10813])).
% 36.25/24.08 tff(12297,assumption,(~until2p8(s54)), introduced(assumption)).
% 36.25/24.08 tff(12298,assumption,(trans(s99, s54)), introduced(assumption)).
% 36.25/24.08 tff(12299,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12300,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s54)) | (~xuntil7(s99)) | until2p8(s54)) <=> (until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12301,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s54)) | (~xuntil7(s99)) | until2p8(s54))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12300])).
% 36.25/24.08 tff(12302,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s54)) | (~xuntil7(s99)) | until2p8(s54))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12301, 12299])).
% 36.25/24.08 tff(12303,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s54)) | (~xuntil7(s99)) | until2p8(s54))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12304,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s54) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s54))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12303, 12302])).
% 36.25/24.08 tff(12305,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12304, 10823, 12298, 11855, 12297, 11856])).
% 36.25/24.08 tff(12306,plain,((~trans(s99, s54)) | until2p8(s54) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12307,plain,
% 36.25/24.08 (~trans(s99, s54)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12306, 11301, 10813])).
% 36.25/24.08 tff(12308,assumption,(~until2p8(s99)), introduced(assumption)).
% 36.25/24.08 tff(12309,assumption,(trans(s99, s99)), introduced(assumption)).
% 36.25/24.08 tff(12310,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12311,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s99)) | (~xuntil7(s99)) | until2p8(s99)) <=> (until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12312,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s99)) | (~xuntil7(s99)) | until2p8(s99))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12311])).
% 36.25/24.08 tff(12313,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s99)) | (~xuntil7(s99)) | until2p8(s99))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12312, 12310])).
% 36.25/24.08 tff(12314,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s99)) | (~xuntil7(s99)) | until2p8(s99))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12315,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s99) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s99))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12314, 12313])).
% 36.25/24.08 tff(12316,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12315, 10823, 12309, 11855, 12308, 11856])).
% 36.25/24.08 tff(12317,plain,((~trans(s99, s99)) | until2p8(s99) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12318,plain,
% 36.25/24.08 (~trans(s99, s99)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12317, 10842, 10813])).
% 36.25/24.08 tff(12319,assumption,(~until2p8(s72)), introduced(assumption)).
% 36.25/24.08 tff(12320,assumption,(trans(s99, s72)), introduced(assumption)).
% 36.25/24.08 tff(12321,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12322,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s72)) | (~xuntil7(s99)) | until2p8(s72)) <=> (until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12323,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s72)) | (~xuntil7(s99)) | until2p8(s72))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12322])).
% 36.25/24.08 tff(12324,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s72)) | (~xuntil7(s99)) | until2p8(s72))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12323, 12321])).
% 36.25/24.08 tff(12325,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s72)) | (~xuntil7(s99)) | until2p8(s72))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12326,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s72) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s72))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12325, 12324])).
% 36.25/24.08 tff(12327,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12326, 10823, 12320, 11855, 12319, 11856])).
% 36.25/24.08 tff(12328,plain,((~trans(s99, s72)) | until2p8(s72) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12329,plain,
% 36.25/24.08 (~trans(s99, s72)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12328, 11121, 10813])).
% 36.25/24.08 tff(12330,assumption,(~until2p8(s24)), introduced(assumption)).
% 36.25/24.08 tff(12331,assumption,(trans(s99, s24)), introduced(assumption)).
% 36.25/24.08 tff(12332,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12333,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s24)) | (~xuntil7(s99)) | until2p8(s24)) <=> (until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12334,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s24)) | (~xuntil7(s99)) | until2p8(s24))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12333])).
% 36.25/24.08 tff(12335,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s24)) | (~xuntil7(s99)) | until2p8(s24))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12334, 12332])).
% 36.25/24.08 tff(12336,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s24)) | (~xuntil7(s99)) | until2p8(s24))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12337,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s24) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s24))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12336, 12335])).
% 36.25/24.08 tff(12338,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12337, 10823, 12331, 11855, 12330, 11856])).
% 36.25/24.08 tff(12339,plain,((~trans(s99, s24)) | until2p8(s24) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12340,plain,
% 36.25/24.08 (~trans(s99, s24)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12339, 11601, 10813])).
% 36.25/24.08 tff(12341,assumption,(~until2p8(s84)), introduced(assumption)).
% 36.25/24.08 tff(12342,assumption,(trans(s99, s84)), introduced(assumption)).
% 36.25/24.08 tff(12343,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12344,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s84)) | (~xuntil7(s99)) | until2p8(s84)) <=> (until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12345,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s84)) | (~xuntil7(s99)) | until2p8(s84))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12344])).
% 36.25/24.08 tff(12346,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s84)) | (~xuntil7(s99)) | until2p8(s84))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12345, 12343])).
% 36.25/24.08 tff(12347,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s84)) | (~xuntil7(s99)) | until2p8(s84))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12348,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s84) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s84))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12347, 12346])).
% 36.25/24.08 tff(12349,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12348, 10823, 12342, 11855, 12341, 11856])).
% 36.25/24.08 tff(12350,plain,((~trans(s99, s84)) | until2p8(s84) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12351,plain,
% 36.25/24.08 (~trans(s99, s84)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12350, 11001, 10813])).
% 36.25/24.08 tff(12352,assumption,(~until2p8(s66)), introduced(assumption)).
% 36.25/24.08 tff(12353,assumption,(trans(s99, s66)), introduced(assumption)).
% 36.25/24.08 tff(12354,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12355,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s66)) | (~xuntil7(s99)) | until2p8(s66)) <=> (until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12356,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s66)) | (~xuntil7(s99)) | until2p8(s66))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12355])).
% 36.25/24.08 tff(12357,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s66)) | (~xuntil7(s99)) | until2p8(s66))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12356, 12354])).
% 36.25/24.08 tff(12358,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s66)) | (~xuntil7(s99)) | until2p8(s66))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12359,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s66) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s66))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12358, 12357])).
% 36.25/24.08 tff(12360,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12359, 10823, 12353, 11855, 12352, 11856])).
% 36.25/24.08 tff(12361,plain,((~trans(s99, s66)) | until2p8(s66) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12362,plain,
% 36.25/24.08 (~trans(s99, s66)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12361, 11181, 10813])).
% 36.25/24.08 tff(12363,assumption,(~until2p8(s37)), introduced(assumption)).
% 36.25/24.08 tff(12364,assumption,(trans(s99, s37)), introduced(assumption)).
% 36.25/24.08 tff(12365,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12366,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s37)) | (~xuntil7(s99)) | until2p8(s37)) <=> (until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12367,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s37)) | (~xuntil7(s99)) | until2p8(s37))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12366])).
% 36.25/24.08 tff(12368,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s37)) | (~xuntil7(s99)) | until2p8(s37))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12367, 12365])).
% 36.25/24.08 tff(12369,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s37)) | (~xuntil7(s99)) | until2p8(s37))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12370,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s37) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s37))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12369, 12368])).
% 36.25/24.08 tff(12371,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12370, 10823, 12364, 11855, 12363, 11856])).
% 36.25/24.08 tff(12372,plain,((~trans(s99, s37)) | until2p8(s37) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12373,plain,
% 36.25/24.08 (~trans(s99, s37)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12372, 11471, 10813])).
% 36.25/24.08 tff(12374,assumption,(~until2p8(s11)), introduced(assumption)).
% 36.25/24.08 tff(12375,assumption,(trans(s99, s11)), introduced(assumption)).
% 36.25/24.08 tff(12376,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12377,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s11)) | (~xuntil7(s99)) | until2p8(s11)) <=> (until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12378,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s11)) | (~xuntil7(s99)) | until2p8(s11))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12377])).
% 36.25/24.08 tff(12379,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s11)) | (~xuntil7(s99)) | until2p8(s11))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12378, 12376])).
% 36.25/24.08 tff(12380,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s11)) | (~xuntil7(s99)) | until2p8(s11))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12381,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s11) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s11))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12380, 12379])).
% 36.25/24.08 tff(12382,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12381, 10823, 12375, 11855, 12374, 11856])).
% 36.25/24.08 tff(12383,plain,((~trans(s99, s11)) | until2p8(s11) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12384,plain,
% 36.25/24.08 (~trans(s99, s11)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12383, 11735, 10813])).
% 36.25/24.08 tff(12385,assumption,(~until2p8(s88)), introduced(assumption)).
% 36.25/24.08 tff(12386,assumption,(trans(s99, s88)), introduced(assumption)).
% 36.25/24.08 tff(12387,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12388,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s88)) | (~xuntil7(s99)) | until2p8(s88)) <=> (until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12389,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s88)) | (~xuntil7(s99)) | until2p8(s88))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12388])).
% 36.25/24.08 tff(12390,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s88)) | (~xuntil7(s99)) | until2p8(s88))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12389, 12387])).
% 36.25/24.08 tff(12391,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s88)) | (~xuntil7(s99)) | until2p8(s88))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12392,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s88) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s88))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12391, 12390])).
% 36.25/24.08 tff(12393,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12392, 10823, 12386, 11855, 12385, 11856])).
% 36.25/24.08 tff(12394,plain,((~trans(s99, s88)) | until2p8(s88) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12395,plain,
% 36.25/24.08 (~trans(s99, s88)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12394, 10961, 10813])).
% 36.25/24.08 tff(12396,assumption,(~until2p8(s74)), introduced(assumption)).
% 36.25/24.08 tff(12397,assumption,(trans(s99, s74)), introduced(assumption)).
% 36.25/24.08 tff(12398,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12399,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s74)) | (~xuntil7(s99)) | until2p8(s74)) <=> (until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12400,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s74)) | (~xuntil7(s99)) | until2p8(s74))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12399])).
% 36.25/24.08 tff(12401,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s74)) | (~xuntil7(s99)) | until2p8(s74))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12400, 12398])).
% 36.25/24.08 tff(12402,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s74)) | (~xuntil7(s99)) | until2p8(s74))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12403,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s74) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s74))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12402, 12401])).
% 36.25/24.08 tff(12404,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12403, 10823, 12397, 11855, 12396, 11856])).
% 36.25/24.08 tff(12405,plain,((~trans(s99, s74)) | until2p8(s74) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12406,plain,
% 36.25/24.08 (~trans(s99, s74)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12405, 11101, 10813])).
% 36.25/24.08 tff(12407,assumption,(~until2p8(s32)), introduced(assumption)).
% 36.25/24.08 tff(12408,assumption,(trans(s99, s32)), introduced(assumption)).
% 36.25/24.08 tff(12409,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12410,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s32)) | (~xuntil7(s99)) | until2p8(s32)) <=> (until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12411,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s32)) | (~xuntil7(s99)) | until2p8(s32))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12410])).
% 36.25/24.08 tff(12412,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s32)) | (~xuntil7(s99)) | until2p8(s32))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12411, 12409])).
% 36.25/24.08 tff(12413,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s32)) | (~xuntil7(s99)) | until2p8(s32))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12414,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s32) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s32))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12413, 12412])).
% 36.25/24.08 tff(12415,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12414, 10823, 12408, 11855, 12407, 11856])).
% 36.25/24.08 tff(12416,plain,((~trans(s99, s32)) | until2p8(s32) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12417,plain,
% 36.25/24.08 (~trans(s99, s32)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12416, 11521, 10813])).
% 36.25/24.08 tff(12418,assumption,(~until2p8(s4)), introduced(assumption)).
% 36.25/24.08 tff(12419,assumption,(trans(s99, s4)), introduced(assumption)).
% 36.25/24.08 tff(12420,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12421,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s4)) | (~xuntil7(s99)) | until2p8(s4)) <=> (until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12422,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s4)) | (~xuntil7(s99)) | until2p8(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12421])).
% 36.25/24.08 tff(12423,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s4)) | (~xuntil7(s99)) | until2p8(s4))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12422, 12420])).
% 36.25/24.08 tff(12424,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s4)) | (~xuntil7(s99)) | until2p8(s4))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12425,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s4) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s4))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12424, 12423])).
% 36.25/24.08 tff(12426,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12425, 10823, 12419, 11855, 12418, 11856])).
% 36.25/24.08 tff(12427,plain,((~trans(s99, s4)) | until2p8(s4) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12428,plain,
% 36.25/24.08 (~trans(s99, s4)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12427, 11812, 10813])).
% 36.25/24.08 tff(12429,assumption,(~until2p8(s97)), introduced(assumption)).
% 36.25/24.08 tff(12430,assumption,(trans(s99, s97)), introduced(assumption)).
% 36.25/24.08 tff(12431,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12432,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s97)) | (~xuntil7(s99)) | until2p8(s97)) <=> (until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12433,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s97)) | (~xuntil7(s99)) | until2p8(s97))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12432])).
% 36.25/24.08 tff(12434,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s97)) | (~xuntil7(s99)) | until2p8(s97))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12433, 12431])).
% 36.25/24.08 tff(12435,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s97)) | (~xuntil7(s99)) | until2p8(s97))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12436,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s97) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s97))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12435, 12434])).
% 36.25/24.08 tff(12437,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12436, 10823, 12430, 11855, 12429, 11856])).
% 36.25/24.08 tff(12438,plain,((~trans(s99, s97)) | until2p8(s97) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.08 tff(12439,plain,
% 36.25/24.08 (~trans(s99, s97)),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12438, 10871, 10813])).
% 36.25/24.08 tff(12440,assumption,(~until2p8(s34)), introduced(assumption)).
% 36.25/24.08 tff(12441,assumption,(trans(s99, s34)), introduced(assumption)).
% 36.25/24.08 tff(12442,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12443,plain,
% 36.25/24.08 (((~last(s99)) | (~trans(s99, s34)) | (~xuntil7(s99)) | until2p8(s34)) <=> (until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34)))),
% 36.25/24.08 inference(rewrite,[status(thm)],[])).
% 36.25/24.08 tff(12444,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s34)) | (~xuntil7(s99)) | until2p8(s34))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34))))),
% 36.25/24.08 inference(monotonicity,[status(thm)],[12443])).
% 36.25/24.08 tff(12445,plain,
% 36.25/24.08 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s34)) | (~xuntil7(s99)) | until2p8(s34))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34)))),
% 36.25/24.08 inference(transitivity,[status(thm)],[12444, 12442])).
% 36.25/24.08 tff(12446,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s34)) | (~xuntil7(s99)) | until2p8(s34))),
% 36.25/24.08 inference(quant_inst,[status(thm)],[])).
% 36.25/24.08 tff(12447,plain,
% 36.25/24.08 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s34) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s34))),
% 36.25/24.08 inference(modus_ponens,[status(thm)],[12446, 12445])).
% 36.25/24.08 tff(12448,plain,
% 36.25/24.08 ($false),
% 36.25/24.08 inference(unit_resolution,[status(thm)],[12447, 10823, 12441, 11855, 12440, 11856])).
% 36.25/24.09 tff(12449,plain,((~trans(s99, s34)) | until2p8(s34) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12450,plain,
% 36.25/24.09 (~trans(s99, s34)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12449, 11501, 10813])).
% 36.25/24.09 tff(12451,assumption,(~until2p8(s71)), introduced(assumption)).
% 36.25/24.09 tff(12452,assumption,(trans(s99, s71)), introduced(assumption)).
% 36.25/24.09 tff(12453,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12454,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s71)) | (~xuntil7(s99)) | until2p8(s71)) <=> (until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12455,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s71)) | (~xuntil7(s99)) | until2p8(s71))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12454])).
% 36.25/24.09 tff(12456,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s71)) | (~xuntil7(s99)) | until2p8(s71))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12455, 12453])).
% 36.25/24.09 tff(12457,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s71)) | (~xuntil7(s99)) | until2p8(s71))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12458,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s71) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s71))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12457, 12456])).
% 36.25/24.09 tff(12459,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12458, 10823, 12452, 11855, 12451, 11856])).
% 36.25/24.09 tff(12460,plain,((~trans(s99, s71)) | until2p8(s71) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12461,plain,
% 36.25/24.09 (~trans(s99, s71)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12460, 11131, 10813])).
% 36.25/24.09 tff(12462,assumption,(~until2p8(s19)), introduced(assumption)).
% 36.25/24.09 tff(12463,assumption,(trans(s99, s19)), introduced(assumption)).
% 36.25/24.09 tff(12464,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12465,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s19)) | (~xuntil7(s99)) | until2p8(s19)) <=> (until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12466,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s19)) | (~xuntil7(s99)) | until2p8(s19))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12465])).
% 36.25/24.09 tff(12467,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s19)) | (~xuntil7(s99)) | until2p8(s19))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12466, 12464])).
% 36.25/24.09 tff(12468,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s19)) | (~xuntil7(s99)) | until2p8(s19))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12469,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s19) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s19))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12468, 12467])).
% 36.25/24.09 tff(12470,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12469, 10823, 12463, 11855, 12462, 11856])).
% 36.25/24.09 tff(12471,plain,((~trans(s99, s19)) | until2p8(s19) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12472,plain,
% 36.25/24.09 (~trans(s99, s19)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12471, 11651, 10813])).
% 36.25/24.09 tff(12473,assumption,(~until2p8(s26)), introduced(assumption)).
% 36.25/24.09 tff(12474,assumption,(trans(s99, s26)), introduced(assumption)).
% 36.25/24.09 tff(12475,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12476,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s26)) | (~xuntil7(s99)) | until2p8(s26)) <=> (until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12477,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s26)) | (~xuntil7(s99)) | until2p8(s26))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12476])).
% 36.25/24.09 tff(12478,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s26)) | (~xuntil7(s99)) | until2p8(s26))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12477, 12475])).
% 36.25/24.09 tff(12479,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s26)) | (~xuntil7(s99)) | until2p8(s26))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12480,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s26) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s26))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12479, 12478])).
% 36.25/24.09 tff(12481,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12480, 10823, 12474, 11855, 12473, 11856])).
% 36.25/24.09 tff(12482,plain,((~trans(s99, s26)) | until2p8(s26) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12483,plain,
% 36.25/24.09 (~trans(s99, s26)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12482, 11581, 10813])).
% 36.25/24.09 tff(12484,assumption,(~until2p8(s12)), introduced(assumption)).
% 36.25/24.09 tff(12485,assumption,(trans(s99, s12)), introduced(assumption)).
% 36.25/24.09 tff(12486,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12487,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s12)) | (~xuntil7(s99)) | until2p8(s12)) <=> (until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12488,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s12)) | (~xuntil7(s99)) | until2p8(s12))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12487])).
% 36.25/24.09 tff(12489,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s12)) | (~xuntil7(s99)) | until2p8(s12))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12488, 12486])).
% 36.25/24.09 tff(12490,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s12)) | (~xuntil7(s99)) | until2p8(s12))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12491,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s12) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s12))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12490, 12489])).
% 36.25/24.09 tff(12492,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12491, 10823, 12485, 11855, 12484, 11856])).
% 36.25/24.09 tff(12493,plain,((~trans(s99, s12)) | until2p8(s12) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12494,plain,
% 36.25/24.09 (~trans(s99, s12)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12493, 11724, 10813])).
% 36.25/24.09 tff(12495,assumption,(~until2p8(s85)), introduced(assumption)).
% 36.25/24.09 tff(12496,assumption,(trans(s99, s85)), introduced(assumption)).
% 36.25/24.09 tff(12497,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12498,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s85)) | (~xuntil7(s99)) | until2p8(s85)) <=> (until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12499,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s85)) | (~xuntil7(s99)) | until2p8(s85))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12498])).
% 36.25/24.09 tff(12500,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s85)) | (~xuntil7(s99)) | until2p8(s85))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12499, 12497])).
% 36.25/24.09 tff(12501,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s85)) | (~xuntil7(s99)) | until2p8(s85))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12502,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s85) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s85))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12501, 12500])).
% 36.25/24.09 tff(12503,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12502, 10823, 12496, 11855, 12495, 11856])).
% 36.25/24.09 tff(12504,plain,((~trans(s99, s85)) | until2p8(s85) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12505,plain,
% 36.25/24.09 (~trans(s99, s85)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12504, 10991, 10813])).
% 36.25/24.09 tff(12506,assumption,(~until2p8(s45)), introduced(assumption)).
% 36.25/24.09 tff(12507,assumption,(trans(s99, s45)), introduced(assumption)).
% 36.25/24.09 tff(12508,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12509,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s45)) | (~xuntil7(s99)) | until2p8(s45)) <=> (until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12510,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s45)) | (~xuntil7(s99)) | until2p8(s45))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12509])).
% 36.25/24.09 tff(12511,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s45)) | (~xuntil7(s99)) | until2p8(s45))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12510, 12508])).
% 36.25/24.09 tff(12512,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s45)) | (~xuntil7(s99)) | until2p8(s45))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12513,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s45) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s45))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12512, 12511])).
% 36.25/24.09 tff(12514,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12513, 10823, 12507, 11855, 12506, 11856])).
% 36.25/24.09 tff(12515,plain,((~trans(s99, s45)) | until2p8(s45) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12516,plain,
% 36.25/24.09 (~trans(s99, s45)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12515, 11391, 10813])).
% 36.25/24.09 tff(12517,assumption,(~until2p8(s81)), introduced(assumption)).
% 36.25/24.09 tff(12518,assumption,(trans(s99, s81)), introduced(assumption)).
% 36.25/24.09 tff(12519,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12520,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s81)) | (~xuntil7(s99)) | until2p8(s81)) <=> (until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12521,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s81)) | (~xuntil7(s99)) | until2p8(s81))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12520])).
% 36.25/24.09 tff(12522,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s81)) | (~xuntil7(s99)) | until2p8(s81))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12521, 12519])).
% 36.25/24.09 tff(12523,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s81)) | (~xuntil7(s99)) | until2p8(s81))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12524,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s81) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s81))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12523, 12522])).
% 36.25/24.09 tff(12525,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12524, 10823, 12518, 11855, 12517, 11856])).
% 36.25/24.09 tff(12526,plain,((~trans(s99, s81)) | until2p8(s81) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12527,plain,
% 36.25/24.09 (~trans(s99, s81)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12526, 11031, 10813])).
% 36.25/24.09 tff(12528,assumption,(~until2p8(s62)), introduced(assumption)).
% 36.25/24.09 tff(12529,assumption,(trans(s99, s62)), introduced(assumption)).
% 36.25/24.09 tff(12530,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12531,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s62)) | (~xuntil7(s99)) | until2p8(s62)) <=> (until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12532,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s62)) | (~xuntil7(s99)) | until2p8(s62))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12531])).
% 36.25/24.09 tff(12533,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s62)) | (~xuntil7(s99)) | until2p8(s62))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12532, 12530])).
% 36.25/24.09 tff(12534,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s62)) | (~xuntil7(s99)) | until2p8(s62))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12535,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s62) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s62))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12534, 12533])).
% 36.25/24.09 tff(12536,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12535, 10823, 12529, 11855, 12528, 11856])).
% 36.25/24.09 tff(12537,plain,((~trans(s99, s62)) | until2p8(s62) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12538,plain,
% 36.25/24.09 (~trans(s99, s62)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12537, 11221, 10813])).
% 36.25/24.09 tff(12539,assumption,(~until2p8(s60)), introduced(assumption)).
% 36.25/24.09 tff(12540,assumption,(trans(s99, s60)), introduced(assumption)).
% 36.25/24.09 tff(12541,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12542,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s60)) | (~xuntil7(s99)) | until2p8(s60)) <=> (until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12543,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s60)) | (~xuntil7(s99)) | until2p8(s60))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12542])).
% 36.25/24.09 tff(12544,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s60)) | (~xuntil7(s99)) | until2p8(s60))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12543, 12541])).
% 36.25/24.09 tff(12545,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s60)) | (~xuntil7(s99)) | until2p8(s60))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12546,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s60) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s60))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12545, 12544])).
% 36.25/24.09 tff(12547,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12546, 10823, 12540, 11855, 12539, 11856])).
% 36.25/24.09 tff(12548,plain,((~trans(s99, s60)) | until2p8(s60) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12549,plain,
% 36.25/24.09 (~trans(s99, s60)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12548, 11241, 10813])).
% 36.25/24.09 tff(12550,assumption,(~until2p8(s82)), introduced(assumption)).
% 36.25/24.09 tff(12551,assumption,(trans(s99, s82)), introduced(assumption)).
% 36.25/24.09 tff(12552,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12553,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s82)) | (~xuntil7(s99)) | until2p8(s82)) <=> (until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12554,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s82)) | (~xuntil7(s99)) | until2p8(s82))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12553])).
% 36.25/24.09 tff(12555,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s82)) | (~xuntil7(s99)) | until2p8(s82))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12554, 12552])).
% 36.25/24.09 tff(12556,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s82)) | (~xuntil7(s99)) | until2p8(s82))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12557,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s82) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s82))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12556, 12555])).
% 36.25/24.09 tff(12558,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12557, 10823, 12551, 11855, 12550, 11856])).
% 36.25/24.09 tff(12559,plain,((~trans(s99, s82)) | until2p8(s82) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12560,plain,
% 36.25/24.09 (~trans(s99, s82)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12559, 11021, 10813])).
% 36.25/24.09 tff(12561,assumption,(~until2p8(s25)), introduced(assumption)).
% 36.25/24.09 tff(12562,assumption,(trans(s99, s25)), introduced(assumption)).
% 36.25/24.09 tff(12563,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12564,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s25)) | (~xuntil7(s99)) | until2p8(s25)) <=> (until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12565,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s25)) | (~xuntil7(s99)) | until2p8(s25))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12564])).
% 36.25/24.09 tff(12566,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s25)) | (~xuntil7(s99)) | until2p8(s25))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12565, 12563])).
% 36.25/24.09 tff(12567,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s25)) | (~xuntil7(s99)) | until2p8(s25))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12568,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s25) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s25))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12567, 12566])).
% 36.25/24.09 tff(12569,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12568, 10823, 12562, 11855, 12561, 11856])).
% 36.25/24.09 tff(12570,plain,((~trans(s99, s25)) | until2p8(s25) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12571,plain,
% 36.25/24.09 (~trans(s99, s25)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12570, 11591, 10813])).
% 36.25/24.09 tff(12572,assumption,(~until2p8(s7)), introduced(assumption)).
% 36.25/24.09 tff(12573,assumption,(trans(s99, s7)), introduced(assumption)).
% 36.25/24.09 tff(12574,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12575,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s7)) | (~xuntil7(s99)) | until2p8(s7)) <=> (until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12576,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s7)) | (~xuntil7(s99)) | until2p8(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12575])).
% 36.25/24.09 tff(12577,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s7)) | (~xuntil7(s99)) | until2p8(s7))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12576, 12574])).
% 36.25/24.09 tff(12578,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s7)) | (~xuntil7(s99)) | until2p8(s7))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12579,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s7) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s7))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12578, 12577])).
% 36.25/24.09 tff(12580,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12579, 10823, 12573, 11855, 12572, 11856])).
% 36.25/24.09 tff(12581,plain,((~trans(s99, s7)) | until2p8(s7) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12582,plain,
% 36.25/24.09 (~trans(s99, s7)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12581, 11779, 10813])).
% 36.25/24.09 tff(12583,assumption,(~until2p8(s65)), introduced(assumption)).
% 36.25/24.09 tff(12584,assumption,(trans(s99, s65)), introduced(assumption)).
% 36.25/24.09 tff(12585,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12586,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s65)) | (~xuntil7(s99)) | until2p8(s65)) <=> (until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12587,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s65)) | (~xuntil7(s99)) | until2p8(s65))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12586])).
% 36.25/24.09 tff(12588,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s65)) | (~xuntil7(s99)) | until2p8(s65))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12587, 12585])).
% 36.25/24.09 tff(12589,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s65)) | (~xuntil7(s99)) | until2p8(s65))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12590,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s65) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s65))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12589, 12588])).
% 36.25/24.09 tff(12591,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12590, 10823, 12584, 11855, 12583, 11856])).
% 36.25/24.09 tff(12592,plain,((~trans(s99, s65)) | until2p8(s65) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12593,plain,
% 36.25/24.09 (~trans(s99, s65)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12592, 11191, 10813])).
% 36.25/24.09 tff(12594,assumption,(~until2p8(s58)), introduced(assumption)).
% 36.25/24.09 tff(12595,assumption,(trans(s99, s58)), introduced(assumption)).
% 36.25/24.09 tff(12596,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12597,plain,
% 36.25/24.09 (((~last(s99)) | (~trans(s99, s58)) | (~xuntil7(s99)) | until2p8(s58)) <=> (until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58)))),
% 36.25/24.09 inference(rewrite,[status(thm)],[])).
% 36.25/24.09 tff(12598,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s58)) | (~xuntil7(s99)) | until2p8(s58))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58))))),
% 36.25/24.09 inference(monotonicity,[status(thm)],[12597])).
% 36.25/24.09 tff(12599,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s58)) | (~xuntil7(s99)) | until2p8(s58))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58)))),
% 36.25/24.09 inference(transitivity,[status(thm)],[12598, 12596])).
% 36.25/24.09 tff(12600,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s58)) | (~xuntil7(s99)) | until2p8(s58))),
% 36.25/24.09 inference(quant_inst,[status(thm)],[])).
% 36.25/24.09 tff(12601,plain,
% 36.25/24.09 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s58) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s58))),
% 36.25/24.09 inference(modus_ponens,[status(thm)],[12600, 12599])).
% 36.25/24.09 tff(12602,plain,
% 36.25/24.09 ($false),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12601, 10823, 12595, 11855, 12594, 11856])).
% 36.25/24.09 tff(12603,plain,((~trans(s99, s58)) | until2p8(s58) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.09 tff(12604,plain,
% 36.25/24.09 (~trans(s99, s58)),
% 36.25/24.09 inference(unit_resolution,[status(thm)],[12603, 11261, 10813])).
% 36.25/24.09 tff(12605,assumption,(~until2p8(s64)), introduced(assumption)).
% 36.25/24.09 tff(12606,assumption,(trans(s99, s64)), introduced(assumption)).
% 36.25/24.09 tff(12607,plain,
% 36.25/24.09 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12608,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s64)) | (~xuntil7(s99)) | until2p8(s64)) <=> (until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12609,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s64)) | (~xuntil7(s99)) | until2p8(s64))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12608])).
% 36.25/24.10 tff(12610,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s64)) | (~xuntil7(s99)) | until2p8(s64))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12609, 12607])).
% 36.25/24.10 tff(12611,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s64)) | (~xuntil7(s99)) | until2p8(s64))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12612,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s64) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s64))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12611, 12610])).
% 36.25/24.10 tff(12613,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12612, 10823, 12606, 11855, 12605, 11856])).
% 36.25/24.10 tff(12614,plain,((~trans(s99, s64)) | until2p8(s64) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12615,plain,
% 36.25/24.10 (~trans(s99, s64)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12614, 11201, 10813])).
% 36.25/24.10 tff(12616,assumption,(~until2p8(s14)), introduced(assumption)).
% 36.25/24.10 tff(12617,assumption,(trans(s99, s14)), introduced(assumption)).
% 36.25/24.10 tff(12618,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12619,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s14)) | (~xuntil7(s99)) | until2p8(s14)) <=> (until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12620,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s14)) | (~xuntil7(s99)) | until2p8(s14))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12619])).
% 36.25/24.10 tff(12621,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s14)) | (~xuntil7(s99)) | until2p8(s14))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12620, 12618])).
% 36.25/24.10 tff(12622,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s14)) | (~xuntil7(s99)) | until2p8(s14))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12623,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s14) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s14))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12622, 12621])).
% 36.25/24.10 tff(12624,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12623, 10823, 12617, 11855, 12616, 11856])).
% 36.25/24.10 tff(12625,plain,((~trans(s99, s14)) | until2p8(s14) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12626,plain,
% 36.25/24.10 (~trans(s99, s14)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12625, 11702, 10813])).
% 36.25/24.10 tff(12627,assumption,(~until2p8(s29)), introduced(assumption)).
% 36.25/24.10 tff(12628,assumption,(trans(s99, s29)), introduced(assumption)).
% 36.25/24.10 tff(12629,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12630,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s29)) | (~xuntil7(s99)) | until2p8(s29)) <=> (until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12631,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s29)) | (~xuntil7(s99)) | until2p8(s29))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12630])).
% 36.25/24.10 tff(12632,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s29)) | (~xuntil7(s99)) | until2p8(s29))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12631, 12629])).
% 36.25/24.10 tff(12633,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s29)) | (~xuntil7(s99)) | until2p8(s29))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12634,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s29) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s29))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12633, 12632])).
% 36.25/24.10 tff(12635,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12634, 10823, 12628, 11855, 12627, 11856])).
% 36.25/24.10 tff(12636,plain,((~trans(s99, s29)) | until2p8(s29) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12637,plain,
% 36.25/24.10 (~trans(s99, s29)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12636, 11551, 10813])).
% 36.25/24.10 tff(12638,assumption,(~until2p8(s79)), introduced(assumption)).
% 36.25/24.10 tff(12639,assumption,(trans(s99, s79)), introduced(assumption)).
% 36.25/24.10 tff(12640,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12641,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s79)) | (~xuntil7(s99)) | until2p8(s79)) <=> (until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12642,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s79)) | (~xuntil7(s99)) | until2p8(s79))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12641])).
% 36.25/24.10 tff(12643,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s79)) | (~xuntil7(s99)) | until2p8(s79))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12642, 12640])).
% 36.25/24.10 tff(12644,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s79)) | (~xuntil7(s99)) | until2p8(s79))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12645,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s79) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s79))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12644, 12643])).
% 36.25/24.10 tff(12646,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12645, 10823, 12639, 11855, 12638, 11856])).
% 36.25/24.10 tff(12647,plain,((~trans(s99, s79)) | until2p8(s79) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12648,plain,
% 36.25/24.10 (~trans(s99, s79)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12647, 11051, 10813])).
% 36.25/24.10 tff(12649,assumption,(~until2p8(s6)), introduced(assumption)).
% 36.25/24.10 tff(12650,assumption,(trans(s99, s6)), introduced(assumption)).
% 36.25/24.10 tff(12651,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12652,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s6)) | (~xuntil7(s99)) | until2p8(s6)) <=> (until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12653,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s6)) | (~xuntil7(s99)) | until2p8(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12652])).
% 36.25/24.10 tff(12654,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s6)) | (~xuntil7(s99)) | until2p8(s6))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12653, 12651])).
% 36.25/24.10 tff(12655,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s6)) | (~xuntil7(s99)) | until2p8(s6))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12656,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s6) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s6))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12655, 12654])).
% 36.25/24.10 tff(12657,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12656, 10823, 12650, 11855, 12649, 11856])).
% 36.25/24.10 tff(12658,plain,((~trans(s99, s6)) | until2p8(s6) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12659,plain,
% 36.25/24.10 (~trans(s99, s6)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12658, 11790, 10813])).
% 36.25/24.10 tff(12660,assumption,(~until2p8(s67)), introduced(assumption)).
% 36.25/24.10 tff(12661,assumption,(trans(s99, s67)), introduced(assumption)).
% 36.25/24.10 tff(12662,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12663,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s67)) | (~xuntil7(s99)) | until2p8(s67)) <=> (until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12664,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s67)) | (~xuntil7(s99)) | until2p8(s67))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12663])).
% 36.25/24.10 tff(12665,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s67)) | (~xuntil7(s99)) | until2p8(s67))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12664, 12662])).
% 36.25/24.10 tff(12666,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s67)) | (~xuntil7(s99)) | until2p8(s67))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12667,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s67) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s67))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12666, 12665])).
% 36.25/24.10 tff(12668,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12667, 10823, 12661, 11855, 12660, 11856])).
% 36.25/24.10 tff(12669,plain,((~trans(s99, s67)) | until2p8(s67) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12670,plain,
% 36.25/24.10 (~trans(s99, s67)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12669, 11171, 10813])).
% 36.25/24.10 tff(12671,assumption,(~until2p8(s80)), introduced(assumption)).
% 36.25/24.10 tff(12672,assumption,(trans(s99, s80)), introduced(assumption)).
% 36.25/24.10 tff(12673,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12674,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s80)) | (~xuntil7(s99)) | until2p8(s80)) <=> (until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12675,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s80)) | (~xuntil7(s99)) | until2p8(s80))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12674])).
% 36.25/24.10 tff(12676,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s80)) | (~xuntil7(s99)) | until2p8(s80))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12675, 12673])).
% 36.25/24.10 tff(12677,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s80)) | (~xuntil7(s99)) | until2p8(s80))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12678,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s80) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s80))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12677, 12676])).
% 36.25/24.10 tff(12679,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12678, 10823, 12672, 11855, 12671, 11856])).
% 36.25/24.10 tff(12680,plain,((~trans(s99, s80)) | until2p8(s80) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12681,plain,
% 36.25/24.10 (~trans(s99, s80)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12680, 11041, 10813])).
% 36.25/24.10 tff(12682,assumption,(~until2p8(s16)), introduced(assumption)).
% 36.25/24.10 tff(12683,assumption,(trans(s99, s16)), introduced(assumption)).
% 36.25/24.10 tff(12684,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12685,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s16)) | (~xuntil7(s99)) | until2p8(s16)) <=> (until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12686,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s16)) | (~xuntil7(s99)) | until2p8(s16))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12685])).
% 36.25/24.10 tff(12687,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s16)) | (~xuntil7(s99)) | until2p8(s16))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12686, 12684])).
% 36.25/24.10 tff(12688,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s16)) | (~xuntil7(s99)) | until2p8(s16))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12689,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s16) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s16))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12688, 12687])).
% 36.25/24.10 tff(12690,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12689, 10823, 12683, 11855, 12682, 11856])).
% 36.25/24.10 tff(12691,plain,((~trans(s99, s16)) | until2p8(s16) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12692,plain,
% 36.25/24.10 (~trans(s99, s16)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12691, 11681, 10813])).
% 36.25/24.10 tff(12693,assumption,(~until2p8(s56)), introduced(assumption)).
% 36.25/24.10 tff(12694,assumption,(trans(s99, s56)), introduced(assumption)).
% 36.25/24.10 tff(12695,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12696,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s56)) | (~xuntil7(s99)) | until2p8(s56)) <=> (until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12697,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s56)) | (~xuntil7(s99)) | until2p8(s56))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12696])).
% 36.25/24.10 tff(12698,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s56)) | (~xuntil7(s99)) | until2p8(s56))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12697, 12695])).
% 36.25/24.10 tff(12699,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s56)) | (~xuntil7(s99)) | until2p8(s56))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12700,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s56) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s56))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12699, 12698])).
% 36.25/24.10 tff(12701,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12700, 10823, 12694, 11855, 12693, 11856])).
% 36.25/24.10 tff(12702,plain,((~trans(s99, s56)) | until2p8(s56) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12703,plain,
% 36.25/24.10 (~trans(s99, s56)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12702, 11281, 10813])).
% 36.25/24.10 tff(12704,assumption,(~until2p8(s53)), introduced(assumption)).
% 36.25/24.10 tff(12705,assumption,(trans(s99, s53)), introduced(assumption)).
% 36.25/24.10 tff(12706,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12707,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s53)) | (~xuntil7(s99)) | until2p8(s53)) <=> (until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12708,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s53)) | (~xuntil7(s99)) | until2p8(s53))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12707])).
% 36.25/24.10 tff(12709,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s53)) | (~xuntil7(s99)) | until2p8(s53))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12708, 12706])).
% 36.25/24.10 tff(12710,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s53)) | (~xuntil7(s99)) | until2p8(s53))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12711,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s53) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s53))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12710, 12709])).
% 36.25/24.10 tff(12712,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12711, 10823, 12705, 11855, 12704, 11856])).
% 36.25/24.10 tff(12713,plain,((~trans(s99, s53)) | until2p8(s53) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12714,plain,
% 36.25/24.10 (~trans(s99, s53)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12713, 11311, 10813])).
% 36.25/24.10 tff(12715,assumption,(~until2p8(s40)), introduced(assumption)).
% 36.25/24.10 tff(12716,assumption,(trans(s99, s40)), introduced(assumption)).
% 36.25/24.10 tff(12717,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12718,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s40)) | (~xuntil7(s99)) | until2p8(s40)) <=> (until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12719,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s40)) | (~xuntil7(s99)) | until2p8(s40))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12718])).
% 36.25/24.10 tff(12720,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s40)) | (~xuntil7(s99)) | until2p8(s40))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12719, 12717])).
% 36.25/24.10 tff(12721,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s40)) | (~xuntil7(s99)) | until2p8(s40))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12722,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s40) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s40))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12721, 12720])).
% 36.25/24.10 tff(12723,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12722, 10823, 12716, 11855, 12715, 11856])).
% 36.25/24.10 tff(12724,plain,((~trans(s99, s40)) | until2p8(s40) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12725,plain,
% 36.25/24.10 (~trans(s99, s40)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12724, 11441, 10813])).
% 36.25/24.10 tff(12726,assumption,(~until2p8(s20)), introduced(assumption)).
% 36.25/24.10 tff(12727,assumption,(trans(s99, s20)), introduced(assumption)).
% 36.25/24.10 tff(12728,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12729,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s20)) | (~xuntil7(s99)) | until2p8(s20)) <=> (until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12730,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s20)) | (~xuntil7(s99)) | until2p8(s20))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12729])).
% 36.25/24.10 tff(12731,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s20)) | (~xuntil7(s99)) | until2p8(s20))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12730, 12728])).
% 36.25/24.10 tff(12732,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s20)) | (~xuntil7(s99)) | until2p8(s20))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12733,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s20) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s20))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12732, 12731])).
% 36.25/24.10 tff(12734,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12733, 10823, 12727, 11855, 12726, 11856])).
% 36.25/24.10 tff(12735,plain,((~trans(s99, s20)) | until2p8(s20) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12736,plain,
% 36.25/24.10 (~trans(s99, s20)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12735, 11641, 10813])).
% 36.25/24.10 tff(12737,assumption,(~until2p8(s69)), introduced(assumption)).
% 36.25/24.10 tff(12738,assumption,(trans(s99, s69)), introduced(assumption)).
% 36.25/24.10 tff(12739,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12740,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s69)) | (~xuntil7(s99)) | until2p8(s69)) <=> (until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12741,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s69)) | (~xuntil7(s99)) | until2p8(s69))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12740])).
% 36.25/24.10 tff(12742,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s69)) | (~xuntil7(s99)) | until2p8(s69))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12741, 12739])).
% 36.25/24.10 tff(12743,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s69)) | (~xuntil7(s99)) | until2p8(s69))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12744,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s69) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s69))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12743, 12742])).
% 36.25/24.10 tff(12745,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12744, 10823, 12738, 11855, 12737, 11856])).
% 36.25/24.10 tff(12746,plain,((~trans(s99, s69)) | until2p8(s69) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12747,plain,
% 36.25/24.10 (~trans(s99, s69)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12746, 11151, 10813])).
% 36.25/24.10 tff(12748,assumption,(~until2p8(s22)), introduced(assumption)).
% 36.25/24.10 tff(12749,assumption,(trans(s99, s22)), introduced(assumption)).
% 36.25/24.10 tff(12750,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12751,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s22)) | (~xuntil7(s99)) | until2p8(s22)) <=> (until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12752,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s22)) | (~xuntil7(s99)) | until2p8(s22))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22))))),
% 36.25/24.10 inference(monotonicity,[status(thm)],[12751])).
% 36.25/24.10 tff(12753,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s22)) | (~xuntil7(s99)) | until2p8(s22))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22)))),
% 36.25/24.10 inference(transitivity,[status(thm)],[12752, 12750])).
% 36.25/24.10 tff(12754,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s22)) | (~xuntil7(s99)) | until2p8(s22))),
% 36.25/24.10 inference(quant_inst,[status(thm)],[])).
% 36.25/24.10 tff(12755,plain,
% 36.25/24.10 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s22) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s22))),
% 36.25/24.10 inference(modus_ponens,[status(thm)],[12754, 12753])).
% 36.25/24.10 tff(12756,plain,
% 36.25/24.10 ($false),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12755, 10823, 12749, 11855, 12748, 11856])).
% 36.25/24.10 tff(12757,plain,((~trans(s99, s22)) | until2p8(s22) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.10 tff(12758,plain,
% 36.25/24.10 (~trans(s99, s22)),
% 36.25/24.10 inference(unit_resolution,[status(thm)],[12757, 11621, 10813])).
% 36.25/24.10 tff(12759,assumption,(~until2p8(s23)), introduced(assumption)).
% 36.25/24.10 tff(12760,assumption,(trans(s99, s23)), introduced(assumption)).
% 36.25/24.10 tff(12761,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12762,plain,
% 36.25/24.10 (((~last(s99)) | (~trans(s99, s23)) | (~xuntil7(s99)) | until2p8(s23)) <=> (until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23)))),
% 36.25/24.10 inference(rewrite,[status(thm)],[])).
% 36.25/24.10 tff(12763,plain,
% 36.25/24.10 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s23)) | (~xuntil7(s99)) | until2p8(s23))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23))))),
% 36.25/24.11 inference(monotonicity,[status(thm)],[12762])).
% 36.25/24.11 tff(12764,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s23)) | (~xuntil7(s99)) | until2p8(s23))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23)))),
% 36.25/24.11 inference(transitivity,[status(thm)],[12763, 12761])).
% 36.25/24.11 tff(12765,plain,
% 36.25/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s23)) | (~xuntil7(s99)) | until2p8(s23))),
% 36.25/24.11 inference(quant_inst,[status(thm)],[])).
% 36.25/24.11 tff(12766,plain,
% 36.25/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s23) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s23))),
% 36.25/24.11 inference(modus_ponens,[status(thm)],[12765, 12764])).
% 36.25/24.11 tff(12767,plain,
% 36.25/24.11 ($false),
% 36.25/24.11 inference(unit_resolution,[status(thm)],[12766, 10823, 12760, 11855, 12759, 11856])).
% 36.25/24.11 tff(12768,plain,((~trans(s99, s23)) | until2p8(s23) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.11 tff(12769,plain,
% 36.25/24.11 (~trans(s99, s23)),
% 36.25/24.11 inference(unit_resolution,[status(thm)],[12768, 11611, 10813])).
% 36.25/24.11 tff(12770,assumption,(~until2p8(s59)), introduced(assumption)).
% 36.25/24.11 tff(12771,assumption,(trans(s99, s59)), introduced(assumption)).
% 36.25/24.11 tff(12772,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59)))),
% 36.25/24.11 inference(rewrite,[status(thm)],[])).
% 36.25/24.11 tff(12773,plain,
% 36.25/24.11 (((~last(s99)) | (~trans(s99, s59)) | (~xuntil7(s99)) | until2p8(s59)) <=> (until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59)))),
% 36.25/24.11 inference(rewrite,[status(thm)],[])).
% 36.25/24.11 tff(12774,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s59)) | (~xuntil7(s99)) | until2p8(s59))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59))))),
% 36.25/24.11 inference(monotonicity,[status(thm)],[12773])).
% 36.25/24.11 tff(12775,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s59)) | (~xuntil7(s99)) | until2p8(s59))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59)))),
% 36.25/24.11 inference(transitivity,[status(thm)],[12774, 12772])).
% 36.25/24.11 tff(12776,plain,
% 36.25/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s59)) | (~xuntil7(s99)) | until2p8(s59))),
% 36.25/24.11 inference(quant_inst,[status(thm)],[])).
% 36.25/24.11 tff(12777,plain,
% 36.25/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s59) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s59))),
% 36.25/24.11 inference(modus_ponens,[status(thm)],[12776, 12775])).
% 36.25/24.11 tff(12778,plain,
% 36.25/24.11 ($false),
% 36.25/24.11 inference(unit_resolution,[status(thm)],[12777, 10823, 12771, 11855, 12770, 11856])).
% 36.25/24.11 tff(12779,plain,((~trans(s99, s59)) | until2p8(s59) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.11 tff(12780,plain,
% 36.25/24.11 (~trans(s99, s59)),
% 36.25/24.11 inference(unit_resolution,[status(thm)],[12779, 11251, 10813])).
% 36.25/24.11 tff(12781,assumption,(~until2p8(s93)), introduced(assumption)).
% 36.25/24.11 tff(12782,assumption,(trans(s99, s93)), introduced(assumption)).
% 36.25/24.11 tff(12783,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93)))),
% 36.25/24.11 inference(rewrite,[status(thm)],[])).
% 36.25/24.11 tff(12784,plain,
% 36.25/24.11 (((~last(s99)) | (~trans(s99, s93)) | (~xuntil7(s99)) | until2p8(s93)) <=> (until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93)))),
% 36.25/24.11 inference(rewrite,[status(thm)],[])).
% 36.25/24.11 tff(12785,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s93)) | (~xuntil7(s99)) | until2p8(s93))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93))))),
% 36.25/24.11 inference(monotonicity,[status(thm)],[12784])).
% 36.25/24.11 tff(12786,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s93)) | (~xuntil7(s99)) | until2p8(s93))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93)))),
% 36.25/24.11 inference(transitivity,[status(thm)],[12785, 12783])).
% 36.25/24.11 tff(12787,plain,
% 36.25/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s93)) | (~xuntil7(s99)) | until2p8(s93))),
% 36.25/24.11 inference(quant_inst,[status(thm)],[])).
% 36.25/24.11 tff(12788,plain,
% 36.25/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s93) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s93))),
% 36.25/24.11 inference(modus_ponens,[status(thm)],[12787, 12786])).
% 36.25/24.11 tff(12789,plain,
% 36.25/24.11 ($false),
% 36.25/24.11 inference(unit_resolution,[status(thm)],[12788, 10823, 12782, 11855, 12781, 11856])).
% 36.25/24.11 tff(12790,plain,((~trans(s99, s93)) | until2p8(s93) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.11 tff(12791,plain,
% 36.25/24.11 (~trans(s99, s93)),
% 36.25/24.11 inference(unit_resolution,[status(thm)],[12790, 10911, 10813])).
% 36.25/24.11 tff(12792,assumption,(~until2p8(s2)), introduced(assumption)).
% 36.25/24.11 tff(12793,assumption,(trans(s99, s2)), introduced(assumption)).
% 36.25/24.11 tff(12794,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2)))),
% 36.25/24.11 inference(rewrite,[status(thm)],[])).
% 36.25/24.11 tff(12795,plain,
% 36.25/24.11 (((~last(s99)) | (~trans(s99, s2)) | (~xuntil7(s99)) | until2p8(s2)) <=> (until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2)))),
% 36.25/24.11 inference(rewrite,[status(thm)],[])).
% 36.25/24.11 tff(12796,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s2)) | (~xuntil7(s99)) | until2p8(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2))))),
% 36.25/24.11 inference(monotonicity,[status(thm)],[12795])).
% 36.25/24.11 tff(12797,plain,
% 36.25/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s2)) | (~xuntil7(s99)) | until2p8(s2))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2)))),
% 36.25/24.11 inference(transitivity,[status(thm)],[12796, 12794])).
% 36.25/24.11 tff(12798,plain,
% 36.25/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s2)) | (~xuntil7(s99)) | until2p8(s2))),
% 36.25/24.11 inference(quant_inst,[status(thm)],[])).
% 36.25/24.11 tff(12799,plain,
% 36.25/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s2) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s2))),
% 36.25/24.11 inference(modus_ponens,[status(thm)],[12798, 12797])).
% 36.25/24.11 tff(12800,plain,
% 36.25/24.11 ($false),
% 36.25/24.11 inference(unit_resolution,[status(thm)],[12799, 10823, 12793, 11855, 12792, 11856])).
% 36.25/24.11 tff(12801,plain,((~trans(s99, s2)) | until2p8(s2) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.25/24.11 tff(12802,plain,
% 36.25/24.11 (~trans(s99, s2)),
% 36.25/24.11 inference(unit_resolution,[status(thm)],[12801, 11834, 10813])).
% 36.30/24.11 tff(12803,assumption,(~until2p8(s92)), introduced(assumption)).
% 36.30/24.11 tff(12804,assumption,(trans(s99, s92)), introduced(assumption)).
% 36.30/24.11 tff(12805,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12806,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s92)) | (~xuntil7(s99)) | until2p8(s92)) <=> (until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12807,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s92)) | (~xuntil7(s99)) | until2p8(s92))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12806])).
% 36.30/24.11 tff(12808,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s92)) | (~xuntil7(s99)) | until2p8(s92))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12807, 12805])).
% 36.30/24.11 tff(12809,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s92)) | (~xuntil7(s99)) | until2p8(s92))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12810,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s92) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s92))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12809, 12808])).
% 36.30/24.11 tff(12811,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12810, 10823, 12804, 11855, 12803, 11856])).
% 36.30/24.11 tff(12812,plain,((~trans(s99, s92)) | until2p8(s92) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12813,plain,
% 36.30/24.11 (~trans(s99, s92)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12812, 10921, 10813])).
% 36.30/24.11 tff(12814,assumption,(~until2p8(s95)), introduced(assumption)).
% 36.30/24.11 tff(12815,assumption,(trans(s99, s95)), introduced(assumption)).
% 36.30/24.11 tff(12816,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12817,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s95)) | (~xuntil7(s99)) | until2p8(s95)) <=> (until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12818,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s95)) | (~xuntil7(s99)) | until2p8(s95))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12817])).
% 36.30/24.11 tff(12819,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s95)) | (~xuntil7(s99)) | until2p8(s95))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12818, 12816])).
% 36.30/24.11 tff(12820,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s95)) | (~xuntil7(s99)) | until2p8(s95))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12821,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s95) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s95))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12820, 12819])).
% 36.30/24.11 tff(12822,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12821, 10823, 12815, 11855, 12814, 11856])).
% 36.30/24.11 tff(12823,plain,((~trans(s99, s95)) | until2p8(s95) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12824,plain,
% 36.30/24.11 (~trans(s99, s95)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12823, 10891, 10813])).
% 36.30/24.11 tff(12825,assumption,(~until2p8(s61)), introduced(assumption)).
% 36.30/24.11 tff(12826,assumption,(trans(s99, s61)), introduced(assumption)).
% 36.30/24.11 tff(12827,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12828,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s61)) | (~xuntil7(s99)) | until2p8(s61)) <=> (until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12829,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s61)) | (~xuntil7(s99)) | until2p8(s61))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12828])).
% 36.30/24.11 tff(12830,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s61)) | (~xuntil7(s99)) | until2p8(s61))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12829, 12827])).
% 36.30/24.11 tff(12831,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s61)) | (~xuntil7(s99)) | until2p8(s61))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12832,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s61) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s61))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12831, 12830])).
% 36.30/24.11 tff(12833,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12832, 10823, 12826, 11855, 12825, 11856])).
% 36.30/24.11 tff(12834,plain,((~trans(s99, s61)) | until2p8(s61) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12835,plain,
% 36.30/24.11 (~trans(s99, s61)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12834, 11231, 10813])).
% 36.30/24.11 tff(12836,assumption,(~until2p8(s78)), introduced(assumption)).
% 36.30/24.11 tff(12837,assumption,(trans(s99, s78)), introduced(assumption)).
% 36.30/24.11 tff(12838,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12839,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s78)) | (~xuntil7(s99)) | until2p8(s78)) <=> (until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12840,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s78)) | (~xuntil7(s99)) | until2p8(s78))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12839])).
% 36.30/24.11 tff(12841,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s78)) | (~xuntil7(s99)) | until2p8(s78))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12840, 12838])).
% 36.30/24.11 tff(12842,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s78)) | (~xuntil7(s99)) | until2p8(s78))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12843,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s78) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s78))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12842, 12841])).
% 36.30/24.11 tff(12844,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12843, 10823, 12837, 11855, 12836, 11856])).
% 36.30/24.11 tff(12845,plain,((~trans(s99, s78)) | until2p8(s78) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12846,plain,
% 36.30/24.11 (~trans(s99, s78)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12845, 11061, 10813])).
% 36.30/24.11 tff(12847,assumption,(~until2p8(s89)), introduced(assumption)).
% 36.30/24.11 tff(12848,assumption,(trans(s99, s89)), introduced(assumption)).
% 36.30/24.11 tff(12849,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12850,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s89)) | (~xuntil7(s99)) | until2p8(s89)) <=> (until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12851,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s89)) | (~xuntil7(s99)) | until2p8(s89))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12850])).
% 36.30/24.11 tff(12852,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s89)) | (~xuntil7(s99)) | until2p8(s89))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12851, 12849])).
% 36.30/24.11 tff(12853,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s89)) | (~xuntil7(s99)) | until2p8(s89))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12854,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s89) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s89))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12853, 12852])).
% 36.30/24.11 tff(12855,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12854, 10823, 12848, 11855, 12847, 11856])).
% 36.30/24.11 tff(12856,plain,((~trans(s99, s89)) | until2p8(s89) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12857,plain,
% 36.30/24.11 (~trans(s99, s89)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12856, 10951, 10813])).
% 36.30/24.11 tff(12858,assumption,(~until2p8(s83)), introduced(assumption)).
% 36.30/24.11 tff(12859,assumption,(trans(s99, s83)), introduced(assumption)).
% 36.30/24.11 tff(12860,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12861,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s83)) | (~xuntil7(s99)) | until2p8(s83)) <=> (until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12862,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s83)) | (~xuntil7(s99)) | until2p8(s83))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12861])).
% 36.30/24.11 tff(12863,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s83)) | (~xuntil7(s99)) | until2p8(s83))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12862, 12860])).
% 36.30/24.11 tff(12864,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s83)) | (~xuntil7(s99)) | until2p8(s83))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12865,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s83) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s83))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12864, 12863])).
% 36.30/24.11 tff(12866,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12865, 10823, 12859, 11855, 12858, 11856])).
% 36.30/24.11 tff(12867,plain,((~trans(s99, s83)) | until2p8(s83) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12868,plain,
% 36.30/24.11 (~trans(s99, s83)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12867, 11011, 10813])).
% 36.30/24.11 tff(12869,assumption,(~until2p8(s90)), introduced(assumption)).
% 36.30/24.11 tff(12870,assumption,(trans(s99, s90)), introduced(assumption)).
% 36.30/24.11 tff(12871,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12872,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s90)) | (~xuntil7(s99)) | until2p8(s90)) <=> (until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12873,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s90)) | (~xuntil7(s99)) | until2p8(s90))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12872])).
% 36.30/24.11 tff(12874,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s90)) | (~xuntil7(s99)) | until2p8(s90))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12873, 12871])).
% 36.30/24.11 tff(12875,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s90)) | (~xuntil7(s99)) | until2p8(s90))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12876,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s90) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s90))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12875, 12874])).
% 36.30/24.11 tff(12877,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12876, 10823, 12870, 11855, 12869, 11856])).
% 36.30/24.11 tff(12878,plain,((~trans(s99, s90)) | until2p8(s90) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12879,plain,
% 36.30/24.11 (~trans(s99, s90)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12878, 10941, 10813])).
% 36.30/24.11 tff(12880,assumption,(~until2p8(s21)), introduced(assumption)).
% 36.30/24.11 tff(12881,assumption,(trans(s99, s21)), introduced(assumption)).
% 36.30/24.11 tff(12882,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12883,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s21)) | (~xuntil7(s99)) | until2p8(s21)) <=> (until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12884,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s21)) | (~xuntil7(s99)) | until2p8(s21))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12883])).
% 36.30/24.11 tff(12885,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s21)) | (~xuntil7(s99)) | until2p8(s21))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12884, 12882])).
% 36.30/24.11 tff(12886,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s21)) | (~xuntil7(s99)) | until2p8(s21))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12887,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s21) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s21))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12886, 12885])).
% 36.30/24.11 tff(12888,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12887, 10823, 12881, 11855, 12880, 11856])).
% 36.30/24.11 tff(12889,plain,((~trans(s99, s21)) | until2p8(s21) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12890,plain,
% 36.30/24.11 (~trans(s99, s21)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12889, 11631, 10813])).
% 36.30/24.11 tff(12891,assumption,(~until2p8(s94)), introduced(assumption)).
% 36.30/24.11 tff(12892,assumption,(trans(s99, s94)), introduced(assumption)).
% 36.30/24.11 tff(12893,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12894,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s94)) | (~xuntil7(s99)) | until2p8(s94)) <=> (until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12895,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s94)) | (~xuntil7(s99)) | until2p8(s94))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12894])).
% 36.30/24.11 tff(12896,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s94)) | (~xuntil7(s99)) | until2p8(s94))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12895, 12893])).
% 36.30/24.11 tff(12897,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s94)) | (~xuntil7(s99)) | until2p8(s94))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12898,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s94) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s94))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12897, 12896])).
% 36.30/24.11 tff(12899,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12898, 10823, 12892, 11855, 12891, 11856])).
% 36.30/24.11 tff(12900,plain,((~trans(s99, s94)) | until2p8(s94) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12901,plain,
% 36.30/24.11 (~trans(s99, s94)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12900, 10901, 10813])).
% 36.30/24.11 tff(12902,assumption,(~until2p8(s33)), introduced(assumption)).
% 36.30/24.11 tff(12903,assumption,(trans(s99, s33)), introduced(assumption)).
% 36.30/24.11 tff(12904,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12905,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s33)) | (~xuntil7(s99)) | until2p8(s33)) <=> (until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12906,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s33)) | (~xuntil7(s99)) | until2p8(s33))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12905])).
% 36.30/24.11 tff(12907,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s33)) | (~xuntil7(s99)) | until2p8(s33))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12906, 12904])).
% 36.30/24.11 tff(12908,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s33)) | (~xuntil7(s99)) | until2p8(s33))),
% 36.30/24.11 inference(quant_inst,[status(thm)],[])).
% 36.30/24.11 tff(12909,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s33) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s33))),
% 36.30/24.11 inference(modus_ponens,[status(thm)],[12908, 12907])).
% 36.30/24.11 tff(12910,plain,
% 36.30/24.11 ($false),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12909, 10823, 12903, 11855, 12902, 11856])).
% 36.30/24.11 tff(12911,plain,((~trans(s99, s33)) | until2p8(s33) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.11 tff(12912,plain,
% 36.30/24.11 (~trans(s99, s33)),
% 36.30/24.11 inference(unit_resolution,[status(thm)],[12911, 11511, 10813])).
% 36.30/24.11 tff(12913,assumption,(~until2p8(s77)), introduced(assumption)).
% 36.30/24.11 tff(12914,assumption,(trans(s99, s77)), introduced(assumption)).
% 36.30/24.11 tff(12915,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12916,plain,
% 36.30/24.11 (((~last(s99)) | (~trans(s99, s77)) | (~xuntil7(s99)) | until2p8(s77)) <=> (until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77)))),
% 36.30/24.11 inference(rewrite,[status(thm)],[])).
% 36.30/24.11 tff(12917,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s77)) | (~xuntil7(s99)) | until2p8(s77))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77))))),
% 36.30/24.11 inference(monotonicity,[status(thm)],[12916])).
% 36.30/24.11 tff(12918,plain,
% 36.30/24.11 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s77)) | (~xuntil7(s99)) | until2p8(s77))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77)))),
% 36.30/24.11 inference(transitivity,[status(thm)],[12917, 12915])).
% 36.30/24.11 tff(12919,plain,
% 36.30/24.11 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s77)) | (~xuntil7(s99)) | until2p8(s77))),
% 36.30/24.12 inference(quant_inst,[status(thm)],[])).
% 36.30/24.12 tff(12920,plain,
% 36.30/24.12 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s77) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s77))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12919, 12918])).
% 36.30/24.12 tff(12921,plain,
% 36.30/24.12 ($false),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12920, 10823, 12914, 11855, 12913, 11856])).
% 36.30/24.12 tff(12922,plain,((~trans(s99, s77)) | until2p8(s77) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.12 tff(12923,plain,
% 36.30/24.12 (~trans(s99, s77)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12922, 11071, 10813])).
% 36.30/24.12 tff(12924,assumption,(~until2p8(s35)), introduced(assumption)).
% 36.30/24.12 tff(12925,assumption,(trans(s99, s35)), introduced(assumption)).
% 36.30/24.12 tff(12926,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12927,plain,
% 36.30/24.12 (((~last(s99)) | (~trans(s99, s35)) | (~xuntil7(s99)) | until2p8(s35)) <=> (until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12928,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s35)) | (~xuntil7(s99)) | until2p8(s35))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35))))),
% 36.30/24.12 inference(monotonicity,[status(thm)],[12927])).
% 36.30/24.12 tff(12929,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s35)) | (~xuntil7(s99)) | until2p8(s35))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35)))),
% 36.30/24.12 inference(transitivity,[status(thm)],[12928, 12926])).
% 36.30/24.12 tff(12930,plain,
% 36.30/24.12 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s35)) | (~xuntil7(s99)) | until2p8(s35))),
% 36.30/24.12 inference(quant_inst,[status(thm)],[])).
% 36.30/24.12 tff(12931,plain,
% 36.30/24.12 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s35) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s35))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12930, 12929])).
% 36.30/24.12 tff(12932,plain,
% 36.30/24.12 ($false),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12931, 10823, 12925, 11855, 12924, 11856])).
% 36.30/24.12 tff(12933,plain,((~trans(s99, s35)) | until2p8(s35) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.12 tff(12934,plain,
% 36.30/24.12 (~trans(s99, s35)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12933, 11491, 10813])).
% 36.30/24.12 tff(12935,assumption,(~until2p8(s31)), introduced(assumption)).
% 36.30/24.12 tff(12936,assumption,(trans(s99, s31)), introduced(assumption)).
% 36.30/24.12 tff(12937,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12938,plain,
% 36.30/24.12 (((~last(s99)) | (~trans(s99, s31)) | (~xuntil7(s99)) | until2p8(s31)) <=> (until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12939,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s31)) | (~xuntil7(s99)) | until2p8(s31))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31))))),
% 36.30/24.12 inference(monotonicity,[status(thm)],[12938])).
% 36.30/24.12 tff(12940,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s31)) | (~xuntil7(s99)) | until2p8(s31))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31)))),
% 36.30/24.12 inference(transitivity,[status(thm)],[12939, 12937])).
% 36.30/24.12 tff(12941,plain,
% 36.30/24.12 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s31)) | (~xuntil7(s99)) | until2p8(s31))),
% 36.30/24.12 inference(quant_inst,[status(thm)],[])).
% 36.30/24.12 tff(12942,plain,
% 36.30/24.12 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s31) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s31))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12941, 12940])).
% 36.30/24.12 tff(12943,plain,
% 36.30/24.12 ($false),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12942, 10823, 12936, 11855, 12935, 11856])).
% 36.30/24.12 tff(12944,plain,((~trans(s99, s31)) | until2p8(s31) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.12 tff(12945,plain,
% 36.30/24.12 (~trans(s99, s31)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12944, 11531, 10813])).
% 36.30/24.12 tff(12946,assumption,(~until2p8(s70)), introduced(assumption)).
% 36.30/24.12 tff(12947,assumption,(trans(s99, s70)), introduced(assumption)).
% 36.30/24.12 tff(12948,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12949,plain,
% 36.30/24.12 (((~last(s99)) | (~trans(s99, s70)) | (~xuntil7(s99)) | until2p8(s70)) <=> (until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12950,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s70)) | (~xuntil7(s99)) | until2p8(s70))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70))))),
% 36.30/24.12 inference(monotonicity,[status(thm)],[12949])).
% 36.30/24.12 tff(12951,plain,
% 36.30/24.12 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s70)) | (~xuntil7(s99)) | until2p8(s70))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70)))),
% 36.30/24.12 inference(transitivity,[status(thm)],[12950, 12948])).
% 36.30/24.12 tff(12952,plain,
% 36.30/24.12 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s70)) | (~xuntil7(s99)) | until2p8(s70))),
% 36.30/24.12 inference(quant_inst,[status(thm)],[])).
% 36.30/24.12 tff(12953,plain,
% 36.30/24.12 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s70) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s70))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12952, 12951])).
% 36.30/24.12 tff(12954,plain,
% 36.30/24.12 ($false),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12953, 10823, 12947, 11855, 12946, 11856])).
% 36.30/24.12 tff(12955,plain,((~trans(s99, s70)) | until2p8(s70) | (~xuntil7(s99))), inference(lemma,lemma(discharge,[]))).
% 36.30/24.12 tff(12956,plain,
% 36.30/24.12 (~trans(s99, s70)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12955, 11141, 10813])).
% 36.30/24.12 tff(12957,assumption,(~loop), introduced(assumption)).
% 36.30/24.12 tff(12958,plain,
% 36.30/24.12 (^[X: $i] : refl((loop | (~last(X)) | (~xuntil7(X))) <=> (loop | (~last(X)) | (~xuntil7(X))))),
% 36.30/24.12 inference(bind,[status(th)],[])).
% 36.30/24.12 tff(12959,plain,
% 36.30/24.12 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 36.30/24.12 inference(quant_intro,[status(thm)],[12958])).
% 36.30/24.12 tff(12960,plain,
% 36.30/24.12 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12961,plain,
% 36.30/24.12 (^[X: $i] : rewrite(((loop | (~last(X))) | (~xuntil7(X))) <=> (loop | (~last(X)) | (~xuntil7(X))))),
% 36.30/24.12 inference(bind,[status(th)],[])).
% 36.30/24.12 tff(12962,plain,
% 36.30/24.12 (![X: $i] : ((loop | (~last(X))) | (~xuntil7(X))) <=> ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 36.30/24.12 inference(quant_intro,[status(thm)],[12961])).
% 36.30/24.12 tff(12963,axiom,(![X: $i] : ((loop | (~last(X))) | (~xuntil7(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty6')).
% 36.30/24.12 tff(12964,plain,
% 36.30/24.12 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12963, 12962])).
% 36.30/24.12 tff(12965,plain,
% 36.30/24.12 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12964, 12960])).
% 36.30/24.12 tff(12966,plain,(
% 36.30/24.12 ![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 36.30/24.12 inference(skolemize,[status(sab)],[12965])).
% 36.30/24.12 tff(12967,plain,
% 36.30/24.12 (![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12966, 12959])).
% 36.30/24.12 tff(12968,plain,
% 36.30/24.12 (((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | (loop | (~last(s99)) | (~xuntil7(s99)))) <=> ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | loop | (~last(s99)) | (~xuntil7(s99)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12969,plain,
% 36.30/24.12 ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | (loop | (~last(s99)) | (~xuntil7(s99)))),
% 36.30/24.12 inference(quant_inst,[status(thm)],[])).
% 36.30/24.12 tff(12970,plain,
% 36.30/24.12 ((~![X: $i] : (loop | (~last(X)) | (~xuntil7(X)))) | loop | (~last(s99)) | (~xuntil7(s99))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12969, 12968])).
% 36.30/24.12 tff(12971,plain,
% 36.30/24.12 (loop | (~xuntil7(s99))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12970, 10823, 12967])).
% 36.30/24.12 tff(12972,plain,
% 36.30/24.12 (~xuntil7(s99)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12971, 12957])).
% 36.30/24.12 tff(12973,plain,
% 36.30/24.12 (^[X: $i] : refl((loop | (~always5(X)) | (~last(X))) <=> (loop | (~always5(X)) | (~last(X))))),
% 36.30/24.12 inference(bind,[status(th)],[])).
% 36.30/24.12 tff(12974,plain,
% 36.30/24.12 (![X: $i] : (loop | (~always5(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 36.30/24.12 inference(quant_intro,[status(thm)],[12973])).
% 36.30/24.12 tff(12975,plain,
% 36.30/24.12 (![X: $i] : (loop | (~always5(X)) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12976,plain,
% 36.30/24.12 (^[X: $i] : rewrite(((loop | (~always5(X))) | (~last(X))) <=> (loop | (~always5(X)) | (~last(X))))),
% 36.30/24.12 inference(bind,[status(th)],[])).
% 36.30/24.12 tff(12977,plain,
% 36.30/24.12 (![X: $i] : ((loop | (~always5(X))) | (~last(X))) <=> ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 36.30/24.12 inference(quant_intro,[status(thm)],[12976])).
% 36.30/24.12 tff(12978,axiom,(![X: $i] : ((loop | (~always5(X))) | (~last(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prpty3')).
% 36.30/24.12 tff(12979,plain,
% 36.30/24.12 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12978, 12977])).
% 36.30/24.12 tff(12980,plain,
% 36.30/24.12 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12979, 12975])).
% 36.30/24.12 tff(12981,plain,(
% 36.30/24.12 ![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 36.30/24.12 inference(skolemize,[status(sab)],[12980])).
% 36.30/24.12 tff(12982,plain,
% 36.30/24.12 (![X: $i] : (loop | (~always5(X)) | (~last(X)))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12981, 12974])).
% 36.30/24.12 tff(12983,plain,
% 36.30/24.12 (((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | (loop | (~always5(s99)) | (~last(s99)))) <=> ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | loop | (~always5(s99)) | (~last(s99)))),
% 36.30/24.12 inference(rewrite,[status(thm)],[])).
% 36.30/24.12 tff(12984,plain,
% 36.30/24.12 ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | (loop | (~always5(s99)) | (~last(s99)))),
% 36.30/24.12 inference(quant_inst,[status(thm)],[])).
% 36.30/24.12 tff(12985,plain,
% 36.30/24.12 ((~![X: $i] : (loop | (~always5(X)) | (~last(X)))) | loop | (~always5(s99)) | (~last(s99))),
% 36.30/24.12 inference(modus_ponens,[status(thm)],[12984, 12983])).
% 36.30/24.12 tff(12986,plain,
% 36.30/24.12 (loop | (~always5(s99))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12985, 10823, 12982])).
% 36.30/24.12 tff(12987,plain,
% 36.30/24.12 (~always5(s99)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12986, 12957])).
% 36.30/24.12 tff(12988,plain,
% 36.30/24.12 (~until6(s99)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10812, 9395, 12987, 12972])).
% 36.30/24.12 tff(12989,plain,
% 36.30/24.12 (~xuntil7(s98)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10805, 12988])).
% 36.30/24.12 tff(12990,plain,
% 36.30/24.12 (~always5(s98)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8976, 12987])).
% 36.30/24.12 tff(12991,plain,
% 36.30/24.12 (xuntil7(s98) | (~until6(s98))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10799, 9395, 12990])).
% 36.30/24.12 tff(12992,plain,
% 36.30/24.12 (~until6(s98)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12991, 12989])).
% 36.30/24.12 tff(12993,plain,
% 36.30/24.12 (~xuntil7(s97)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10792, 12992])).
% 36.30/24.12 tff(12994,plain,
% 36.30/24.12 (~always5(s97)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8984, 12990])).
% 36.30/24.12 tff(12995,plain,
% 36.30/24.12 (xuntil7(s97) | (~until6(s97))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10786, 9395, 12994])).
% 36.30/24.12 tff(12996,plain,
% 36.30/24.12 (~until6(s97)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12995, 12993])).
% 36.30/24.12 tff(12997,plain,
% 36.30/24.12 (~xuntil7(s96)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10779, 12996])).
% 36.30/24.12 tff(12998,plain,
% 36.30/24.12 (~always5(s96)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[47, 12994])).
% 36.30/24.12 tff(12999,plain,
% 36.30/24.12 (xuntil7(s96) | (~until6(s96))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10773, 9395, 12998])).
% 36.30/24.12 tff(13000,plain,
% 36.30/24.12 (~until6(s96)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[12999, 12997])).
% 36.30/24.12 tff(13001,plain,
% 36.30/24.12 (~xuntil7(s95)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10766, 13000])).
% 36.30/24.12 tff(13002,plain,
% 36.30/24.12 (~always5(s95)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[32, 12998])).
% 36.30/24.12 tff(13003,plain,
% 36.30/24.12 (xuntil7(s95) | (~until6(s95))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10760, 9395, 13002])).
% 36.30/24.12 tff(13004,plain,
% 36.30/24.12 (~until6(s95)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13003, 13001])).
% 36.30/24.12 tff(13005,plain,
% 36.30/24.12 (~xuntil7(s94)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10753, 13004])).
% 36.30/24.12 tff(13006,plain,
% 36.30/24.12 (~always5(s94)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8686, 13002])).
% 36.30/24.12 tff(13007,plain,
% 36.30/24.12 (xuntil7(s94) | (~until6(s94))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10747, 9395, 13006])).
% 36.30/24.12 tff(13008,plain,
% 36.30/24.12 (~until6(s94)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13007, 13005])).
% 36.30/24.12 tff(13009,plain,
% 36.30/24.12 (~xuntil7(s93)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10740, 13008])).
% 36.30/24.12 tff(13010,plain,
% 36.30/24.12 (~always5(s93)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8694, 13006])).
% 36.30/24.12 tff(13011,plain,
% 36.30/24.12 (xuntil7(s93) | (~until6(s93))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10734, 9395, 13010])).
% 36.30/24.12 tff(13012,plain,
% 36.30/24.12 (~until6(s93)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13011, 13009])).
% 36.30/24.12 tff(13013,plain,
% 36.30/24.12 (~xuntil7(s92)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10727, 13012])).
% 36.30/24.12 tff(13014,plain,
% 36.30/24.12 (~always5(s92)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8702, 13010])).
% 36.30/24.12 tff(13015,plain,
% 36.30/24.12 (xuntil7(s92) | (~until6(s92))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10721, 9395, 13014])).
% 36.30/24.12 tff(13016,plain,
% 36.30/24.12 (~until6(s92)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13015, 13013])).
% 36.30/24.12 tff(13017,plain,
% 36.30/24.12 (~xuntil7(s91)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10714, 13016])).
% 36.30/24.12 tff(13018,plain,
% 36.30/24.12 (~always5(s91)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8710, 13014])).
% 36.30/24.12 tff(13019,plain,
% 36.30/24.12 (xuntil7(s91) | (~until6(s91))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10708, 9395, 13018])).
% 36.30/24.12 tff(13020,plain,
% 36.30/24.12 (~until6(s91)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13019, 13017])).
% 36.30/24.12 tff(13021,plain,
% 36.30/24.12 (~xuntil7(s90)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10701, 13020])).
% 36.30/24.12 tff(13022,plain,
% 36.30/24.12 (~always5(s90)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8718, 13018])).
% 36.30/24.12 tff(13023,plain,
% 36.30/24.12 (xuntil7(s90) | (~until6(s90))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10695, 9395, 13022])).
% 36.30/24.12 tff(13024,plain,
% 36.30/24.12 (~until6(s90)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13023, 13021])).
% 36.30/24.12 tff(13025,plain,
% 36.30/24.12 (~xuntil7(s89)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10688, 13024])).
% 36.30/24.12 tff(13026,plain,
% 36.30/24.12 (~always5(s89)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8726, 13022])).
% 36.30/24.12 tff(13027,plain,
% 36.30/24.12 (xuntil7(s89) | (~until6(s89))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10682, 9395, 13026])).
% 36.30/24.12 tff(13028,plain,
% 36.30/24.12 (~until6(s89)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13027, 13025])).
% 36.30/24.12 tff(13029,plain,
% 36.30/24.12 (~xuntil7(s88)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10675, 13028])).
% 36.30/24.12 tff(13030,plain,
% 36.30/24.12 (~always5(s88)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8734, 13026])).
% 36.30/24.12 tff(13031,plain,
% 36.30/24.12 (xuntil7(s88) | (~until6(s88))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10669, 9395, 13030])).
% 36.30/24.12 tff(13032,plain,
% 36.30/24.12 (~until6(s88)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13031, 13029])).
% 36.30/24.12 tff(13033,plain,
% 36.30/24.12 (~xuntil7(s87)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10662, 13032])).
% 36.30/24.12 tff(13034,plain,
% 36.30/24.12 (~always5(s87)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8742, 13030])).
% 36.30/24.12 tff(13035,plain,
% 36.30/24.12 (xuntil7(s87) | (~until6(s87))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10656, 9395, 13034])).
% 36.30/24.12 tff(13036,plain,
% 36.30/24.12 (~until6(s87)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13035, 13033])).
% 36.30/24.12 tff(13037,plain,
% 36.30/24.12 (~xuntil7(s86)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10649, 13036])).
% 36.30/24.12 tff(13038,plain,
% 36.30/24.12 (~always5(s86)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8750, 13034])).
% 36.30/24.12 tff(13039,plain,
% 36.30/24.12 (xuntil7(s86) | (~until6(s86))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10643, 9395, 13038])).
% 36.30/24.12 tff(13040,plain,
% 36.30/24.12 (~until6(s86)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13039, 13037])).
% 36.30/24.12 tff(13041,plain,
% 36.30/24.12 (~xuntil7(s85)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10636, 13040])).
% 36.30/24.12 tff(13042,plain,
% 36.30/24.12 (~always5(s85)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8758, 13038])).
% 36.30/24.12 tff(13043,plain,
% 36.30/24.12 (xuntil7(s85) | (~until6(s85))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10630, 9395, 13042])).
% 36.30/24.12 tff(13044,plain,
% 36.30/24.12 (~until6(s85)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13043, 13041])).
% 36.30/24.12 tff(13045,plain,
% 36.30/24.12 (~xuntil7(s84)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10623, 13044])).
% 36.30/24.12 tff(13046,plain,
% 36.30/24.12 (~always5(s84)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8766, 13042])).
% 36.30/24.12 tff(13047,plain,
% 36.30/24.12 (xuntil7(s84) | (~until6(s84))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10617, 9395, 13046])).
% 36.30/24.12 tff(13048,plain,
% 36.30/24.12 (~until6(s84)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13047, 13045])).
% 36.30/24.12 tff(13049,plain,
% 36.30/24.12 (~xuntil7(s83)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10610, 13048])).
% 36.30/24.12 tff(13050,plain,
% 36.30/24.12 (~always5(s83)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8774, 13046])).
% 36.30/24.12 tff(13051,plain,
% 36.30/24.12 (xuntil7(s83) | (~until6(s83))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10604, 9395, 13050])).
% 36.30/24.12 tff(13052,plain,
% 36.30/24.12 (~until6(s83)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13051, 13049])).
% 36.30/24.12 tff(13053,plain,
% 36.30/24.12 (~xuntil7(s82)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10597, 13052])).
% 36.30/24.12 tff(13054,plain,
% 36.30/24.12 (~always5(s82)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8782, 13050])).
% 36.30/24.12 tff(13055,plain,
% 36.30/24.12 (xuntil7(s82) | (~until6(s82))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10591, 9395, 13054])).
% 36.30/24.12 tff(13056,plain,
% 36.30/24.12 (~until6(s82)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13055, 13053])).
% 36.30/24.12 tff(13057,plain,
% 36.30/24.12 (~xuntil7(s81)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10584, 13056])).
% 36.30/24.12 tff(13058,plain,
% 36.30/24.12 (~always5(s81)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8790, 13054])).
% 36.30/24.12 tff(13059,plain,
% 36.30/24.12 (xuntil7(s81) | (~until6(s81))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10578, 9395, 13058])).
% 36.30/24.12 tff(13060,plain,
% 36.30/24.12 (~until6(s81)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13059, 13057])).
% 36.30/24.12 tff(13061,plain,
% 36.30/24.12 (~xuntil7(s80)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10571, 13060])).
% 36.30/24.12 tff(13062,plain,
% 36.30/24.12 (~always5(s80)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8798, 13058])).
% 36.30/24.12 tff(13063,plain,
% 36.30/24.12 (xuntil7(s80) | (~until6(s80))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10565, 9395, 13062])).
% 36.30/24.12 tff(13064,plain,
% 36.30/24.12 (~until6(s80)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13063, 13061])).
% 36.30/24.12 tff(13065,plain,
% 36.30/24.12 (~xuntil7(s79)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10558, 13064])).
% 36.30/24.12 tff(13066,plain,
% 36.30/24.12 (~always5(s79)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8806, 13062])).
% 36.30/24.12 tff(13067,plain,
% 36.30/24.12 (xuntil7(s79) | (~until6(s79))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10552, 9395, 13066])).
% 36.30/24.12 tff(13068,plain,
% 36.30/24.12 (~until6(s79)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13067, 13065])).
% 36.30/24.12 tff(13069,plain,
% 36.30/24.12 (~xuntil7(s78)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10545, 13068])).
% 36.30/24.12 tff(13070,plain,
% 36.30/24.12 (~always5(s78)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8814, 13066])).
% 36.30/24.12 tff(13071,plain,
% 36.30/24.12 (xuntil7(s78) | (~until6(s78))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10539, 9395, 13070])).
% 36.30/24.12 tff(13072,plain,
% 36.30/24.12 (~until6(s78)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13071, 13069])).
% 36.30/24.12 tff(13073,plain,
% 36.30/24.12 (~xuntil7(s77)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10532, 13072])).
% 36.30/24.12 tff(13074,plain,
% 36.30/24.12 (~always5(s77)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8822, 13070])).
% 36.30/24.12 tff(13075,plain,
% 36.30/24.12 (xuntil7(s77) | (~until6(s77))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10526, 9395, 13074])).
% 36.30/24.12 tff(13076,plain,
% 36.30/24.12 (~until6(s77)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13075, 13073])).
% 36.30/24.12 tff(13077,plain,
% 36.30/24.12 (~xuntil7(s76)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10519, 13076])).
% 36.30/24.12 tff(13078,plain,
% 36.30/24.12 (~always5(s76)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8830, 13074])).
% 36.30/24.12 tff(13079,plain,
% 36.30/24.12 (xuntil7(s76) | (~until6(s76))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10513, 9395, 13078])).
% 36.30/24.12 tff(13080,plain,
% 36.30/24.12 (~until6(s76)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13079, 13077])).
% 36.30/24.12 tff(13081,plain,
% 36.30/24.12 (~xuntil7(s75)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10506, 13080])).
% 36.30/24.12 tff(13082,plain,
% 36.30/24.12 (~always5(s75)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8838, 13078])).
% 36.30/24.12 tff(13083,plain,
% 36.30/24.12 (xuntil7(s75) | (~until6(s75))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10500, 9395, 13082])).
% 36.30/24.12 tff(13084,plain,
% 36.30/24.12 (~until6(s75)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13083, 13081])).
% 36.30/24.12 tff(13085,plain,
% 36.30/24.12 (~xuntil7(s74)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10493, 13084])).
% 36.30/24.12 tff(13086,plain,
% 36.30/24.12 (~always5(s74)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8846, 13082])).
% 36.30/24.12 tff(13087,plain,
% 36.30/24.12 (xuntil7(s74) | (~until6(s74))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10487, 9395, 13086])).
% 36.30/24.12 tff(13088,plain,
% 36.30/24.12 (~until6(s74)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13087, 13085])).
% 36.30/24.12 tff(13089,plain,
% 36.30/24.12 (~xuntil7(s73)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10480, 13088])).
% 36.30/24.12 tff(13090,plain,
% 36.30/24.12 (~always5(s73)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8854, 13086])).
% 36.30/24.12 tff(13091,plain,
% 36.30/24.12 (xuntil7(s73) | (~until6(s73))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10474, 9395, 13090])).
% 36.30/24.12 tff(13092,plain,
% 36.30/24.12 (~until6(s73)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13091, 13089])).
% 36.30/24.12 tff(13093,plain,
% 36.30/24.12 (~xuntil7(s72)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10467, 13092])).
% 36.30/24.12 tff(13094,plain,
% 36.30/24.12 (~always5(s72)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8862, 13090])).
% 36.30/24.12 tff(13095,plain,
% 36.30/24.12 (xuntil7(s72) | (~until6(s72))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10461, 9395, 13094])).
% 36.30/24.12 tff(13096,plain,
% 36.30/24.12 (~until6(s72)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13095, 13093])).
% 36.30/24.12 tff(13097,plain,
% 36.30/24.12 (~xuntil7(s71)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10454, 13096])).
% 36.30/24.12 tff(13098,plain,
% 36.30/24.12 (~always5(s71)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8870, 13094])).
% 36.30/24.12 tff(13099,plain,
% 36.30/24.12 (xuntil7(s71) | (~until6(s71))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10448, 9395, 13098])).
% 36.30/24.12 tff(13100,plain,
% 36.30/24.12 (~until6(s71)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13099, 13097])).
% 36.30/24.12 tff(13101,plain,
% 36.30/24.12 (~xuntil7(s70)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10441, 13100])).
% 36.30/24.12 tff(13102,plain,
% 36.30/24.12 (~always5(s70)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8878, 13098])).
% 36.30/24.12 tff(13103,plain,
% 36.30/24.12 (xuntil7(s70) | (~until6(s70))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10435, 9395, 13102])).
% 36.30/24.12 tff(13104,plain,
% 36.30/24.12 (~until6(s70)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13103, 13101])).
% 36.30/24.12 tff(13105,plain,
% 36.30/24.12 (~xuntil7(s69)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10428, 13104])).
% 36.30/24.12 tff(13106,plain,
% 36.30/24.12 (~always5(s69)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8886, 13102])).
% 36.30/24.12 tff(13107,plain,
% 36.30/24.12 (xuntil7(s69) | (~until6(s69))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10422, 9395, 13106])).
% 36.30/24.12 tff(13108,plain,
% 36.30/24.12 (~until6(s69)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13107, 13105])).
% 36.30/24.12 tff(13109,plain,
% 36.30/24.12 (~xuntil7(s68)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10415, 13108])).
% 36.30/24.12 tff(13110,plain,
% 36.30/24.12 (~always5(s68)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8894, 13106])).
% 36.30/24.12 tff(13111,plain,
% 36.30/24.12 (xuntil7(s68) | (~until6(s68))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10409, 9395, 13110])).
% 36.30/24.12 tff(13112,plain,
% 36.30/24.12 (~until6(s68)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13111, 13109])).
% 36.30/24.12 tff(13113,plain,
% 36.30/24.12 (~xuntil7(s67)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10402, 13112])).
% 36.30/24.12 tff(13114,plain,
% 36.30/24.12 (~always5(s67)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8902, 13110])).
% 36.30/24.12 tff(13115,plain,
% 36.30/24.12 (xuntil7(s67) | (~until6(s67))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10396, 9395, 13114])).
% 36.30/24.12 tff(13116,plain,
% 36.30/24.12 (~until6(s67)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13115, 13113])).
% 36.30/24.12 tff(13117,plain,
% 36.30/24.12 (~xuntil7(s66)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10389, 13116])).
% 36.30/24.12 tff(13118,plain,
% 36.30/24.12 (~always5(s66)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8910, 13114])).
% 36.30/24.12 tff(13119,plain,
% 36.30/24.12 (xuntil7(s66) | (~until6(s66))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10383, 9395, 13118])).
% 36.30/24.12 tff(13120,plain,
% 36.30/24.12 (~until6(s66)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13119, 13117])).
% 36.30/24.12 tff(13121,plain,
% 36.30/24.12 (~xuntil7(s65)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10376, 13120])).
% 36.30/24.12 tff(13122,plain,
% 36.30/24.12 (~always5(s65)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8918, 13118])).
% 36.30/24.12 tff(13123,plain,
% 36.30/24.12 (xuntil7(s65) | (~until6(s65))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10370, 9395, 13122])).
% 36.30/24.12 tff(13124,plain,
% 36.30/24.12 (~until6(s65)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13123, 13121])).
% 36.30/24.12 tff(13125,plain,
% 36.30/24.12 (~xuntil7(s64)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10363, 13124])).
% 36.30/24.12 tff(13126,plain,
% 36.30/24.12 (~always5(s64)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8926, 13122])).
% 36.30/24.12 tff(13127,plain,
% 36.30/24.12 (xuntil7(s64) | (~until6(s64))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10357, 9395, 13126])).
% 36.30/24.12 tff(13128,plain,
% 36.30/24.12 (~until6(s64)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13127, 13125])).
% 36.30/24.12 tff(13129,plain,
% 36.30/24.12 (~xuntil7(s63)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10350, 13128])).
% 36.30/24.12 tff(13130,plain,
% 36.30/24.12 (~always5(s63)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8934, 13126])).
% 36.30/24.12 tff(13131,plain,
% 36.30/24.12 (xuntil7(s63) | (~until6(s63))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10344, 9395, 13130])).
% 36.30/24.12 tff(13132,plain,
% 36.30/24.12 (~until6(s63)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13131, 13129])).
% 36.30/24.12 tff(13133,plain,
% 36.30/24.12 (~xuntil7(s62)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10337, 13132])).
% 36.30/24.12 tff(13134,plain,
% 36.30/24.12 (~always5(s62)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8942, 13130])).
% 36.30/24.12 tff(13135,plain,
% 36.30/24.12 (xuntil7(s62) | (~until6(s62))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10331, 9395, 13134])).
% 36.30/24.12 tff(13136,plain,
% 36.30/24.12 (~until6(s62)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13135, 13133])).
% 36.30/24.12 tff(13137,plain,
% 36.30/24.12 (~xuntil7(s61)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10324, 13136])).
% 36.30/24.12 tff(13138,plain,
% 36.30/24.12 (~always5(s61)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8950, 13134])).
% 36.30/24.12 tff(13139,plain,
% 36.30/24.12 (xuntil7(s61) | (~until6(s61))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10318, 9395, 13138])).
% 36.30/24.12 tff(13140,plain,
% 36.30/24.12 (~until6(s61)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13139, 13137])).
% 36.30/24.12 tff(13141,plain,
% 36.30/24.12 (~xuntil7(s60)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10311, 13140])).
% 36.30/24.12 tff(13142,plain,
% 36.30/24.12 (~always5(s60)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8958, 13138])).
% 36.30/24.12 tff(13143,plain,
% 36.30/24.12 (xuntil7(s60) | (~until6(s60))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10305, 9395, 13142])).
% 36.30/24.12 tff(13144,plain,
% 36.30/24.12 (~until6(s60)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13143, 13141])).
% 36.30/24.12 tff(13145,plain,
% 36.30/24.12 (~xuntil7(s59)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10298, 13144])).
% 36.30/24.12 tff(13146,plain,
% 36.30/24.12 (~always5(s59)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[8966, 13142])).
% 36.30/24.12 tff(13147,plain,
% 36.30/24.12 (xuntil7(s59) | (~until6(s59))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10292, 9395, 13146])).
% 36.30/24.12 tff(13148,plain,
% 36.30/24.12 (~until6(s59)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13147, 13145])).
% 36.30/24.12 tff(13149,plain,
% 36.30/24.12 (~xuntil7(s58)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10285, 13148])).
% 36.30/24.12 tff(13150,plain,
% 36.30/24.12 (~always5(s58)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9030, 13146])).
% 36.30/24.12 tff(13151,plain,
% 36.30/24.12 (xuntil7(s58) | (~until6(s58))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10279, 9395, 13150])).
% 36.30/24.12 tff(13152,plain,
% 36.30/24.12 (~until6(s58)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13151, 13149])).
% 36.30/24.12 tff(13153,plain,
% 36.30/24.12 (~xuntil7(s57)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10272, 13152])).
% 36.30/24.12 tff(13154,plain,
% 36.30/24.12 (~always5(s57)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9038, 13150])).
% 36.30/24.12 tff(13155,plain,
% 36.30/24.12 (xuntil7(s57) | (~until6(s57))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10266, 9395, 13154])).
% 36.30/24.12 tff(13156,plain,
% 36.30/24.12 (~until6(s57)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13155, 13153])).
% 36.30/24.12 tff(13157,plain,
% 36.30/24.12 (~xuntil7(s56)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10259, 13156])).
% 36.30/24.12 tff(13158,plain,
% 36.30/24.12 (~always5(s56)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9046, 13154])).
% 36.30/24.12 tff(13159,plain,
% 36.30/24.12 (xuntil7(s56) | (~until6(s56))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10253, 9395, 13158])).
% 36.30/24.12 tff(13160,plain,
% 36.30/24.12 (~until6(s56)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13159, 13157])).
% 36.30/24.12 tff(13161,plain,
% 36.30/24.12 (~xuntil7(s55)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10246, 13160])).
% 36.30/24.12 tff(13162,plain,
% 36.30/24.12 (~always5(s55)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9054, 13158])).
% 36.30/24.12 tff(13163,plain,
% 36.30/24.12 (xuntil7(s55) | (~until6(s55))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10240, 9395, 13162])).
% 36.30/24.12 tff(13164,plain,
% 36.30/24.12 (~until6(s55)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13163, 13161])).
% 36.30/24.12 tff(13165,plain,
% 36.30/24.12 (~xuntil7(s54)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10233, 13164])).
% 36.30/24.12 tff(13166,plain,
% 36.30/24.12 (~always5(s54)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9062, 13162])).
% 36.30/24.12 tff(13167,plain,
% 36.30/24.12 (xuntil7(s54) | (~until6(s54))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10227, 9395, 13166])).
% 36.30/24.12 tff(13168,plain,
% 36.30/24.12 (~until6(s54)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13167, 13165])).
% 36.30/24.12 tff(13169,plain,
% 36.30/24.12 (~xuntil7(s53)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10220, 13168])).
% 36.30/24.12 tff(13170,plain,
% 36.30/24.12 (~always5(s53)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9070, 13166])).
% 36.30/24.12 tff(13171,plain,
% 36.30/24.12 (xuntil7(s53) | (~until6(s53))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10214, 9395, 13170])).
% 36.30/24.12 tff(13172,plain,
% 36.30/24.12 (~until6(s53)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13171, 13169])).
% 36.30/24.12 tff(13173,plain,
% 36.30/24.12 (~xuntil7(s52)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10207, 13172])).
% 36.30/24.12 tff(13174,plain,
% 36.30/24.12 (~always5(s52)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9078, 13170])).
% 36.30/24.12 tff(13175,plain,
% 36.30/24.12 (xuntil7(s52) | (~until6(s52))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10201, 9395, 13174])).
% 36.30/24.12 tff(13176,plain,
% 36.30/24.12 (~until6(s52)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13175, 13173])).
% 36.30/24.12 tff(13177,plain,
% 36.30/24.12 (~xuntil7(s51)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10194, 13176])).
% 36.30/24.12 tff(13178,plain,
% 36.30/24.12 (~always5(s51)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9086, 13174])).
% 36.30/24.12 tff(13179,plain,
% 36.30/24.12 (xuntil7(s51) | (~until6(s51))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10188, 9395, 13178])).
% 36.30/24.12 tff(13180,plain,
% 36.30/24.12 (~until6(s51)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13179, 13177])).
% 36.30/24.12 tff(13181,plain,
% 36.30/24.12 (~xuntil7(s50)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10181, 13180])).
% 36.30/24.12 tff(13182,plain,
% 36.30/24.12 (~always5(s50)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9094, 13178])).
% 36.30/24.12 tff(13183,plain,
% 36.30/24.12 (~always5(s49)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9102, 13182])).
% 36.30/24.12 tff(13184,plain,
% 36.30/24.12 (~always5(s48)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9110, 13183])).
% 36.30/24.12 tff(13185,plain,
% 36.30/24.12 (~always5(s47)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9118, 13184])).
% 36.30/24.12 tff(13186,plain,
% 36.30/24.12 (~always5(s46)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9126, 13185])).
% 36.30/24.12 tff(13187,plain,
% 36.30/24.12 (~always5(s45)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9134, 13186])).
% 36.30/24.12 tff(13188,plain,
% 36.30/24.12 (~always5(s44)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9142, 13187])).
% 36.30/24.12 tff(13189,plain,
% 36.30/24.12 (~always5(s43)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9150, 13188])).
% 36.30/24.12 tff(13190,plain,
% 36.30/24.12 (~always5(s42)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9158, 13189])).
% 36.30/24.12 tff(13191,plain,
% 36.30/24.12 (~always5(s41)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9166, 13190])).
% 36.30/24.12 tff(13192,plain,
% 36.30/24.12 (~always5(s40)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9174, 13191])).
% 36.30/24.12 tff(13193,plain,
% 36.30/24.12 (~always5(s39)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9182, 13192])).
% 36.30/24.12 tff(13194,plain,
% 36.30/24.12 (~always5(s38)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9190, 13193])).
% 36.30/24.12 tff(13195,plain,
% 36.30/24.12 (~always5(s37)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9198, 13194])).
% 36.30/24.12 tff(13196,plain,
% 36.30/24.12 (~always5(s36)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9206, 13195])).
% 36.30/24.12 tff(13197,plain,
% 36.30/24.12 (~always5(s35)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9214, 13196])).
% 36.30/24.12 tff(13198,plain,
% 36.30/24.12 (~always5(s34)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9222, 13197])).
% 36.30/24.12 tff(13199,plain,
% 36.30/24.12 (~always5(s33)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9230, 13198])).
% 36.30/24.12 tff(13200,plain,
% 36.30/24.12 (~always5(s32)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9238, 13199])).
% 36.30/24.12 tff(13201,plain,
% 36.30/24.12 (~always5(s31)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9246, 13200])).
% 36.30/24.12 tff(13202,plain,
% 36.30/24.12 (~always5(s30)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9254, 13201])).
% 36.30/24.12 tff(13203,plain,
% 36.30/24.12 (~always5(s29)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9262, 13202])).
% 36.30/24.12 tff(13204,plain,
% 36.30/24.12 (~always5(s28)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9270, 13203])).
% 36.30/24.12 tff(13205,plain,
% 36.30/24.12 (~always5(s27)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9278, 13204])).
% 36.30/24.12 tff(13206,plain,
% 36.30/24.12 (~always5(s26)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9286, 13205])).
% 36.30/24.12 tff(13207,plain,
% 36.30/24.12 (~always5(s25)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9294, 13206])).
% 36.30/24.12 tff(13208,plain,
% 36.30/24.12 (~always5(s24)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9302, 13207])).
% 36.30/24.12 tff(13209,plain,
% 36.30/24.12 (~always5(s23)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9310, 13208])).
% 36.30/24.12 tff(13210,plain,
% 36.30/24.12 (~always5(s22)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9318, 13209])).
% 36.30/24.12 tff(13211,plain,
% 36.30/24.12 (~always5(s21)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9326, 13210])).
% 36.30/24.12 tff(13212,plain,
% 36.30/24.12 (~always5(s20)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9334, 13211])).
% 36.30/24.12 tff(13213,plain,
% 36.30/24.12 (~always5(s19)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9342, 13212])).
% 36.30/24.12 tff(13214,plain,
% 36.30/24.12 (~always5(s18)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9350, 13213])).
% 36.30/24.12 tff(13215,plain,
% 36.30/24.12 (~always5(s17)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9358, 13214])).
% 36.30/24.12 tff(13216,plain,
% 36.30/24.12 (~always5(s16)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9366, 13215])).
% 36.30/24.12 tff(13217,plain,
% 36.30/24.12 (~always5(s15)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9374, 13216])).
% 36.30/24.12 tff(13218,plain,
% 36.30/24.12 (~always5(s14)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9383, 13217])).
% 36.30/24.12 tff(13219,plain,
% 36.30/24.12 (~always5(s13)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9437, 13218])).
% 36.30/24.12 tff(13220,plain,
% 36.30/24.12 (~always5(s12)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9458, 13219])).
% 36.30/24.12 tff(13221,plain,
% 36.30/24.12 (~always5(s11)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9479, 13220])).
% 36.30/24.12 tff(13222,plain,
% 36.30/24.12 (~always5(s10)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9500, 13221])).
% 36.30/24.12 tff(13223,plain,
% 36.30/24.12 (~always5(s9)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9521, 13222])).
% 36.30/24.12 tff(13224,plain,
% 36.30/24.12 (~always5(s8)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9542, 13223])).
% 36.30/24.12 tff(13225,plain,
% 36.30/24.12 (~always5(s7)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9558, 13224])).
% 36.30/24.12 tff(13226,plain,
% 36.30/24.12 (~always5(s6)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9566, 13225])).
% 36.30/24.12 tff(13227,plain,
% 36.30/24.12 (~always5(s5)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9574, 13226])).
% 36.30/24.12 tff(13228,plain,
% 36.30/24.12 (~always5(s4)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9582, 13227])).
% 36.30/24.12 tff(13229,plain,
% 36.30/24.12 (~always5(s3)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9590, 13228])).
% 36.30/24.12 tff(13230,plain,
% 36.30/24.12 (~always5(s2)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9598, 13229])).
% 36.30/24.12 tff(13231,plain,
% 36.30/24.12 (~always5(s1)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9606, 13230])).
% 36.30/24.12 tff(13232,plain,
% 36.30/24.12 (~always5(s0)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9614, 13231])).
% 36.30/24.12 tff(13233,plain,
% 36.30/24.12 (xuntil7(s0)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9625, 13232])).
% 36.30/24.12 tff(13234,plain,
% 36.30/24.12 (until6(s1)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9630, 13233])).
% 36.30/24.12 tff(13235,plain,
% 36.30/24.12 (xuntil7(s1)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9637, 9395, 13234, 13231])).
% 36.30/24.12 tff(13236,plain,
% 36.30/24.12 (until6(s2)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9642, 13235])).
% 36.30/24.12 tff(13237,plain,
% 36.30/24.12 (xuntil7(s2) | (~until6(s2))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9649, 9395, 13230])).
% 36.30/24.12 tff(13238,plain,
% 36.30/24.12 (xuntil7(s2)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13237, 13236])).
% 36.30/24.12 tff(13239,plain,
% 36.30/24.12 (until6(s3)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9655, 13238])).
% 36.30/24.12 tff(13240,plain,
% 36.30/24.12 (xuntil7(s3) | (~until6(s3))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9662, 9395, 13229])).
% 36.30/24.12 tff(13241,plain,
% 36.30/24.12 (xuntil7(s3)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13240, 13239])).
% 36.30/24.12 tff(13242,plain,
% 36.30/24.12 (until6(s4)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9668, 13241])).
% 36.30/24.12 tff(13243,plain,
% 36.30/24.12 (xuntil7(s4) | (~until6(s4))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9675, 9395, 13228])).
% 36.30/24.12 tff(13244,plain,
% 36.30/24.12 (xuntil7(s4)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13243, 13242])).
% 36.30/24.12 tff(13245,plain,
% 36.30/24.12 (until6(s5)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9681, 13244])).
% 36.30/24.12 tff(13246,plain,
% 36.30/24.12 (xuntil7(s5) | (~until6(s5))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9688, 9395, 13227])).
% 36.30/24.12 tff(13247,plain,
% 36.30/24.12 (xuntil7(s5)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13246, 13245])).
% 36.30/24.12 tff(13248,plain,
% 36.30/24.12 (until6(s6)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9694, 13247])).
% 36.30/24.12 tff(13249,plain,
% 36.30/24.12 (xuntil7(s6) | (~until6(s6))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9701, 9395, 13226])).
% 36.30/24.12 tff(13250,plain,
% 36.30/24.12 (xuntil7(s6)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13249, 13248])).
% 36.30/24.12 tff(13251,plain,
% 36.30/24.12 (until6(s7)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9707, 13250])).
% 36.30/24.12 tff(13252,plain,
% 36.30/24.12 (xuntil7(s7) | (~until6(s7))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9714, 9395, 13225])).
% 36.30/24.12 tff(13253,plain,
% 36.30/24.12 (xuntil7(s7)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13252, 13251])).
% 36.30/24.12 tff(13254,plain,
% 36.30/24.12 (until6(s8)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9720, 13253])).
% 36.30/24.12 tff(13255,plain,
% 36.30/24.12 (xuntil7(s8) | (~until6(s8))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9549, 9395, 13224])).
% 36.30/24.12 tff(13256,plain,
% 36.30/24.12 (xuntil7(s8)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13255, 13254])).
% 36.30/24.12 tff(13257,plain,
% 36.30/24.12 (until6(s9)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9534, 13256])).
% 36.30/24.12 tff(13258,plain,
% 36.30/24.12 (xuntil7(s9) | (~until6(s9))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9528, 9395, 13223])).
% 36.30/24.12 tff(13259,plain,
% 36.30/24.12 (xuntil7(s9)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13258, 13257])).
% 36.30/24.12 tff(13260,plain,
% 36.30/24.12 (until6(s10)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9513, 13259])).
% 36.30/24.12 tff(13261,plain,
% 36.30/24.12 (xuntil7(s10) | (~until6(s10))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9507, 9395, 13222])).
% 36.30/24.12 tff(13262,plain,
% 36.30/24.12 (xuntil7(s10)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13261, 13260])).
% 36.30/24.12 tff(13263,plain,
% 36.30/24.12 (until6(s11)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9492, 13262])).
% 36.30/24.12 tff(13264,plain,
% 36.30/24.12 (xuntil7(s11) | (~until6(s11))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9486, 9395, 13221])).
% 36.30/24.12 tff(13265,plain,
% 36.30/24.12 (xuntil7(s11)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13264, 13263])).
% 36.30/24.12 tff(13266,plain,
% 36.30/24.12 (until6(s12)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9471, 13265])).
% 36.30/24.12 tff(13267,plain,
% 36.30/24.12 (xuntil7(s12) | (~until6(s12))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9465, 9395, 13220])).
% 36.30/24.12 tff(13268,plain,
% 36.30/24.12 (xuntil7(s12)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13267, 13266])).
% 36.30/24.12 tff(13269,plain,
% 36.30/24.12 (until6(s13)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9450, 13268])).
% 36.30/24.12 tff(13270,plain,
% 36.30/24.12 (xuntil7(s13) | (~until6(s13))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9444, 9395, 13219])).
% 36.30/24.12 tff(13271,plain,
% 36.30/24.12 (xuntil7(s13)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13270, 13269])).
% 36.30/24.12 tff(13272,plain,
% 36.30/24.12 (until6(s14)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9429, 13271])).
% 36.30/24.12 tff(13273,plain,
% 36.30/24.12 (xuntil7(s14) | (~until6(s14))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9424, 9395, 13218])).
% 36.30/24.12 tff(13274,plain,
% 36.30/24.12 (xuntil7(s14)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13273, 13272])).
% 36.30/24.12 tff(13275,plain,
% 36.30/24.12 (until6(s15)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9417, 13274])).
% 36.30/24.12 tff(13276,plain,
% 36.30/24.12 (xuntil7(s15) | (~until6(s15))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9401, 9395, 13217])).
% 36.30/24.12 tff(13277,plain,
% 36.30/24.12 (xuntil7(s15)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13276, 13275])).
% 36.30/24.12 tff(13278,plain,
% 36.30/24.12 (until6(s16)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9727, 13277])).
% 36.30/24.12 tff(13279,plain,
% 36.30/24.12 (xuntil7(s16) | (~until6(s16))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9734, 9395, 13216])).
% 36.30/24.12 tff(13280,plain,
% 36.30/24.12 (xuntil7(s16)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13279, 13278])).
% 36.30/24.12 tff(13281,plain,
% 36.30/24.12 (until6(s17)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9739, 13280])).
% 36.30/24.12 tff(13282,plain,
% 36.30/24.12 (xuntil7(s17) | (~until6(s17))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9746, 9395, 13215])).
% 36.30/24.12 tff(13283,plain,
% 36.30/24.12 (xuntil7(s17)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13282, 13281])).
% 36.30/24.12 tff(13284,plain,
% 36.30/24.12 (until6(s18)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9752, 13283])).
% 36.30/24.12 tff(13285,plain,
% 36.30/24.12 (xuntil7(s18) | (~until6(s18))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9759, 9395, 13214])).
% 36.30/24.12 tff(13286,plain,
% 36.30/24.12 (xuntil7(s18)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13285, 13284])).
% 36.30/24.12 tff(13287,plain,
% 36.30/24.12 (until6(s19)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9765, 13286])).
% 36.30/24.12 tff(13288,plain,
% 36.30/24.12 (xuntil7(s19) | (~until6(s19))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9772, 9395, 13213])).
% 36.30/24.12 tff(13289,plain,
% 36.30/24.12 (xuntil7(s19)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13288, 13287])).
% 36.30/24.12 tff(13290,plain,
% 36.30/24.12 (until6(s20)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9778, 13289])).
% 36.30/24.12 tff(13291,plain,
% 36.30/24.12 (xuntil7(s20) | (~until6(s20))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9785, 9395, 13212])).
% 36.30/24.12 tff(13292,plain,
% 36.30/24.12 (xuntil7(s20)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13291, 13290])).
% 36.30/24.12 tff(13293,plain,
% 36.30/24.12 (until6(s21)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9791, 13292])).
% 36.30/24.12 tff(13294,plain,
% 36.30/24.12 (xuntil7(s21) | (~until6(s21))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9798, 9395, 13211])).
% 36.30/24.12 tff(13295,plain,
% 36.30/24.12 (xuntil7(s21)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13294, 13293])).
% 36.30/24.12 tff(13296,plain,
% 36.30/24.12 (until6(s22)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9804, 13295])).
% 36.30/24.12 tff(13297,plain,
% 36.30/24.12 (xuntil7(s22) | (~until6(s22))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9811, 9395, 13210])).
% 36.30/24.12 tff(13298,plain,
% 36.30/24.12 (xuntil7(s22)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13297, 13296])).
% 36.30/24.12 tff(13299,plain,
% 36.30/24.12 (until6(s23)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9817, 13298])).
% 36.30/24.12 tff(13300,plain,
% 36.30/24.12 (xuntil7(s23) | (~until6(s23))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9824, 9395, 13209])).
% 36.30/24.12 tff(13301,plain,
% 36.30/24.12 (xuntil7(s23)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13300, 13299])).
% 36.30/24.12 tff(13302,plain,
% 36.30/24.12 (until6(s24)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9830, 13301])).
% 36.30/24.12 tff(13303,plain,
% 36.30/24.12 (xuntil7(s24) | (~until6(s24))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9837, 9395, 13208])).
% 36.30/24.12 tff(13304,plain,
% 36.30/24.12 (xuntil7(s24)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13303, 13302])).
% 36.30/24.12 tff(13305,plain,
% 36.30/24.12 (until6(s25)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9843, 13304])).
% 36.30/24.12 tff(13306,plain,
% 36.30/24.12 (xuntil7(s25) | (~until6(s25))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9850, 9395, 13207])).
% 36.30/24.12 tff(13307,plain,
% 36.30/24.12 (xuntil7(s25)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13306, 13305])).
% 36.30/24.12 tff(13308,plain,
% 36.30/24.12 (until6(s26)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9856, 13307])).
% 36.30/24.12 tff(13309,plain,
% 36.30/24.12 (xuntil7(s26) | (~until6(s26))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9863, 9395, 13206])).
% 36.30/24.12 tff(13310,plain,
% 36.30/24.12 (xuntil7(s26)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13309, 13308])).
% 36.30/24.12 tff(13311,plain,
% 36.30/24.12 (until6(s27)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9869, 13310])).
% 36.30/24.12 tff(13312,plain,
% 36.30/24.12 (xuntil7(s27) | (~until6(s27))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9876, 9395, 13205])).
% 36.30/24.12 tff(13313,plain,
% 36.30/24.12 (xuntil7(s27)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13312, 13311])).
% 36.30/24.12 tff(13314,plain,
% 36.30/24.12 (until6(s28)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9882, 13313])).
% 36.30/24.12 tff(13315,plain,
% 36.30/24.12 (xuntil7(s28) | (~until6(s28))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9889, 9395, 13204])).
% 36.30/24.12 tff(13316,plain,
% 36.30/24.12 (xuntil7(s28)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13315, 13314])).
% 36.30/24.12 tff(13317,plain,
% 36.30/24.12 (until6(s29)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9895, 13316])).
% 36.30/24.12 tff(13318,plain,
% 36.30/24.12 (xuntil7(s29) | (~until6(s29))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9902, 9395, 13203])).
% 36.30/24.12 tff(13319,plain,
% 36.30/24.12 (xuntil7(s29)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13318, 13317])).
% 36.30/24.12 tff(13320,plain,
% 36.30/24.12 (until6(s30)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9908, 13319])).
% 36.30/24.12 tff(13321,plain,
% 36.30/24.12 (xuntil7(s30) | (~until6(s30))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9915, 9395, 13202])).
% 36.30/24.12 tff(13322,plain,
% 36.30/24.12 (xuntil7(s30)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13321, 13320])).
% 36.30/24.12 tff(13323,plain,
% 36.30/24.12 (until6(s31)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9921, 13322])).
% 36.30/24.12 tff(13324,plain,
% 36.30/24.12 (xuntil7(s31) | (~until6(s31))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9928, 9395, 13201])).
% 36.30/24.12 tff(13325,plain,
% 36.30/24.12 (xuntil7(s31)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13324, 13323])).
% 36.30/24.12 tff(13326,plain,
% 36.30/24.12 (until6(s32)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9934, 13325])).
% 36.30/24.12 tff(13327,plain,
% 36.30/24.12 (xuntil7(s32) | (~until6(s32))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9941, 9395, 13200])).
% 36.30/24.12 tff(13328,plain,
% 36.30/24.12 (xuntil7(s32)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13327, 13326])).
% 36.30/24.12 tff(13329,plain,
% 36.30/24.12 (until6(s33)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9947, 13328])).
% 36.30/24.12 tff(13330,plain,
% 36.30/24.12 (xuntil7(s33) | (~until6(s33))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9954, 9395, 13199])).
% 36.30/24.12 tff(13331,plain,
% 36.30/24.12 (xuntil7(s33)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13330, 13329])).
% 36.30/24.12 tff(13332,plain,
% 36.30/24.12 (until6(s34)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9960, 13331])).
% 36.30/24.12 tff(13333,plain,
% 36.30/24.12 (xuntil7(s34) | (~until6(s34))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9967, 9395, 13198])).
% 36.30/24.12 tff(13334,plain,
% 36.30/24.12 (xuntil7(s34)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13333, 13332])).
% 36.30/24.12 tff(13335,plain,
% 36.30/24.12 (until6(s35)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9973, 13334])).
% 36.30/24.12 tff(13336,plain,
% 36.30/24.12 (xuntil7(s35) | (~until6(s35))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9980, 9395, 13197])).
% 36.30/24.12 tff(13337,plain,
% 36.30/24.12 (xuntil7(s35)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13336, 13335])).
% 36.30/24.12 tff(13338,plain,
% 36.30/24.12 (until6(s36)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9986, 13337])).
% 36.30/24.12 tff(13339,plain,
% 36.30/24.12 (xuntil7(s36) | (~until6(s36))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9993, 9395, 13196])).
% 36.30/24.12 tff(13340,plain,
% 36.30/24.12 (xuntil7(s36)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13339, 13338])).
% 36.30/24.12 tff(13341,plain,
% 36.30/24.12 (until6(s37)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[9999, 13340])).
% 36.30/24.12 tff(13342,plain,
% 36.30/24.12 (xuntil7(s37) | (~until6(s37))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10006, 9395, 13195])).
% 36.30/24.12 tff(13343,plain,
% 36.30/24.12 (xuntil7(s37)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13342, 13341])).
% 36.30/24.12 tff(13344,plain,
% 36.30/24.12 (until6(s38)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10012, 13343])).
% 36.30/24.12 tff(13345,plain,
% 36.30/24.12 (xuntil7(s38) | (~until6(s38))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10019, 9395, 13194])).
% 36.30/24.12 tff(13346,plain,
% 36.30/24.12 (xuntil7(s38)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13345, 13344])).
% 36.30/24.12 tff(13347,plain,
% 36.30/24.12 (until6(s39)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10025, 13346])).
% 36.30/24.12 tff(13348,plain,
% 36.30/24.12 (xuntil7(s39) | (~until6(s39))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10032, 9395, 13193])).
% 36.30/24.12 tff(13349,plain,
% 36.30/24.12 (xuntil7(s39)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13348, 13347])).
% 36.30/24.12 tff(13350,plain,
% 36.30/24.12 (until6(s40)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10038, 13349])).
% 36.30/24.12 tff(13351,plain,
% 36.30/24.12 (xuntil7(s40) | (~until6(s40))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10045, 9395, 13192])).
% 36.30/24.12 tff(13352,plain,
% 36.30/24.12 (xuntil7(s40)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13351, 13350])).
% 36.30/24.12 tff(13353,plain,
% 36.30/24.12 (until6(s41)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10051, 13352])).
% 36.30/24.12 tff(13354,plain,
% 36.30/24.12 (xuntil7(s41) | (~until6(s41))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10058, 9395, 13191])).
% 36.30/24.12 tff(13355,plain,
% 36.30/24.12 (xuntil7(s41)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13354, 13353])).
% 36.30/24.12 tff(13356,plain,
% 36.30/24.12 (until6(s42)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10064, 13355])).
% 36.30/24.12 tff(13357,plain,
% 36.30/24.12 (xuntil7(s42) | (~until6(s42))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10071, 9395, 13190])).
% 36.30/24.12 tff(13358,plain,
% 36.30/24.12 (xuntil7(s42)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13357, 13356])).
% 36.30/24.12 tff(13359,plain,
% 36.30/24.12 (until6(s43)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10077, 13358])).
% 36.30/24.12 tff(13360,plain,
% 36.30/24.12 (xuntil7(s43) | (~until6(s43))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10084, 9395, 13189])).
% 36.30/24.12 tff(13361,plain,
% 36.30/24.12 (xuntil7(s43)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13360, 13359])).
% 36.30/24.12 tff(13362,plain,
% 36.30/24.12 (until6(s44)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10090, 13361])).
% 36.30/24.12 tff(13363,plain,
% 36.30/24.12 (xuntil7(s44) | (~until6(s44))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10097, 9395, 13188])).
% 36.30/24.12 tff(13364,plain,
% 36.30/24.12 (xuntil7(s44)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13363, 13362])).
% 36.30/24.12 tff(13365,plain,
% 36.30/24.12 (until6(s45)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10103, 13364])).
% 36.30/24.12 tff(13366,plain,
% 36.30/24.12 (xuntil7(s45) | (~until6(s45))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10110, 9395, 13187])).
% 36.30/24.12 tff(13367,plain,
% 36.30/24.12 (xuntil7(s45)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13366, 13365])).
% 36.30/24.12 tff(13368,plain,
% 36.30/24.12 (until6(s46)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10116, 13367])).
% 36.30/24.12 tff(13369,plain,
% 36.30/24.12 (xuntil7(s46) | (~until6(s46))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10123, 9395, 13186])).
% 36.30/24.12 tff(13370,plain,
% 36.30/24.12 (xuntil7(s46)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13369, 13368])).
% 36.30/24.12 tff(13371,plain,
% 36.30/24.12 (until6(s47)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10129, 13370])).
% 36.30/24.12 tff(13372,plain,
% 36.30/24.12 (xuntil7(s47) | (~until6(s47))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10136, 9395, 13185])).
% 36.30/24.12 tff(13373,plain,
% 36.30/24.12 (xuntil7(s47)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13372, 13371])).
% 36.30/24.12 tff(13374,plain,
% 36.30/24.12 (until6(s48)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10142, 13373])).
% 36.30/24.12 tff(13375,plain,
% 36.30/24.12 (xuntil7(s48) | (~until6(s48))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10149, 9395, 13184])).
% 36.30/24.12 tff(13376,plain,
% 36.30/24.12 (xuntil7(s48)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13375, 13374])).
% 36.30/24.12 tff(13377,plain,
% 36.30/24.12 (until6(s49)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10155, 13376])).
% 36.30/24.12 tff(13378,plain,
% 36.30/24.12 (xuntil7(s49) | (~until6(s49))),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10162, 9395, 13183])).
% 36.30/24.12 tff(13379,plain,
% 36.30/24.12 (xuntil7(s49)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[13378, 13377])).
% 36.30/24.12 tff(13380,plain,
% 36.30/24.12 (until6(s50)),
% 36.30/24.12 inference(unit_resolution,[status(thm)],[10168, 13379])).
% 36.30/24.13 tff(13381,plain,
% 36.30/24.13 (xuntil7(s50) | (~until6(s50))),
% 36.30/24.13 inference(unit_resolution,[status(thm)],[10175, 9395, 13182])).
% 36.30/24.13 tff(13382,plain,
% 36.30/24.13 ($false),
% 36.30/24.13 inference(unit_resolution,[status(thm)],[13381, 13380, 13181])).
% 36.30/24.13 tff(13383,plain,(loop), inference(lemma,lemma(discharge,[]))).
% 36.30/24.13 tff(13384,plain,
% 36.30/24.13 (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 36.30/24.13 inference(rewrite,[status(thm)],[])).
% 36.30/24.13 tff(13385,plain,
% 36.30/24.13 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98)) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 36.30/24.13 inference(rewrite,[status(thm)],[])).
% 36.30/24.13 tff(13386,plain,
% 36.30/24.13 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97)) | trans(s99, s98)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98))),
% 36.30/24.13 inference(rewrite,[status(thm)],[])).
% 36.30/24.13 tff(13387,plain,
% 36.30/24.13 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96)) | trans(s99, s97)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97))),
% 36.30/24.14 inference(rewrite,[status(thm)],[])).
% 36.30/24.14 tff(13388,plain,
% 36.30/24.14 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95)) | trans(s99, s96)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96))),
% 36.30/24.14 inference(rewrite,[status(thm)],[])).
% 36.30/24.14 tff(13389,plain,
% 36.30/24.14 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94)) | trans(s99, s95)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95))),
% 36.30/24.14 inference(rewrite,[status(thm)],[])).
% 36.30/24.14 tff(13390,plain,
% 36.30/24.14 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93)) | trans(s99, s94)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94))),
% 36.34/24.15 inference(rewrite,[status(thm)],[])).
% 36.34/24.15 tff(13391,plain,
% 36.34/24.15 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92)) | trans(s99, s93)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93))),
% 36.34/24.15 inference(rewrite,[status(thm)],[])).
% 36.34/24.15 tff(13392,plain,
% 36.34/24.15 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91)) | trans(s99, s92)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92))),
% 36.34/24.15 inference(rewrite,[status(thm)],[])).
% 36.34/24.15 tff(13393,plain,
% 36.34/24.15 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90)) | trans(s99, s91)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91))),
% 36.34/24.15 inference(rewrite,[status(thm)],[])).
% 36.34/24.15 tff(13394,plain,
% 36.34/24.15 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89)) | trans(s99, s90)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90))),
% 36.34/24.16 inference(rewrite,[status(thm)],[])).
% 36.34/24.16 tff(13395,plain,
% 36.34/24.16 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88)) | trans(s99, s89)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89))),
% 36.34/24.16 inference(rewrite,[status(thm)],[])).
% 36.34/24.16 tff(13396,plain,
% 36.34/24.16 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87)) | trans(s99, s88)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88))),
% 36.34/24.16 inference(rewrite,[status(thm)],[])).
% 36.34/24.16 tff(13397,plain,
% 36.34/24.16 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86)) | trans(s99, s87)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87))),
% 36.34/24.16 inference(rewrite,[status(thm)],[])).
% 36.34/24.16 tff(13398,plain,
% 36.34/24.16 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85)) | trans(s99, s86)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86))),
% 36.34/24.17 inference(rewrite,[status(thm)],[])).
% 36.34/24.17 tff(13399,plain,
% 36.34/24.17 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84)) | trans(s99, s85)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85))),
% 36.34/24.17 inference(rewrite,[status(thm)],[])).
% 36.34/24.17 tff(13400,plain,
% 36.34/24.17 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83)) | trans(s99, s84)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84))),
% 36.34/24.17 inference(rewrite,[status(thm)],[])).
% 36.34/24.17 tff(13401,plain,
% 36.34/24.17 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82)) | trans(s99, s83)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83))),
% 36.34/24.17 inference(rewrite,[status(thm)],[])).
% 36.34/24.17 tff(13402,plain,
% 36.34/24.17 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81)) | trans(s99, s82)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82))),
% 36.34/24.17 inference(rewrite,[status(thm)],[])).
% 36.34/24.17 tff(13403,plain,
% 36.34/24.17 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80)) | trans(s99, s81)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81))),
% 36.34/24.18 inference(rewrite,[status(thm)],[])).
% 36.34/24.18 tff(13404,plain,
% 36.34/24.18 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79)) | trans(s99, s80)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80))),
% 36.34/24.18 inference(rewrite,[status(thm)],[])).
% 36.34/24.18 tff(13405,plain,
% 36.34/24.18 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78)) | trans(s99, s79)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79))),
% 36.34/24.18 inference(rewrite,[status(thm)],[])).
% 36.34/24.18 tff(13406,plain,
% 36.34/24.18 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77)) | trans(s99, s78)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78))),
% 36.34/24.18 inference(rewrite,[status(thm)],[])).
% 36.34/24.18 tff(13407,plain,
% 36.34/24.18 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76)) | trans(s99, s77)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77))),
% 36.34/24.19 inference(rewrite,[status(thm)],[])).
% 36.34/24.19 tff(13408,plain,
% 36.34/24.19 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75)) | trans(s99, s76)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76))),
% 36.34/24.19 inference(rewrite,[status(thm)],[])).
% 36.34/24.19 tff(13409,plain,
% 36.34/24.19 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74)) | trans(s99, s75)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75))),
% 36.34/24.19 inference(rewrite,[status(thm)],[])).
% 36.34/24.19 tff(13410,plain,
% 36.34/24.19 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73)) | trans(s99, s74)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74))),
% 36.34/24.19 inference(rewrite,[status(thm)],[])).
% 36.34/24.19 tff(13411,plain,
% 36.34/24.19 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72)) | trans(s99, s73)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73))),
% 36.34/24.20 inference(rewrite,[status(thm)],[])).
% 36.34/24.20 tff(13412,plain,
% 36.34/24.20 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71)) | trans(s99, s72)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72))),
% 36.34/24.20 inference(rewrite,[status(thm)],[])).
% 36.34/24.20 tff(13413,plain,
% 36.34/24.20 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70)) | trans(s99, s71)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71))),
% 36.34/24.20 inference(rewrite,[status(thm)],[])).
% 36.34/24.20 tff(13414,plain,
% 36.34/24.20 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69)) | trans(s99, s70)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70))),
% 36.34/24.20 inference(rewrite,[status(thm)],[])).
% 36.34/24.20 tff(13415,plain,
% 36.34/24.20 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68)) | trans(s99, s69)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69))),
% 36.34/24.20 inference(rewrite,[status(thm)],[])).
% 36.34/24.20 tff(13416,plain,
% 36.34/24.20 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67)) | trans(s99, s68)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68))),
% 36.34/24.21 inference(rewrite,[status(thm)],[])).
% 36.34/24.21 tff(13417,plain,
% 36.34/24.21 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66)) | trans(s99, s67)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67))),
% 36.34/24.21 inference(rewrite,[status(thm)],[])).
% 36.34/24.21 tff(13418,plain,
% 36.34/24.21 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65)) | trans(s99, s66)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66))),
% 36.34/24.21 inference(rewrite,[status(thm)],[])).
% 36.34/24.21 tff(13419,plain,
% 36.34/24.21 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64)) | trans(s99, s65)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65))),
% 36.34/24.21 inference(rewrite,[status(thm)],[])).
% 36.34/24.21 tff(13420,plain,
% 36.34/24.21 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63)) | trans(s99, s64)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64))),
% 36.34/24.21 inference(rewrite,[status(thm)],[])).
% 36.34/24.21 tff(13421,plain,
% 36.34/24.21 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62)) | trans(s99, s63)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63))),
% 36.34/24.22 inference(rewrite,[status(thm)],[])).
% 36.34/24.22 tff(13422,plain,
% 36.34/24.22 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61)) | trans(s99, s62)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62))),
% 36.34/24.22 inference(rewrite,[status(thm)],[])).
% 36.34/24.22 tff(13423,plain,
% 36.34/24.22 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60)) | trans(s99, s61)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61))),
% 36.34/24.22 inference(rewrite,[status(thm)],[])).
% 36.34/24.22 tff(13424,plain,
% 36.34/24.22 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59)) | trans(s99, s60)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60))),
% 36.34/24.22 inference(rewrite,[status(thm)],[])).
% 36.34/24.22 tff(13425,plain,
% 36.34/24.22 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58)) | trans(s99, s59)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59))),
% 36.34/24.22 inference(rewrite,[status(thm)],[])).
% 36.34/24.22 tff(13426,plain,
% 36.34/24.22 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57)) | trans(s99, s58)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58))),
% 36.34/24.23 inference(rewrite,[status(thm)],[])).
% 36.34/24.23 tff(13427,plain,
% 36.34/24.23 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56)) | trans(s99, s57)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57))),
% 36.34/24.23 inference(rewrite,[status(thm)],[])).
% 36.34/24.23 tff(13428,plain,
% 36.34/24.23 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55)) | trans(s99, s56)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56))),
% 36.34/24.23 inference(rewrite,[status(thm)],[])).
% 36.34/24.23 tff(13429,plain,
% 36.34/24.23 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54)) | trans(s99, s55)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55))),
% 36.34/24.23 inference(rewrite,[status(thm)],[])).
% 36.34/24.23 tff(13430,plain,
% 36.34/24.23 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53)) | trans(s99, s54)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54))),
% 36.34/24.23 inference(rewrite,[status(thm)],[])).
% 36.34/24.23 tff(13431,plain,
% 36.34/24.23 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52)) | trans(s99, s53)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53))),
% 36.34/24.23 inference(rewrite,[status(thm)],[])).
% 36.34/24.23 tff(13432,plain,
% 36.34/24.23 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51)) | trans(s99, s52)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52))),
% 36.43/24.23 inference(rewrite,[status(thm)],[])).
% 36.43/24.23 tff(13433,plain,
% 36.43/24.23 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50)) | trans(s99, s51)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51))),
% 36.43/24.23 inference(rewrite,[status(thm)],[])).
% 36.43/24.23 tff(13434,plain,
% 36.43/24.23 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49)) | trans(s99, s50)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50))),
% 36.43/24.24 inference(rewrite,[status(thm)],[])).
% 36.43/24.24 tff(13435,plain,
% 36.43/24.24 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48)) | trans(s99, s49)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49))),
% 36.43/24.24 inference(rewrite,[status(thm)],[])).
% 36.43/24.24 tff(13436,plain,
% 36.43/24.24 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47)) | trans(s99, s48)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48))),
% 36.43/24.24 inference(rewrite,[status(thm)],[])).
% 36.43/24.24 tff(13437,plain,
% 36.43/24.24 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46)) | trans(s99, s47)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47))),
% 36.43/24.24 inference(rewrite,[status(thm)],[])).
% 36.43/24.24 tff(13438,plain,
% 36.43/24.24 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45)) | trans(s99, s46)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46))),
% 36.43/24.24 inference(rewrite,[status(thm)],[])).
% 36.43/24.24 tff(13439,plain,
% 36.43/24.24 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44)) | trans(s99, s45)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45))),
% 36.43/24.24 inference(rewrite,[status(thm)],[])).
% 36.43/24.24 tff(13440,plain,
% 36.43/24.24 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43)) | trans(s99, s44)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44))),
% 36.43/24.24 inference(rewrite,[status(thm)],[])).
% 36.43/24.24 tff(13441,plain,
% 36.43/24.24 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42)) | trans(s99, s43)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13442,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41)) | trans(s99, s42)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13443,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40)) | trans(s99, s41)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13444,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39)) | trans(s99, s40)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13445,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38)) | trans(s99, s39)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13446,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37)) | trans(s99, s38)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13447,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36)) | trans(s99, s37)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13448,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35)) | trans(s99, s36)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13449,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34)) | trans(s99, s35)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35))),
% 36.43/24.25 inference(rewrite,[status(thm)],[])).
% 36.43/24.25 tff(13450,plain,
% 36.43/24.25 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33)) | trans(s99, s34)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13451,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32)) | trans(s99, s33)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13452,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31)) | trans(s99, s32)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13453,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30)) | trans(s99, s31)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13454,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29)) | trans(s99, s30)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13455,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28)) | trans(s99, s29)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13456,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27)) | trans(s99, s28)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13457,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26)) | trans(s99, s27)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13458,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25)) | trans(s99, s26)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13459,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24)) | trans(s99, s25)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25))),
% 36.43/24.26 inference(rewrite,[status(thm)],[])).
% 36.43/24.26 tff(13460,plain,
% 36.43/24.26 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23)) | trans(s99, s24)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13461,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22)) | trans(s99, s23)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13462,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21)) | trans(s99, s22)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13463,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20)) | trans(s99, s21)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13464,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19)) | trans(s99, s20)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13465,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18)) | trans(s99, s19)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13466,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17)) | trans(s99, s18)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13467,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16)) | trans(s99, s17)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13468,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15)) | trans(s99, s16)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13469,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14)) | trans(s99, s15)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13470,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13)) | trans(s99, s14)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13471,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12)) | trans(s99, s13)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13472,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11)) | trans(s99, s12)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13473,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10)) | trans(s99, s11)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13474,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9)) | trans(s99, s10)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13475,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8)) | trans(s99, s9)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13476,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7)) | trans(s99, s8)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13477,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6)) | trans(s99, s7)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13478,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5)) | trans(s99, s6)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13479,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4)) | trans(s99, s5)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13480,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3)) | trans(s99, s4)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13481,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2)) | trans(s99, s3)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13482,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0) | trans(s99, s1)) | trans(s99, s2)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13483,plain,
% 36.43/24.27 ((((~loop) | trans(s99, s0)) | trans(s99, s1)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1))),
% 36.43/24.27 inference(rewrite,[status(thm)],[])).
% 36.43/24.27 tff(13484,plain,
% 36.43/24.27 (((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1)) | trans(s99, s2))),
% 36.43/24.27 inference(monotonicity,[status(thm)],[13483])).
% 36.43/24.27 tff(13485,plain,
% 36.43/24.27 (((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2))),
% 36.43/24.27 inference(transitivity,[status(thm)],[13484, 13482])).
% 36.43/24.27 tff(13486,plain,
% 36.43/24.27 ((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2)) | trans(s99, s3))),
% 36.43/24.27 inference(monotonicity,[status(thm)],[13485])).
% 36.43/24.27 tff(13487,plain,
% 36.43/24.27 ((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3))),
% 36.43/24.27 inference(transitivity,[status(thm)],[13486, 13481])).
% 36.43/24.27 tff(13488,plain,
% 36.43/24.27 (((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3)) | trans(s99, s4))),
% 36.43/24.27 inference(monotonicity,[status(thm)],[13487])).
% 36.43/24.27 tff(13489,plain,
% 36.43/24.27 (((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4))),
% 36.43/24.27 inference(transitivity,[status(thm)],[13488, 13480])).
% 36.43/24.27 tff(13490,plain,
% 36.43/24.27 ((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4)) | trans(s99, s5))),
% 36.43/24.27 inference(monotonicity,[status(thm)],[13489])).
% 36.43/24.27 tff(13491,plain,
% 36.43/24.27 ((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5))),
% 36.43/24.27 inference(transitivity,[status(thm)],[13490, 13479])).
% 36.43/24.27 tff(13492,plain,
% 36.43/24.27 (((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5)) | trans(s99, s6))),
% 36.43/24.27 inference(monotonicity,[status(thm)],[13491])).
% 36.43/24.27 tff(13493,plain,
% 36.43/24.27 (((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6))),
% 36.43/24.27 inference(transitivity,[status(thm)],[13492, 13478])).
% 36.43/24.27 tff(13494,plain,
% 36.43/24.27 ((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6)) | trans(s99, s7))),
% 36.43/24.27 inference(monotonicity,[status(thm)],[13493])).
% 36.43/24.27 tff(13495,plain,
% 36.43/24.27 ((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7))),
% 36.43/24.27 inference(transitivity,[status(thm)],[13494, 13477])).
% 36.43/24.27 tff(13496,plain,
% 36.43/24.27 (((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7)) | trans(s99, s8))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13495])).
% 36.43/24.28 tff(13497,plain,
% 36.43/24.28 (((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13496, 13476])).
% 36.43/24.28 tff(13498,plain,
% 36.43/24.28 ((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8)) | trans(s99, s9))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13497])).
% 36.43/24.28 tff(13499,plain,
% 36.43/24.28 ((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13498, 13475])).
% 36.43/24.28 tff(13500,plain,
% 36.43/24.28 (((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9)) | trans(s99, s10))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13499])).
% 36.43/24.28 tff(13501,plain,
% 36.43/24.28 (((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13500, 13474])).
% 36.43/24.28 tff(13502,plain,
% 36.43/24.28 ((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10)) | trans(s99, s11))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13501])).
% 36.43/24.28 tff(13503,plain,
% 36.43/24.28 ((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13502, 13473])).
% 36.43/24.28 tff(13504,plain,
% 36.43/24.28 (((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11)) | trans(s99, s12))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13503])).
% 36.43/24.28 tff(13505,plain,
% 36.43/24.28 (((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13504, 13472])).
% 36.43/24.28 tff(13506,plain,
% 36.43/24.28 ((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12)) | trans(s99, s13))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13505])).
% 36.43/24.28 tff(13507,plain,
% 36.43/24.28 ((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13506, 13471])).
% 36.43/24.28 tff(13508,plain,
% 36.43/24.28 (((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13)) | trans(s99, s14))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13507])).
% 36.43/24.28 tff(13509,plain,
% 36.43/24.28 (((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13508, 13470])).
% 36.43/24.28 tff(13510,plain,
% 36.43/24.28 ((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14)) | trans(s99, s15))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13509])).
% 36.43/24.28 tff(13511,plain,
% 36.43/24.28 ((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13510, 13469])).
% 36.43/24.28 tff(13512,plain,
% 36.43/24.28 (((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15)) | trans(s99, s16))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13511])).
% 36.43/24.28 tff(13513,plain,
% 36.43/24.28 (((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13512, 13468])).
% 36.43/24.28 tff(13514,plain,
% 36.43/24.28 ((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16)) | trans(s99, s17))),
% 36.43/24.28 inference(monotonicity,[status(thm)],[13513])).
% 36.43/24.28 tff(13515,plain,
% 36.43/24.28 ((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17))),
% 36.43/24.28 inference(transitivity,[status(thm)],[13514, 13467])).
% 36.43/24.28 tff(13516,plain,
% 36.43/24.28 (((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17)) | trans(s99, s18))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13515])).
% 36.48/24.29 tff(13517,plain,
% 36.48/24.29 (((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18))),
% 36.48/24.29 inference(transitivity,[status(thm)],[13516, 13466])).
% 36.48/24.29 tff(13518,plain,
% 36.48/24.29 ((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18)) | trans(s99, s19))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13517])).
% 36.48/24.29 tff(13519,plain,
% 36.48/24.29 ((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19))),
% 36.48/24.29 inference(transitivity,[status(thm)],[13518, 13465])).
% 36.48/24.29 tff(13520,plain,
% 36.48/24.29 (((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19)) | trans(s99, s20))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13519])).
% 36.48/24.29 tff(13521,plain,
% 36.48/24.29 (((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20))),
% 36.48/24.29 inference(transitivity,[status(thm)],[13520, 13464])).
% 36.48/24.29 tff(13522,plain,
% 36.48/24.29 ((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20)) | trans(s99, s21))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13521])).
% 36.48/24.29 tff(13523,plain,
% 36.48/24.29 ((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21))),
% 36.48/24.29 inference(transitivity,[status(thm)],[13522, 13463])).
% 36.48/24.29 tff(13524,plain,
% 36.48/24.29 (((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21)) | trans(s99, s22))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13523])).
% 36.48/24.29 tff(13525,plain,
% 36.48/24.29 (((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22))),
% 36.48/24.29 inference(transitivity,[status(thm)],[13524, 13462])).
% 36.48/24.29 tff(13526,plain,
% 36.48/24.29 ((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22)) | trans(s99, s23))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13525])).
% 36.48/24.29 tff(13527,plain,
% 36.48/24.29 ((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23))),
% 36.48/24.29 inference(transitivity,[status(thm)],[13526, 13461])).
% 36.48/24.29 tff(13528,plain,
% 36.48/24.29 (((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23)) | trans(s99, s24))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13527])).
% 36.48/24.29 tff(13529,plain,
% 36.48/24.29 (((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24))),
% 36.48/24.29 inference(transitivity,[status(thm)],[13528, 13460])).
% 36.48/24.29 tff(13530,plain,
% 36.48/24.29 ((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24)) | trans(s99, s25))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13529])).
% 36.48/24.29 tff(13531,plain,
% 36.48/24.29 ((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25))),
% 36.48/24.29 inference(transitivity,[status(thm)],[13530, 13459])).
% 36.48/24.29 tff(13532,plain,
% 36.48/24.29 (((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25)) | trans(s99, s26))),
% 36.48/24.29 inference(monotonicity,[status(thm)],[13531])).
% 36.48/24.29 tff(13533,plain,
% 36.48/24.29 (((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26))),
% 36.48/24.30 inference(transitivity,[status(thm)],[13532, 13458])).
% 36.48/24.30 tff(13534,plain,
% 36.48/24.30 ((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26)) | trans(s99, s27))),
% 36.48/24.30 inference(monotonicity,[status(thm)],[13533])).
% 36.48/24.30 tff(13535,plain,
% 36.48/24.30 ((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27))),
% 36.48/24.30 inference(transitivity,[status(thm)],[13534, 13457])).
% 36.48/24.30 tff(13536,plain,
% 36.48/24.30 (((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27)) | trans(s99, s28))),
% 36.48/24.30 inference(monotonicity,[status(thm)],[13535])).
% 36.48/24.30 tff(13537,plain,
% 36.48/24.30 (((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28))),
% 36.48/24.30 inference(transitivity,[status(thm)],[13536, 13456])).
% 36.48/24.30 tff(13538,plain,
% 36.48/24.30 ((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28)) | trans(s99, s29))),
% 36.48/24.30 inference(monotonicity,[status(thm)],[13537])).
% 36.48/24.30 tff(13539,plain,
% 36.48/24.30 ((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29))),
% 36.48/24.30 inference(transitivity,[status(thm)],[13538, 13455])).
% 36.48/24.30 tff(13540,plain,
% 36.48/24.30 (((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29)) | trans(s99, s30))),
% 36.48/24.30 inference(monotonicity,[status(thm)],[13539])).
% 36.48/24.30 tff(13541,plain,
% 36.48/24.30 (((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30))),
% 36.48/24.30 inference(transitivity,[status(thm)],[13540, 13454])).
% 36.48/24.30 tff(13542,plain,
% 36.48/24.30 ((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30)) | trans(s99, s31))),
% 36.48/24.30 inference(monotonicity,[status(thm)],[13541])).
% 36.48/24.30 tff(13543,plain,
% 36.48/24.30 ((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31))),
% 36.48/24.31 inference(transitivity,[status(thm)],[13542, 13453])).
% 36.48/24.31 tff(13544,plain,
% 36.48/24.31 (((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31)) | trans(s99, s32))),
% 36.48/24.31 inference(monotonicity,[status(thm)],[13543])).
% 36.48/24.31 tff(13545,plain,
% 36.48/24.31 (((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32))),
% 36.48/24.31 inference(transitivity,[status(thm)],[13544, 13452])).
% 36.48/24.31 tff(13546,plain,
% 36.48/24.31 ((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32)) | trans(s99, s33))),
% 36.48/24.31 inference(monotonicity,[status(thm)],[13545])).
% 36.48/24.31 tff(13547,plain,
% 36.48/24.31 ((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33))),
% 36.48/24.31 inference(transitivity,[status(thm)],[13546, 13451])).
% 36.48/24.31 tff(13548,plain,
% 36.48/24.31 (((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33)) | trans(s99, s34))),
% 36.48/24.31 inference(monotonicity,[status(thm)],[13547])).
% 36.48/24.31 tff(13549,plain,
% 36.48/24.31 (((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34))),
% 36.48/24.31 inference(transitivity,[status(thm)],[13548, 13450])).
% 36.48/24.31 tff(13550,plain,
% 36.48/24.31 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34)) | trans(s99, s35))),
% 36.48/24.31 inference(monotonicity,[status(thm)],[13549])).
% 36.48/24.31 tff(13551,plain,
% 36.48/24.31 ((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35))),
% 36.48/24.31 inference(transitivity,[status(thm)],[13550, 13449])).
% 36.48/24.31 tff(13552,plain,
% 36.48/24.31 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35)) | trans(s99, s36))),
% 36.48/24.32 inference(monotonicity,[status(thm)],[13551])).
% 36.48/24.32 tff(13553,plain,
% 36.48/24.32 (((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36))),
% 36.48/24.32 inference(transitivity,[status(thm)],[13552, 13448])).
% 36.48/24.32 tff(13554,plain,
% 36.48/24.32 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36)) | trans(s99, s37))),
% 36.48/24.32 inference(monotonicity,[status(thm)],[13553])).
% 36.48/24.32 tff(13555,plain,
% 36.48/24.32 ((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37))),
% 36.48/24.32 inference(transitivity,[status(thm)],[13554, 13447])).
% 36.48/24.32 tff(13556,plain,
% 36.48/24.32 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37)) | trans(s99, s38))),
% 36.48/24.32 inference(monotonicity,[status(thm)],[13555])).
% 36.48/24.32 tff(13557,plain,
% 36.48/24.32 (((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38))),
% 36.48/24.32 inference(transitivity,[status(thm)],[13556, 13446])).
% 36.48/24.32 tff(13558,plain,
% 36.48/24.32 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38)) | trans(s99, s39))),
% 36.48/24.32 inference(monotonicity,[status(thm)],[13557])).
% 36.48/24.32 tff(13559,plain,
% 36.48/24.32 ((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39))),
% 36.48/24.32 inference(transitivity,[status(thm)],[13558, 13445])).
% 36.48/24.32 tff(13560,plain,
% 36.48/24.32 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39)) | trans(s99, s40))),
% 36.48/24.32 inference(monotonicity,[status(thm)],[13559])).
% 36.48/24.32 tff(13561,plain,
% 36.48/24.32 (((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40))),
% 36.48/24.32 inference(transitivity,[status(thm)],[13560, 13444])).
% 36.48/24.32 tff(13562,plain,
% 36.48/24.32 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40)) | trans(s99, s41))),
% 36.48/24.33 inference(monotonicity,[status(thm)],[13561])).
% 36.48/24.33 tff(13563,plain,
% 36.48/24.33 ((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41))),
% 36.48/24.33 inference(transitivity,[status(thm)],[13562, 13443])).
% 36.48/24.33 tff(13564,plain,
% 36.48/24.33 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41)) | trans(s99, s42))),
% 36.48/24.33 inference(monotonicity,[status(thm)],[13563])).
% 36.48/24.33 tff(13565,plain,
% 36.48/24.33 (((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42))),
% 36.48/24.33 inference(transitivity,[status(thm)],[13564, 13442])).
% 36.48/24.33 tff(13566,plain,
% 36.48/24.33 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42)) | trans(s99, s43))),
% 36.48/24.33 inference(monotonicity,[status(thm)],[13565])).
% 36.48/24.33 tff(13567,plain,
% 36.48/24.33 ((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43))),
% 36.48/24.33 inference(transitivity,[status(thm)],[13566, 13441])).
% 36.48/24.33 tff(13568,plain,
% 36.48/24.33 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43)) | trans(s99, s44))),
% 36.48/24.33 inference(monotonicity,[status(thm)],[13567])).
% 36.48/24.33 tff(13569,plain,
% 36.48/24.33 (((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44))),
% 36.48/24.34 inference(transitivity,[status(thm)],[13568, 13440])).
% 36.48/24.34 tff(13570,plain,
% 36.48/24.34 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44)) | trans(s99, s45))),
% 36.48/24.34 inference(monotonicity,[status(thm)],[13569])).
% 36.48/24.34 tff(13571,plain,
% 36.48/24.34 ((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45))),
% 36.48/24.34 inference(transitivity,[status(thm)],[13570, 13439])).
% 36.48/24.34 tff(13572,plain,
% 36.48/24.34 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45)) | trans(s99, s46))),
% 36.48/24.34 inference(monotonicity,[status(thm)],[13571])).
% 36.48/24.34 tff(13573,plain,
% 36.48/24.34 (((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46))),
% 36.48/24.34 inference(transitivity,[status(thm)],[13572, 13438])).
% 36.48/24.34 tff(13574,plain,
% 36.48/24.34 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46)) | trans(s99, s47))),
% 36.48/24.34 inference(monotonicity,[status(thm)],[13573])).
% 36.48/24.34 tff(13575,plain,
% 36.48/24.34 ((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47))),
% 36.48/24.34 inference(transitivity,[status(thm)],[13574, 13437])).
% 36.48/24.34 tff(13576,plain,
% 36.48/24.34 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47)) | trans(s99, s48))),
% 36.48/24.35 inference(monotonicity,[status(thm)],[13575])).
% 36.48/24.35 tff(13577,plain,
% 36.48/24.35 (((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48))),
% 36.48/24.35 inference(transitivity,[status(thm)],[13576, 13436])).
% 36.48/24.35 tff(13578,plain,
% 36.48/24.35 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48)) | trans(s99, s49))),
% 36.48/24.35 inference(monotonicity,[status(thm)],[13577])).
% 36.48/24.35 tff(13579,plain,
% 36.48/24.35 ((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49))),
% 36.48/24.35 inference(transitivity,[status(thm)],[13578, 13435])).
% 36.48/24.35 tff(13580,plain,
% 36.48/24.35 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49)) | trans(s99, s50))),
% 36.48/24.35 inference(monotonicity,[status(thm)],[13579])).
% 36.48/24.35 tff(13581,plain,
% 36.48/24.35 (((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50))),
% 36.48/24.35 inference(transitivity,[status(thm)],[13580, 13434])).
% 36.48/24.35 tff(13582,plain,
% 36.48/24.35 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50)) | trans(s99, s51))),
% 36.48/24.36 inference(monotonicity,[status(thm)],[13581])).
% 36.48/24.36 tff(13583,plain,
% 36.48/24.36 ((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51))),
% 36.48/24.36 inference(transitivity,[status(thm)],[13582, 13433])).
% 36.48/24.36 tff(13584,plain,
% 36.48/24.36 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51)) | trans(s99, s52))),
% 36.48/24.36 inference(monotonicity,[status(thm)],[13583])).
% 36.48/24.36 tff(13585,plain,
% 36.48/24.36 (((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52))),
% 36.48/24.36 inference(transitivity,[status(thm)],[13584, 13432])).
% 36.48/24.36 tff(13586,plain,
% 36.48/24.36 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52)) | trans(s99, s53))),
% 36.56/24.36 inference(monotonicity,[status(thm)],[13585])).
% 36.56/24.36 tff(13587,plain,
% 36.56/24.36 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53))),
% 36.56/24.36 inference(transitivity,[status(thm)],[13586, 13431])).
% 36.56/24.36 tff(13588,plain,
% 36.56/24.36 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53)) | trans(s99, s54))),
% 36.56/24.37 inference(monotonicity,[status(thm)],[13587])).
% 36.56/24.37 tff(13589,plain,
% 36.56/24.37 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54))),
% 36.56/24.37 inference(transitivity,[status(thm)],[13588, 13430])).
% 36.56/24.37 tff(13590,plain,
% 36.56/24.37 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54)) | trans(s99, s55))),
% 36.56/24.37 inference(monotonicity,[status(thm)],[13589])).
% 36.56/24.37 tff(13591,plain,
% 36.56/24.37 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55))),
% 36.56/24.37 inference(transitivity,[status(thm)],[13590, 13429])).
% 36.56/24.37 tff(13592,plain,
% 36.56/24.37 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55)) | trans(s99, s56))),
% 36.56/24.37 inference(monotonicity,[status(thm)],[13591])).
% 36.56/24.37 tff(13593,plain,
% 36.56/24.37 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56))),
% 36.56/24.37 inference(transitivity,[status(thm)],[13592, 13428])).
% 36.56/24.37 tff(13594,plain,
% 36.56/24.37 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56)) | trans(s99, s57))),
% 36.57/24.38 inference(monotonicity,[status(thm)],[13593])).
% 36.57/24.38 tff(13595,plain,
% 36.57/24.38 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57))),
% 36.57/24.38 inference(transitivity,[status(thm)],[13594, 13427])).
% 36.57/24.38 tff(13596,plain,
% 36.57/24.38 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57)) | trans(s99, s58))),
% 36.57/24.38 inference(monotonicity,[status(thm)],[13595])).
% 36.57/24.38 tff(13597,plain,
% 36.57/24.38 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58))),
% 36.57/24.38 inference(transitivity,[status(thm)],[13596, 13426])).
% 36.57/24.38 tff(13598,plain,
% 36.57/24.38 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58)) | trans(s99, s59))),
% 36.57/24.38 inference(monotonicity,[status(thm)],[13597])).
% 36.57/24.38 tff(13599,plain,
% 36.57/24.38 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59))),
% 36.57/24.38 inference(transitivity,[status(thm)],[13598, 13425])).
% 36.57/24.38 tff(13600,plain,
% 36.57/24.38 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59)) | trans(s99, s60))),
% 36.57/24.38 inference(monotonicity,[status(thm)],[13599])).
% 36.57/24.38 tff(13601,plain,
% 36.57/24.38 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60))),
% 36.57/24.39 inference(transitivity,[status(thm)],[13600, 13424])).
% 36.57/24.39 tff(13602,plain,
% 36.57/24.39 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60)) | trans(s99, s61))),
% 36.57/24.39 inference(monotonicity,[status(thm)],[13601])).
% 36.57/24.39 tff(13603,plain,
% 36.57/24.39 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61))),
% 36.57/24.39 inference(transitivity,[status(thm)],[13602, 13423])).
% 36.57/24.39 tff(13604,plain,
% 36.57/24.39 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61)) | trans(s99, s62))),
% 36.57/24.39 inference(monotonicity,[status(thm)],[13603])).
% 36.57/24.39 tff(13605,plain,
% 36.57/24.39 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62))),
% 36.57/24.39 inference(transitivity,[status(thm)],[13604, 13422])).
% 36.57/24.39 tff(13606,plain,
% 36.57/24.39 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62)) | trans(s99, s63))),
% 36.57/24.40 inference(monotonicity,[status(thm)],[13605])).
% 36.57/24.40 tff(13607,plain,
% 36.57/24.40 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63))),
% 36.57/24.40 inference(transitivity,[status(thm)],[13606, 13421])).
% 36.57/24.40 tff(13608,plain,
% 36.57/24.40 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63)) | trans(s99, s64))),
% 36.57/24.40 inference(monotonicity,[status(thm)],[13607])).
% 36.57/24.40 tff(13609,plain,
% 36.57/24.40 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64))),
% 36.57/24.40 inference(transitivity,[status(thm)],[13608, 13420])).
% 36.57/24.40 tff(13610,plain,
% 36.57/24.40 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64)) | trans(s99, s65))),
% 36.57/24.41 inference(monotonicity,[status(thm)],[13609])).
% 36.57/24.41 tff(13611,plain,
% 36.57/24.41 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65))),
% 36.57/24.41 inference(transitivity,[status(thm)],[13610, 13419])).
% 36.57/24.41 tff(13612,plain,
% 36.57/24.41 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65)) | trans(s99, s66))),
% 36.57/24.41 inference(monotonicity,[status(thm)],[13611])).
% 36.57/24.41 tff(13613,plain,
% 36.57/24.41 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66))),
% 36.57/24.41 inference(transitivity,[status(thm)],[13612, 13418])).
% 36.57/24.41 tff(13614,plain,
% 36.57/24.41 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66)) | trans(s99, s67))),
% 36.57/24.41 inference(monotonicity,[status(thm)],[13613])).
% 36.57/24.41 tff(13615,plain,
% 36.57/24.41 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67))),
% 36.57/24.41 inference(transitivity,[status(thm)],[13614, 13417])).
% 36.57/24.41 tff(13616,plain,
% 36.57/24.41 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67)) | trans(s99, s68))),
% 36.57/24.41 inference(monotonicity,[status(thm)],[13615])).
% 36.57/24.41 tff(13617,plain,
% 36.57/24.41 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68))),
% 36.57/24.42 inference(transitivity,[status(thm)],[13616, 13416])).
% 36.57/24.42 tff(13618,plain,
% 36.57/24.42 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68)) | trans(s99, s69))),
% 36.62/24.42 inference(monotonicity,[status(thm)],[13617])).
% 36.62/24.42 tff(13619,plain,
% 36.62/24.42 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69))),
% 36.62/24.42 inference(transitivity,[status(thm)],[13618, 13415])).
% 36.62/24.42 tff(13620,plain,
% 36.62/24.42 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69)) | trans(s99, s70))),
% 36.62/24.42 inference(monotonicity,[status(thm)],[13619])).
% 36.62/24.42 tff(13621,plain,
% 36.62/24.42 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70))),
% 36.62/24.43 inference(transitivity,[status(thm)],[13620, 13414])).
% 36.62/24.43 tff(13622,plain,
% 36.62/24.43 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70)) | trans(s99, s71))),
% 36.62/24.43 inference(monotonicity,[status(thm)],[13621])).
% 36.62/24.43 tff(13623,plain,
% 36.62/24.43 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71))),
% 36.62/24.43 inference(transitivity,[status(thm)],[13622, 13413])).
% 36.62/24.43 tff(13624,plain,
% 36.62/24.43 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71)) | trans(s99, s72))),
% 36.62/24.43 inference(monotonicity,[status(thm)],[13623])).
% 36.62/24.43 tff(13625,plain,
% 36.62/24.43 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72))),
% 36.62/24.44 inference(transitivity,[status(thm)],[13624, 13412])).
% 36.62/24.44 tff(13626,plain,
% 36.62/24.44 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72)) | trans(s99, s73))),
% 36.62/24.44 inference(monotonicity,[status(thm)],[13625])).
% 36.62/24.44 tff(13627,plain,
% 36.62/24.44 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73))),
% 36.62/24.44 inference(transitivity,[status(thm)],[13626, 13411])).
% 36.62/24.44 tff(13628,plain,
% 36.62/24.44 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73)) | trans(s99, s74))),
% 36.62/24.44 inference(monotonicity,[status(thm)],[13627])).
% 36.62/24.44 tff(13629,plain,
% 36.62/24.44 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74))),
% 36.62/24.44 inference(transitivity,[status(thm)],[13628, 13410])).
% 36.62/24.44 tff(13630,plain,
% 36.62/24.44 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74)) | trans(s99, s75))),
% 36.64/24.45 inference(monotonicity,[status(thm)],[13629])).
% 36.64/24.45 tff(13631,plain,
% 36.64/24.45 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75))),
% 36.64/24.45 inference(transitivity,[status(thm)],[13630, 13409])).
% 36.64/24.45 tff(13632,plain,
% 36.64/24.45 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75)) | trans(s99, s76))),
% 36.64/24.45 inference(monotonicity,[status(thm)],[13631])).
% 36.64/24.45 tff(13633,plain,
% 36.64/24.45 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76))),
% 36.64/24.45 inference(transitivity,[status(thm)],[13632, 13408])).
% 36.64/24.45 tff(13634,plain,
% 36.64/24.45 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76)) | trans(s99, s77))),
% 36.64/24.46 inference(monotonicity,[status(thm)],[13633])).
% 36.64/24.46 tff(13635,plain,
% 36.64/24.46 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77))),
% 36.64/24.46 inference(transitivity,[status(thm)],[13634, 13407])).
% 36.64/24.46 tff(13636,plain,
% 36.64/24.46 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77)) | trans(s99, s78))),
% 36.64/24.46 inference(monotonicity,[status(thm)],[13635])).
% 36.64/24.46 tff(13637,plain,
% 36.64/24.46 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78))),
% 36.64/24.46 inference(transitivity,[status(thm)],[13636, 13406])).
% 36.64/24.46 tff(13638,plain,
% 36.64/24.46 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78)) | trans(s99, s79))),
% 36.64/24.46 inference(monotonicity,[status(thm)],[13637])).
% 36.64/24.46 tff(13639,plain,
% 36.64/24.46 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79))),
% 36.64/24.47 inference(transitivity,[status(thm)],[13638, 13405])).
% 36.64/24.47 tff(13640,plain,
% 36.64/24.47 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79)) | trans(s99, s80))),
% 36.64/24.47 inference(monotonicity,[status(thm)],[13639])).
% 36.64/24.47 tff(13641,plain,
% 36.64/24.47 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80))),
% 36.64/24.47 inference(transitivity,[status(thm)],[13640, 13404])).
% 36.64/24.47 tff(13642,plain,
% 36.64/24.47 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80)) | trans(s99, s81))),
% 36.64/24.47 inference(monotonicity,[status(thm)],[13641])).
% 36.64/24.47 tff(13643,plain,
% 36.64/24.47 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81))),
% 36.64/24.48 inference(transitivity,[status(thm)],[13642, 13403])).
% 36.64/24.48 tff(13644,plain,
% 36.64/24.48 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81)) | trans(s99, s82))),
% 36.64/24.48 inference(monotonicity,[status(thm)],[13643])).
% 36.64/24.48 tff(13645,plain,
% 36.64/24.48 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82))),
% 36.64/24.48 inference(transitivity,[status(thm)],[13644, 13402])).
% 36.64/24.48 tff(13646,plain,
% 36.64/24.48 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82)) | trans(s99, s83))),
% 36.64/24.48 inference(monotonicity,[status(thm)],[13645])).
% 36.64/24.48 tff(13647,plain,
% 36.64/24.48 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83))),
% 36.64/24.49 inference(transitivity,[status(thm)],[13646, 13401])).
% 36.64/24.49 tff(13648,plain,
% 36.64/24.49 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83)) | trans(s99, s84))),
% 36.64/24.49 inference(monotonicity,[status(thm)],[13647])).
% 36.64/24.49 tff(13649,plain,
% 36.64/24.49 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84))),
% 36.64/24.49 inference(transitivity,[status(thm)],[13648, 13400])).
% 36.64/24.49 tff(13650,plain,
% 36.64/24.49 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84)) | trans(s99, s85))),
% 36.64/24.50 inference(monotonicity,[status(thm)],[13649])).
% 36.64/24.50 tff(13651,plain,
% 36.64/24.50 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85))),
% 36.64/24.50 inference(transitivity,[status(thm)],[13650, 13399])).
% 36.64/24.50 tff(13652,plain,
% 36.64/24.50 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85)) | trans(s99, s86))),
% 36.64/24.50 inference(monotonicity,[status(thm)],[13651])).
% 36.64/24.50 tff(13653,plain,
% 36.64/24.50 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86))),
% 36.64/24.50 inference(transitivity,[status(thm)],[13652, 13398])).
% 36.64/24.50 tff(13654,plain,
% 36.64/24.50 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86)) | trans(s99, s87))),
% 36.64/24.50 inference(monotonicity,[status(thm)],[13653])).
% 36.64/24.50 tff(13655,plain,
% 36.64/24.50 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87))),
% 36.64/24.51 inference(transitivity,[status(thm)],[13654, 13397])).
% 36.64/24.51 tff(13656,plain,
% 36.64/24.51 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87)) | trans(s99, s88))),
% 36.64/24.51 inference(monotonicity,[status(thm)],[13655])).
% 36.64/24.51 tff(13657,plain,
% 36.64/24.51 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88))),
% 36.64/24.51 inference(transitivity,[status(thm)],[13656, 13396])).
% 36.64/24.51 tff(13658,plain,
% 36.64/24.51 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88)) | trans(s99, s89))),
% 36.64/24.51 inference(monotonicity,[status(thm)],[13657])).
% 36.64/24.51 tff(13659,plain,
% 36.64/24.51 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89))),
% 36.64/24.52 inference(transitivity,[status(thm)],[13658, 13395])).
% 36.64/24.52 tff(13660,plain,
% 36.64/24.52 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89)) | trans(s99, s90))),
% 36.71/24.52 inference(monotonicity,[status(thm)],[13659])).
% 36.71/24.52 tff(13661,plain,
% 36.71/24.52 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90))),
% 36.71/24.52 inference(transitivity,[status(thm)],[13660, 13394])).
% 36.71/24.52 tff(13662,plain,
% 36.71/24.52 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90)) | trans(s99, s91))),
% 36.71/24.53 inference(monotonicity,[status(thm)],[13661])).
% 36.71/24.53 tff(13663,plain,
% 36.71/24.53 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91))),
% 36.71/24.53 inference(transitivity,[status(thm)],[13662, 13393])).
% 36.71/24.53 tff(13664,plain,
% 36.71/24.53 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91)) | trans(s99, s92))),
% 36.71/24.53 inference(monotonicity,[status(thm)],[13663])).
% 36.71/24.53 tff(13665,plain,
% 36.71/24.53 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92))),
% 36.71/24.53 inference(transitivity,[status(thm)],[13664, 13392])).
% 36.71/24.53 tff(13666,plain,
% 36.71/24.53 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92)) | trans(s99, s93))),
% 36.71/24.54 inference(monotonicity,[status(thm)],[13665])).
% 36.71/24.54 tff(13667,plain,
% 36.71/24.54 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93))),
% 36.71/24.54 inference(transitivity,[status(thm)],[13666, 13391])).
% 36.71/24.54 tff(13668,plain,
% 36.71/24.54 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93)) | trans(s99, s94))),
% 36.71/24.54 inference(monotonicity,[status(thm)],[13667])).
% 36.71/24.54 tff(13669,plain,
% 36.71/24.54 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94))),
% 36.71/24.54 inference(transitivity,[status(thm)],[13668, 13390])).
% 36.71/24.54 tff(13670,plain,
% 36.71/24.54 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94)) | trans(s99, s95))),
% 36.71/24.55 inference(monotonicity,[status(thm)],[13669])).
% 36.71/24.55 tff(13671,plain,
% 36.71/24.55 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95))),
% 36.71/24.55 inference(transitivity,[status(thm)],[13670, 13389])).
% 36.71/24.55 tff(13672,plain,
% 36.71/24.55 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95)) | trans(s99, s96))),
% 36.71/24.55 inference(monotonicity,[status(thm)],[13671])).
% 36.71/24.55 tff(13673,plain,
% 36.71/24.55 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96))),
% 36.71/24.56 inference(transitivity,[status(thm)],[13672, 13388])).
% 36.71/24.56 tff(13674,plain,
% 36.71/24.56 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96)) | trans(s99, s97))),
% 36.71/24.56 inference(monotonicity,[status(thm)],[13673])).
% 36.71/24.56 tff(13675,plain,
% 36.71/24.56 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97))),
% 36.71/24.56 inference(transitivity,[status(thm)],[13674, 13387])).
% 36.71/24.56 tff(13676,plain,
% 36.71/24.56 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97)) | trans(s99, s98))),
% 36.71/24.56 inference(monotonicity,[status(thm)],[13675])).
% 36.71/24.56 tff(13677,plain,
% 36.71/24.56 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98))),
% 36.71/24.57 inference(transitivity,[status(thm)],[13676, 13386])).
% 36.71/24.57 tff(13678,plain,
% 36.71/24.57 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)) <=> (((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98)) | trans(s99, s99))),
% 36.71/24.57 inference(monotonicity,[status(thm)],[13677])).
% 36.71/24.57 tff(13679,plain,
% 36.71/24.57 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)) <=> ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99))),
% 36.77/24.57 inference(transitivity,[status(thm)],[13678, 13385])).
% 36.77/24.57 tff(13680,axiom,(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((~loop) | trans(s99, s0)) | trans(s99, s1)) | trans(s99, s2)) | trans(s99, s3)) | trans(s99, s4)) | trans(s99, s5)) | trans(s99, s6)) | trans(s99, s7)) | trans(s99, s8)) | trans(s99, s9)) | trans(s99, s10)) | trans(s99, s11)) | trans(s99, s12)) | trans(s99, s13)) | trans(s99, s14)) | trans(s99, s15)) | trans(s99, s16)) | trans(s99, s17)) | trans(s99, s18)) | trans(s99, s19)) | trans(s99, s20)) | trans(s99, s21)) | trans(s99, s22)) | trans(s99, s23)) | trans(s99, s24)) | trans(s99, s25)) | trans(s99, s26)) | trans(s99, s27)) | trans(s99, s28)) | trans(s99, s29)) | trans(s99, s30)) | trans(s99, s31)) | trans(s99, s32)) | trans(s99, s33)) | trans(s99, s34)) | trans(s99, s35)) | trans(s99, s36)) | trans(s99, s37)) | trans(s99, s38)) | trans(s99, s39)) | trans(s99, s40)) | trans(s99, s41)) | trans(s99, s42)) | trans(s99, s43)) | trans(s99, s44)) | trans(s99, s45)) | trans(s99, s46)) | trans(s99, s47)) | trans(s99, s48)) | trans(s99, s49)) | trans(s99, s50)) | trans(s99, s51)) | trans(s99, s52)) | trans(s99, s53)) | trans(s99, s54)) | trans(s99, s55)) | trans(s99, s56)) | trans(s99, s57)) | trans(s99, s58)) | trans(s99, s59)) | trans(s99, s60)) | trans(s99, s61)) | trans(s99, s62)) | trans(s99, s63)) | trans(s99, s64)) | trans(s99, s65)) | trans(s99, s66)) | trans(s99, s67)) | trans(s99, s68)) | trans(s99, s69)) | trans(s99, s70)) | trans(s99, s71)) | trans(s99, s72)) | trans(s99, s73)) | trans(s99, s74)) | trans(s99, s75)) | trans(s99, s76)) | trans(s99, s77)) | trans(s99, s78)) | trans(s99, s79)) | trans(s99, s80)) | trans(s99, s81)) | trans(s99, s82)) | trans(s99, s83)) | trans(s99, s84)) | trans(s99, s85)) | trans(s99, s86)) | trans(s99, s87)) | trans(s99, s88)) | trans(s99, s89)) | trans(s99, s90)) | trans(s99, s91)) | trans(s99, s92)) | trans(s99, s93)) | trans(s99, s94)) | trans(s99, s95)) | trans(s99, s96)) | trans(s99, s97)) | trans(s99, s98)) | trans(s99, s99)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bound102')).
% 36.77/24.58 tff(13681,plain,
% 36.77/24.58 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.58 inference(modus_ponens,[status(thm)],[13680, 13679])).
% 36.77/24.58 tff(13682,plain,
% 36.77/24.58 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.58 inference(modus_ponens,[status(thm)],[13681, 13384])).
% 36.77/24.58 tff(13683,plain,
% 36.77/24.58 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.58 inference(modus_ponens,[status(thm)],[13682, 13384])).
% 36.77/24.58 tff(13684,plain,
% 36.77/24.58 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.58 inference(modus_ponens,[status(thm)],[13683, 13384])).
% 36.77/24.58 tff(13685,plain,
% 36.77/24.58 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.58 inference(modus_ponens,[status(thm)],[13684, 13384])).
% 36.77/24.58 tff(13686,plain,
% 36.77/24.58 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.58 inference(modus_ponens,[status(thm)],[13685, 13384])).
% 36.77/24.58 tff(13687,plain,
% 36.77/24.59 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13686, 13384])).
% 36.77/24.59 tff(13688,plain,
% 36.77/24.59 ((~loop) | trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13687, 13384])).
% 36.77/24.59 tff(13689,plain,
% 36.77/24.59 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98) | trans(s99, s99)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13688, 13383])).
% 36.77/24.59 tff(13690,plain,
% 36.77/24.59 (trans(s99, s1)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13689, 12956, 12945, 12934, 12923, 12912, 12901, 12890, 12879, 12868, 12857, 12846, 12835, 12824, 12813, 12802, 12791, 12780, 12769, 12758, 12747, 12736, 12725, 12714, 12703, 12692, 12681, 12670, 12659, 12648, 12637, 12626, 12615, 12604, 12593, 12582, 12571, 12560, 12549, 12538, 12527, 12516, 12505, 12494, 12483, 12472, 12461, 12450, 12439, 12428, 12417, 12406, 12395, 12384, 12373, 12362, 12351, 12340, 12329, 12318, 12307, 12296, 12285, 12274, 12263, 12241, 12230, 12219, 12208, 12197, 12186, 12175, 12164, 12153, 12142, 12131, 12120, 12109, 12098, 12087, 12076, 12065, 12054, 12043, 12032, 12021, 12010, 11999, 11988, 11977, 11966, 11955, 11944, 11933, 11922, 11911, 11900, 11889, 11878, 11867])).
% 36.77/24.59 tff(13691,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1)))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13692,plain,
% 36.77/24.59 (((~last(s99)) | (~trans(s99, s1)) | (~xuntil7(s99)) | until2p8(s1)) <=> (until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13693,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s1)) | (~xuntil7(s99)) | until2p8(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | (until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13692])).
% 36.77/24.59 tff(13694,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s1)) | (~xuntil7(s99)) | until2p8(s1))) <=> ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13693, 13691])).
% 36.77/24.59 tff(13695,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | ((~last(s99)) | (~trans(s99, s1)) | (~xuntil7(s99)) | until2p8(s1))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13696,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~last(X)) | (~trans(X, Y)) | (~xuntil7(X)) | until2p8(Y))) | until2p8(s1) | (~last(s99)) | (~xuntil7(s99)) | (~trans(s99, s1))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13695, 13694])).
% 36.77/24.59 tff(13697,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13696, 10823, 13690, 11855, 11845, 10813])).
% 36.77/24.59 tff(13698,plain,(always5(s99) | always5(s1)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13699,plain,
% 36.77/24.59 (always5(s1)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13698, 8969])).
% 36.77/24.59 tff(13700,plain,
% 36.77/24.59 (always5(s2)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9606, 13699])).
% 36.77/24.59 tff(13701,plain,
% 36.77/24.59 (always5(s3)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9598, 13700])).
% 36.77/24.59 tff(13702,plain,
% 36.77/24.59 (always5(s4)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9590, 13701])).
% 36.77/24.59 tff(13703,plain,
% 36.77/24.59 (always5(s5)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9582, 13702])).
% 36.77/24.59 tff(13704,plain,
% 36.77/24.59 (always5(s6)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9574, 13703])).
% 36.77/24.59 tff(13705,plain,
% 36.77/24.59 (always5(s7)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9566, 13704])).
% 36.77/24.59 tff(13706,plain,
% 36.77/24.59 (always5(s8)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9558, 13705])).
% 36.77/24.59 tff(13707,plain,
% 36.77/24.59 (always5(s9)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9542, 13706])).
% 36.77/24.59 tff(13708,plain,
% 36.77/24.59 (always5(s10)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9521, 13707])).
% 36.77/24.59 tff(13709,plain,
% 36.77/24.59 (always5(s11)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9500, 13708])).
% 36.77/24.59 tff(13710,plain,
% 36.77/24.59 (always5(s12)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9479, 13709])).
% 36.77/24.59 tff(13711,plain,
% 36.77/24.59 (always5(s13)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9458, 13710])).
% 36.77/24.59 tff(13712,plain,
% 36.77/24.59 (always5(s14)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9437, 13711])).
% 36.77/24.59 tff(13713,plain,
% 36.77/24.59 (always5(s15)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9383, 13712])).
% 36.77/24.59 tff(13714,plain,
% 36.77/24.59 (always5(s16)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9374, 13713])).
% 36.77/24.59 tff(13715,plain,
% 36.77/24.59 (always5(s17)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9366, 13714])).
% 36.77/24.59 tff(13716,plain,
% 36.77/24.59 (always5(s18)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9358, 13715])).
% 36.77/24.59 tff(13717,plain,
% 36.77/24.59 (always5(s19)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9350, 13716])).
% 36.77/24.59 tff(13718,plain,
% 36.77/24.59 (always5(s20)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9342, 13717])).
% 36.77/24.59 tff(13719,plain,
% 36.77/24.59 (always5(s21)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9334, 13718])).
% 36.77/24.59 tff(13720,plain,
% 36.77/24.59 (always5(s22)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9326, 13719])).
% 36.77/24.59 tff(13721,plain,
% 36.77/24.59 (always5(s23)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9318, 13720])).
% 36.77/24.59 tff(13722,plain,
% 36.77/24.59 (always5(s24)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9310, 13721])).
% 36.77/24.59 tff(13723,plain,
% 36.77/24.59 (always5(s25)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9302, 13722])).
% 36.77/24.59 tff(13724,plain,
% 36.77/24.59 (always5(s26)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9294, 13723])).
% 36.77/24.59 tff(13725,plain,
% 36.77/24.59 (always5(s27)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9286, 13724])).
% 36.77/24.59 tff(13726,plain,
% 36.77/24.59 (always5(s28)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9278, 13725])).
% 36.77/24.59 tff(13727,plain,
% 36.77/24.59 (always5(s29)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9270, 13726])).
% 36.77/24.59 tff(13728,plain,
% 36.77/24.59 (always5(s30)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9262, 13727])).
% 36.77/24.59 tff(13729,plain,
% 36.77/24.59 (always5(s31)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9254, 13728])).
% 36.77/24.59 tff(13730,plain,
% 36.77/24.59 (always5(s32)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9246, 13729])).
% 36.77/24.59 tff(13731,plain,
% 36.77/24.59 (always5(s33)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9238, 13730])).
% 36.77/24.59 tff(13732,plain,
% 36.77/24.59 (always5(s34)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9230, 13731])).
% 36.77/24.59 tff(13733,plain,
% 36.77/24.59 (always5(s35)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9222, 13732])).
% 36.77/24.59 tff(13734,plain,
% 36.77/24.59 (always5(s36)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9214, 13733])).
% 36.77/24.59 tff(13735,plain,
% 36.77/24.59 (always5(s37)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9206, 13734])).
% 36.77/24.59 tff(13736,plain,
% 36.77/24.59 (always5(s38)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9198, 13735])).
% 36.77/24.59 tff(13737,plain,
% 36.77/24.59 (always5(s39)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9190, 13736])).
% 36.77/24.59 tff(13738,plain,
% 36.77/24.59 (always5(s40)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9182, 13737])).
% 36.77/24.59 tff(13739,plain,
% 36.77/24.59 (always5(s41)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9174, 13738])).
% 36.77/24.59 tff(13740,plain,
% 36.77/24.59 (always5(s42)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9166, 13739])).
% 36.77/24.59 tff(13741,plain,
% 36.77/24.59 (always5(s43)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9158, 13740])).
% 36.77/24.59 tff(13742,plain,
% 36.77/24.59 (always5(s44)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9150, 13741])).
% 36.77/24.59 tff(13743,plain,
% 36.77/24.59 (always5(s45)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9142, 13742])).
% 36.77/24.59 tff(13744,plain,
% 36.77/24.59 (always5(s46)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9134, 13743])).
% 36.77/24.59 tff(13745,plain,
% 36.77/24.59 (always5(s47)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9126, 13744])).
% 36.77/24.59 tff(13746,plain,
% 36.77/24.59 (always5(s48)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9118, 13745])).
% 36.77/24.59 tff(13747,plain,
% 36.77/24.59 (always5(s49)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9110, 13746])).
% 36.77/24.59 tff(13748,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[9102, 13747, 9095])).
% 36.77/24.59 tff(13749,plain,(always5(s99)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13750,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s87) | (~trans(s99, s87)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s87) | (~trans(s99, s87)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13751,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s87)) | always5(s87)) <=> ((~always5(s99)) | always5(s87) | (~trans(s99, s87)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13752,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s87)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s87) | (~trans(s99, s87))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13751])).
% 36.77/24.59 tff(13753,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s87)) | always5(s87))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s87) | (~trans(s99, s87)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13752, 13750])).
% 36.77/24.59 tff(13754,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s87)) | always5(s87))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13755,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s87) | (~trans(s99, s87))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13754, 13753])).
% 36.77/24.59 tff(13756,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13755, 12056, 25, 13749, 8968])).
% 36.77/24.59 tff(13757,plain,((~trans(s99, s87)) | always5(s87)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13758,plain,
% 36.77/24.59 (~trans(s99, s87)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13757, 8743])).
% 36.77/24.59 tff(13759,assumption,(~always5(s70)), introduced(assumption)).
% 36.77/24.59 tff(13760,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s70) | (~trans(s99, s70)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s70) | (~trans(s99, s70)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13761,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s70)) | always5(s70)) <=> ((~always5(s99)) | always5(s70) | (~trans(s99, s70)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13762,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s70)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s70) | (~trans(s99, s70))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13761])).
% 36.77/24.59 tff(13763,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s70)) | always5(s70))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s70) | (~trans(s99, s70)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13762, 13760])).
% 36.77/24.59 tff(13764,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s70)) | always5(s70))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13765,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s70) | (~trans(s99, s70))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13764, 13763])).
% 36.77/24.59 tff(13766,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13765, 12947, 25, 13749, 13759])).
% 36.77/24.59 tff(13767,plain,((~trans(s99, s70)) | always5(s70)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13768,plain,
% 36.77/24.59 (~trans(s99, s70)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13767, 8879])).
% 36.77/24.59 tff(13769,assumption,(~always5(s86)), introduced(assumption)).
% 36.77/24.59 tff(13770,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s86) | (~trans(s99, s86)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s86) | (~trans(s99, s86)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13771,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s86)) | always5(s86)) <=> ((~always5(s99)) | always5(s86) | (~trans(s99, s86)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13772,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s86)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s86) | (~trans(s99, s86))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13771])).
% 36.77/24.59 tff(13773,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s86)) | always5(s86))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s86) | (~trans(s99, s86)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13772, 13770])).
% 36.77/24.59 tff(13774,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s86)) | always5(s86))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13775,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s86) | (~trans(s99, s86))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13774, 13773])).
% 36.77/24.59 tff(13776,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13775, 11869, 25, 13749, 13769])).
% 36.77/24.59 tff(13777,plain,((~trans(s99, s86)) | always5(s86)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13778,plain,
% 36.77/24.59 (~trans(s99, s86)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13777, 8751])).
% 36.77/24.59 tff(13779,assumption,(~always5(s76)), introduced(assumption)).
% 36.77/24.59 tff(13780,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s76) | (~trans(s99, s76)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s76) | (~trans(s99, s76)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13781,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s76)) | always5(s76)) <=> ((~always5(s99)) | always5(s76) | (~trans(s99, s76)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13782,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s76)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s76) | (~trans(s99, s76))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13781])).
% 36.77/24.59 tff(13783,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s76)) | always5(s76))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s76) | (~trans(s99, s76)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13782, 13780])).
% 36.77/24.59 tff(13784,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s76)) | always5(s76))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13785,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s76) | (~trans(s99, s76))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13784, 13783])).
% 36.77/24.59 tff(13786,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13785, 12034, 25, 13749, 13779])).
% 36.77/24.59 tff(13787,plain,((~trans(s99, s76)) | always5(s76)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13788,plain,
% 36.77/24.59 (~trans(s99, s76)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13787, 8831])).
% 36.77/24.59 tff(13789,assumption,(~always5(s75)), introduced(assumption)).
% 36.77/24.59 tff(13790,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s75) | (~trans(s99, s75)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s75) | (~trans(s99, s75)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13791,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s75)) | always5(s75)) <=> ((~always5(s99)) | always5(s75) | (~trans(s99, s75)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13792,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s75)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s75) | (~trans(s99, s75))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13791])).
% 36.77/24.59 tff(13793,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s75)) | always5(s75))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s75) | (~trans(s99, s75)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13792, 13790])).
% 36.77/24.59 tff(13794,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s75)) | always5(s75))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13795,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s75) | (~trans(s99, s75))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13794, 13793])).
% 36.77/24.59 tff(13796,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13795, 12144, 25, 13749, 13789])).
% 36.77/24.59 tff(13797,plain,((~trans(s99, s75)) | always5(s75)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13798,plain,
% 36.77/24.59 (~trans(s99, s75)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13797, 8839])).
% 36.77/24.59 tff(13799,assumption,(~always5(s68)), introduced(assumption)).
% 36.77/24.59 tff(13800,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s68) | (~trans(s99, s68)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s68) | (~trans(s99, s68)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13801,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s68)) | always5(s68)) <=> ((~always5(s99)) | always5(s68) | (~trans(s99, s68)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13802,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s68)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s68) | (~trans(s99, s68))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13801])).
% 36.77/24.59 tff(13803,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s68)) | always5(s68))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s68) | (~trans(s99, s68)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13802, 13800])).
% 36.77/24.59 tff(13804,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s68)) | always5(s68))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13805,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s68) | (~trans(s99, s68))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13804, 13803])).
% 36.77/24.59 tff(13806,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13805, 12089, 25, 13749, 13799])).
% 36.77/24.59 tff(13807,plain,((~trans(s99, s68)) | always5(s68)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13808,plain,
% 36.77/24.59 (~trans(s99, s68)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13807, 8895])).
% 36.77/24.59 tff(13809,assumption,(~always5(s89)), introduced(assumption)).
% 36.77/24.59 tff(13810,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s89) | (~trans(s99, s89)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s89) | (~trans(s99, s89)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13811,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s89)) | always5(s89)) <=> ((~always5(s99)) | always5(s89) | (~trans(s99, s89)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13812,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s89)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s89) | (~trans(s99, s89))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13811])).
% 36.77/24.59 tff(13813,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s89)) | always5(s89))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s89) | (~trans(s99, s89)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13812, 13810])).
% 36.77/24.59 tff(13814,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s89)) | always5(s89))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13815,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s89) | (~trans(s99, s89))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13814, 13813])).
% 36.77/24.59 tff(13816,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13815, 12848, 25, 13749, 13809])).
% 36.77/24.59 tff(13817,plain,((~trans(s99, s89)) | always5(s89)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13818,plain,
% 36.77/24.59 (~trans(s99, s89)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13817, 8727])).
% 36.77/24.59 tff(13819,assumption,(~always5(s91)), introduced(assumption)).
% 36.77/24.59 tff(13820,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s91) | (~trans(s99, s91)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s91) | (~trans(s99, s91)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13821,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s91)) | always5(s91)) <=> ((~always5(s99)) | always5(s91) | (~trans(s99, s91)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13822,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s91)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s91) | (~trans(s99, s91))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13821])).
% 36.77/24.59 tff(13823,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s91)) | always5(s91))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s91) | (~trans(s99, s91)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13822, 13820])).
% 36.77/24.59 tff(13824,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s91)) | always5(s91))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13825,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s91) | (~trans(s99, s91))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13824, 13823])).
% 36.77/24.59 tff(13826,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13825, 12155, 25, 13749, 13819])).
% 36.77/24.59 tff(13827,plain,((~trans(s99, s91)) | always5(s91)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13828,plain,
% 36.77/24.59 (~trans(s99, s91)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13827, 8711])).
% 36.77/24.59 tff(13829,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s95) | (~trans(s99, s95)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s95) | (~trans(s99, s95)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13830,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s95)) | always5(s95)) <=> ((~always5(s99)) | always5(s95) | (~trans(s99, s95)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13831,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s95)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s95) | (~trans(s99, s95))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13830])).
% 36.77/24.59 tff(13832,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s95)) | always5(s95))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s95) | (~trans(s99, s95)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13831, 13829])).
% 36.77/24.59 tff(13833,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s95)) | always5(s95))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13834,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s95) | (~trans(s99, s95))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13833, 13832])).
% 36.77/24.59 tff(13835,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13834, 12815, 25, 13749, 8679])).
% 36.77/24.59 tff(13836,plain,((~trans(s99, s95)) | always5(s95)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13837,plain,
% 36.77/24.59 (~trans(s99, s95)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13836, 8679])).
% 36.77/24.59 tff(13838,assumption,(~trans(s99, s96)), introduced(assumption)).
% 36.77/24.59 tff(13839,assumption,(~always5(s63)), introduced(assumption)).
% 36.77/24.59 tff(13840,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s63) | (~trans(s99, s63)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s63) | (~trans(s99, s63)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13841,plain,
% 36.77/24.59 (((~always5(s99)) | (~trans(s99, s63)) | always5(s63)) <=> ((~always5(s99)) | always5(s63) | (~trans(s99, s63)))),
% 36.77/24.59 inference(rewrite,[status(thm)],[])).
% 36.77/24.59 tff(13842,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s63)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s63) | (~trans(s99, s63))))),
% 36.77/24.59 inference(monotonicity,[status(thm)],[13841])).
% 36.77/24.59 tff(13843,plain,
% 36.77/24.59 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s63)) | always5(s63))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s63) | (~trans(s99, s63)))),
% 36.77/24.59 inference(transitivity,[status(thm)],[13842, 13840])).
% 36.77/24.59 tff(13844,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s63)) | always5(s63))),
% 36.77/24.59 inference(quant_inst,[status(thm)],[])).
% 36.77/24.59 tff(13845,plain,
% 36.77/24.59 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s63) | (~trans(s99, s63))),
% 36.77/24.59 inference(modus_ponens,[status(thm)],[13844, 13843])).
% 36.77/24.59 tff(13846,plain,
% 36.77/24.59 ($false),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13845, 11880, 25, 13749, 13839])).
% 36.77/24.59 tff(13847,plain,((~trans(s99, s63)) | always5(s63)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.59 tff(13848,plain,
% 36.77/24.59 (~trans(s99, s63)),
% 36.77/24.59 inference(unit_resolution,[status(thm)],[13847, 8935])).
% 36.77/24.59 tff(13849,assumption,(~m_counter_cell_v_carry_out(c_bit1, s51)), introduced(assumption)).
% 36.77/24.59 tff(13850,plain,
% 36.77/24.59 (((~![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, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | m_counter_cell_v_carry_out(c_bit1, s51))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | m_counter_cell_v_carry_out(c_bit1, s51))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13851,plain,
% 36.77/24.60 ((~![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_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | m_counter_cell_v_carry_out(c_bit1, s51))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13852,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s51)) | (~m_counter_cell_v_value(c_bit1, s51)) | m_counter_cell_v_carry_out(c_bit1, s51)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13851, 13850])).
% 36.77/24.60 tff(13853,plain,
% 36.77/24.60 ($false),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13852, 3031, 6736, 6735, 13849])).
% 36.77/24.60 tff(13854,plain,(m_counter_cell_v_carry_out(c_bit1, s51) | (~m_counter_cell_v_value(c_bit1, s51)) | (~m_counter_cell_v_carry_in(c_bit1, s51))), inference(lemma,lemma(discharge,[]))).
% 36.77/24.60 tff(13855,plain,
% 36.77/24.60 (m_counter_cell_v_carry_out(c_bit1, s51) | (~m_counter_cell_v_value(c_bit1, s51))),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13854, 6734])).
% 36.77/24.60 tff(13856,plain,
% 36.77/24.60 (m_counter_cell_v_carry_out(c_bit1, s51)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13855, 6725])).
% 36.77/24.60 tff(13857,assumption,(~m_counter_cell_v_carry_in(c_bit2, s51)), introduced(assumption)).
% 36.77/24.60 tff(13858,assumption,(m_counter_cell_v_carry_out(c_bit1, s51)), introduced(assumption)).
% 36.77/24.60 tff(13859,plain,
% 36.77/24.60 (((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s51)) | m_counter_cell_v_carry_in(c_bit2, s51))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s51)) | m_counter_cell_v_carry_in(c_bit2, s51))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13860,plain,
% 36.77/24.60 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s51)) | m_counter_cell_v_carry_in(c_bit2, s51))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13861,plain,
% 36.77/24.60 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s51)) | m_counter_cell_v_carry_in(c_bit2, s51)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13860, 13859])).
% 36.77/24.60 tff(13862,plain,
% 36.77/24.60 ($false),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13861, 4417, 13858, 13857])).
% 36.77/24.60 tff(13863,plain,(m_counter_cell_v_carry_in(c_bit2, s51) | (~m_counter_cell_v_carry_out(c_bit1, s51))), inference(lemma,lemma(discharge,[]))).
% 36.77/24.60 tff(13864,plain,
% 36.77/24.60 (m_counter_cell_v_carry_in(c_bit2, s51)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13863, 13856])).
% 36.77/24.60 tff(13865,assumption,(node4(c_bit1, s49)), introduced(assumption)).
% 36.77/24.60 tff(13866,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s49) | (~node4(c_bit1, s49)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s49) | (~node4(c_bit1, s49)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13867,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s49) | (~node4(c_bit1, s49)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13868,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s49) | (~node4(c_bit1, s49))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13867, 13866])).
% 36.77/24.60 tff(13869,plain,
% 36.77/24.60 ($false),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13868, 2875, 6682, 13865])).
% 36.77/24.60 tff(13870,plain,((~node4(c_bit1, s49)) | m_counter_cell_v_value(c_bit1, s49)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.60 tff(13871,plain,
% 36.77/24.60 (~node4(c_bit1, s49)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13870, 6672])).
% 36.77/24.60 tff(13872,assumption,(m_counter_cell_v_carry_out(c_bit1, s49)), introduced(assumption)).
% 36.77/24.60 tff(13873,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s49)) | node4(c_bit1, s49))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s49)) | node4(c_bit1, s49))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13874,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s49)) | node4(c_bit1, s49))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13875,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s49)) | node4(c_bit1, s49)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13874, 13873])).
% 36.77/24.60 tff(13876,plain,
% 36.77/24.60 ($false),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13875, 2887, 13872, 13871])).
% 36.77/24.60 tff(13877,plain,(~m_counter_cell_v_carry_out(c_bit1, s49)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.60 tff(13878,plain,
% 36.77/24.60 (((~![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, s49)) | m_counter_cell_v_carry_out(c_bit1, s49))) <=> ((~![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, s49)) | m_counter_cell_v_carry_out(c_bit1, s49))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13879,plain,
% 36.77/24.60 ((~![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, s49)) | m_counter_cell_v_carry_out(c_bit1, s49))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13880,plain,
% 36.77/24.60 ((~![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, s49)) | m_counter_cell_v_carry_out(c_bit1, s49)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13879, 13878])).
% 36.77/24.60 tff(13881,plain,
% 36.77/24.60 (~m_counter_cell_v_carry_in(c_bit2, s49)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13880, 3167, 13877])).
% 36.77/24.60 tff(13882,plain,
% 36.77/24.60 (((~![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_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))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13883,plain,
% 36.77/24.60 ((~![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_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | m_counter_cell_v_carry_out(c_bit1, s47))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13884,plain,
% 36.77/24.60 ((~![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_bit1, s47)) | (~m_counter_cell_v_value(c_bit1, s47)) | m_counter_cell_v_carry_out(c_bit1, s47)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13883, 13882])).
% 36.77/24.60 tff(13885,plain,
% 36.77/24.60 ((~m_counter_cell_v_value(c_bit1, s47)) | m_counter_cell_v_carry_out(c_bit1, s47)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13884, 3031, 6621])).
% 36.77/24.60 tff(13886,plain,
% 36.77/24.60 (m_counter_cell_v_carry_out(c_bit1, s47)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13885, 6612])).
% 36.77/24.60 tff(13887,plain,
% 36.77/24.60 (((~![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, s47)) | m_counter_cell_v_carry_in(c_bit2, s47))) <=> ((~![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, s47)) | m_counter_cell_v_carry_in(c_bit2, s47))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13888,plain,
% 36.77/24.60 ((~![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, s47)) | m_counter_cell_v_carry_in(c_bit2, s47))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13889,plain,
% 36.77/24.60 ((~![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, s47)) | m_counter_cell_v_carry_in(c_bit2, s47)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13888, 13887])).
% 36.77/24.60 tff(13890,plain,
% 36.77/24.60 (m_counter_cell_v_carry_in(c_bit2, s47)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13889, 4417, 13886])).
% 36.77/24.60 tff(13891,plain,
% 36.77/24.60 (~node1(c_bit2, s46)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[6590, 6427])).
% 36.77/24.60 tff(13892,plain,
% 36.77/24.60 (m_counter_cell_v_value(c_bit2, s47)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[6598, 13891])).
% 36.77/24.60 tff(13893,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : ((~m_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, s47)) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node2(c_bit2, 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_bit2, s47)) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node2(c_bit2, s47)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13894,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : ((~m_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, s47)) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node2(c_bit2, s47)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13895,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : ((~m_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, s47)) | (~m_counter_cell_v_value(c_bit2, s47)) | (~node2(c_bit2, s47))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13894, 13893])).
% 36.77/24.60 tff(13896,plain,
% 36.77/24.60 ((~m_counter_cell_v_carry_in(c_bit2, s47)) | (~node2(c_bit2, s47))),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13895, 219, 13892])).
% 36.77/24.60 tff(13897,plain,
% 36.77/24.60 (~node2(c_bit2, s47)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13896, 13890])).
% 36.77/24.60 tff(13898,plain,
% 36.77/24.60 (~m_counter_cell_v_value(c_bit2, s48)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[6543, 13897])).
% 36.77/24.60 tff(13899,assumption,(node4(c_bit1, s48)), introduced(assumption)).
% 36.77/24.60 tff(13900,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s48) | (~node4(c_bit1, s48)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s48) | (~node4(c_bit1, s48)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13901,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s48) | (~node4(c_bit1, s48)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13902,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s48) | (~node4(c_bit1, s48))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13901, 13900])).
% 36.77/24.60 tff(13903,plain,
% 36.77/24.60 ($false),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13902, 3076, 6652, 13899])).
% 36.77/24.60 tff(13904,plain,(~node4(c_bit1, s48)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.60 tff(13905,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s48)) | node4(c_bit1, s48))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s48)) | node4(c_bit1, s48))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13906,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s48)) | node4(c_bit1, s48))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13907,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s48)) | node4(c_bit1, s48)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13906, 13905])).
% 36.77/24.60 tff(13908,plain,
% 36.77/24.60 (~m_counter_cell_v_carry_out(c_bit1, s48)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13907, 2887, 13904])).
% 36.77/24.60 tff(13909,plain,
% 36.77/24.60 (((~![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, s48)) | m_counter_cell_v_carry_out(c_bit1, s48))) <=> ((~![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, s48)) | m_counter_cell_v_carry_out(c_bit1, s48))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13910,plain,
% 36.77/24.60 ((~![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, s48)) | m_counter_cell_v_carry_out(c_bit1, s48))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13911,plain,
% 36.77/24.60 ((~![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, s48)) | m_counter_cell_v_carry_out(c_bit1, s48)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13910, 13909])).
% 36.77/24.60 tff(13912,plain,
% 36.77/24.60 (~m_counter_cell_v_carry_in(c_bit2, s48)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13911, 3167, 13908])).
% 36.77/24.60 tff(13913,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : (m_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, s48) | m_counter_cell_v_value(c_bit2, s48) | (~node2(c_bit2, 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_bit2, s48) | m_counter_cell_v_value(c_bit2, s48) | (~node2(c_bit2, s48)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13914,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_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, s48) | m_counter_cell_v_value(c_bit2, s48) | (~node2(c_bit2, s48)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13915,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_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, s48) | m_counter_cell_v_value(c_bit2, s48) | (~node2(c_bit2, s48))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13914, 13913])).
% 36.77/24.60 tff(13916,plain,
% 36.77/24.60 (m_counter_cell_v_value(c_bit2, s48) | (~node2(c_bit2, s48))),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13915, 3291, 13912])).
% 36.77/24.60 tff(13917,plain,
% 36.77/24.60 (~node2(c_bit2, s48)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13916, 13898])).
% 36.77/24.60 tff(13918,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit2, s48, s49))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit2, s48, s49))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13919,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s48, s49)) | node3(c_bit2, s48, s49))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13920,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s48, s49)) | node3(c_bit2, s48, s49)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13919, 13918])).
% 36.77/24.60 tff(13921,plain,
% 36.77/24.60 (node3(c_bit2, s48, s49)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13920, 81, 1546])).
% 36.77/24.60 tff(13922,plain,
% 36.77/24.60 (((~![Y: $i, 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, s49)) | node2(c_bit2, s48) | (~node3(c_bit2, 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_bit2, s49)) | node2(c_bit2, s48) | (~node3(c_bit2, s48, s49)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13923,plain,
% 36.77/24.60 ((node2(c_bit2, s48) | (~node3(c_bit2, s48, s49)) | (~m_counter_cell_v_value(c_bit2, s49))) <=> ((~m_counter_cell_v_value(c_bit2, s49)) | node2(c_bit2, s48) | (~node3(c_bit2, s48, s49)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13924,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s48) | (~node3(c_bit2, s48, s49)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s49)) | node2(c_bit2, s48) | (~node3(c_bit2, s48, s49))))),
% 36.77/24.60 inference(monotonicity,[status(thm)],[13923])).
% 36.77/24.60 tff(13925,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s48) | (~node3(c_bit2, s48, s49)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s49)) | node2(c_bit2, s48) | (~node3(c_bit2, s48, s49)))),
% 36.77/24.60 inference(transitivity,[status(thm)],[13924, 13922])).
% 36.77/24.60 tff(13926,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s48) | (~node3(c_bit2, s48, s49)) | (~m_counter_cell_v_value(c_bit2, s49)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13927,plain,
% 36.77/24.60 ((~![Y: $i, 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, s49)) | node2(c_bit2, s48) | (~node3(c_bit2, s48, s49))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13926, 13925])).
% 36.77/24.60 tff(13928,plain,
% 36.77/24.60 ((~m_counter_cell_v_value(c_bit2, s49)) | node2(c_bit2, s48)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13927, 234, 13921])).
% 36.77/24.60 tff(13929,plain,
% 36.77/24.60 (~m_counter_cell_v_value(c_bit2, s49)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13928, 13917])).
% 36.77/24.60 tff(13930,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : (m_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, s49) | m_counter_cell_v_value(c_bit2, s49) | (~node2(c_bit2, 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_bit2, s49) | m_counter_cell_v_value(c_bit2, s49) | (~node2(c_bit2, s49)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13931,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_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, s49) | m_counter_cell_v_value(c_bit2, s49) | (~node2(c_bit2, s49)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13932,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_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, s49) | m_counter_cell_v_value(c_bit2, s49) | (~node2(c_bit2, s49))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13931, 13930])).
% 36.77/24.60 tff(13933,plain,
% 36.77/24.60 (m_counter_cell_v_carry_in(c_bit2, s49) | (~node2(c_bit2, s49))),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13932, 3291, 13929])).
% 36.77/24.60 tff(13934,plain,
% 36.77/24.60 (~node2(c_bit2, s49)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13933, 13881])).
% 36.77/24.60 tff(13935,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit2, s49, s50))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit2, s49, s50))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13936,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s49, s50)) | node3(c_bit2, s49, s50))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13937,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s49, s50)) | node3(c_bit2, s49, s50)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13936, 13935])).
% 36.77/24.60 tff(13938,plain,
% 36.77/24.60 (node3(c_bit2, s49, s50)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13937, 81, 1574])).
% 36.77/24.60 tff(13939,plain,
% 36.77/24.60 (((~![Y: $i, 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, s50)) | node2(c_bit2, s49) | (~node3(c_bit2, s49, s50)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s50)) | node2(c_bit2, s49) | (~node3(c_bit2, s49, s50)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13940,plain,
% 36.77/24.60 ((node2(c_bit2, s49) | (~node3(c_bit2, s49, s50)) | (~m_counter_cell_v_value(c_bit2, s50))) <=> ((~m_counter_cell_v_value(c_bit2, s50)) | node2(c_bit2, s49) | (~node3(c_bit2, s49, s50)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13941,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s49) | (~node3(c_bit2, s49, s50)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s50)) | node2(c_bit2, s49) | (~node3(c_bit2, s49, s50))))),
% 36.77/24.60 inference(monotonicity,[status(thm)],[13940])).
% 36.77/24.60 tff(13942,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s49) | (~node3(c_bit2, s49, s50)) | (~m_counter_cell_v_value(c_bit2, 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_bit2, s50)) | node2(c_bit2, s49) | (~node3(c_bit2, s49, s50)))),
% 36.77/24.60 inference(transitivity,[status(thm)],[13941, 13939])).
% 36.77/24.60 tff(13943,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s49) | (~node3(c_bit2, s49, s50)) | (~m_counter_cell_v_value(c_bit2, s50)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13944,plain,
% 36.77/24.60 ((~![Y: $i, 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, s50)) | node2(c_bit2, s49) | (~node3(c_bit2, s49, s50))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13943, 13942])).
% 36.77/24.60 tff(13945,plain,
% 36.77/24.60 ((~m_counter_cell_v_value(c_bit2, s50)) | node2(c_bit2, s49)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13944, 234, 13938])).
% 36.77/24.60 tff(13946,plain,
% 36.77/24.60 (~m_counter_cell_v_value(c_bit2, s50)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13945, 13934])).
% 36.77/24.60 tff(13947,plain,
% 36.77/24.60 (((~![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)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13948,plain,
% 36.77/24.60 ((~![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)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13949,plain,
% 36.77/24.60 ((~![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))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13948, 13947])).
% 36.77/24.60 tff(13950,plain,
% 36.77/24.60 (~node4(c_bit1, s50)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13949, 3076, 3128])).
% 36.77/24.60 tff(13951,plain,
% 36.77/24.60 (((~![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))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13952,plain,
% 36.77/24.60 ((~![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))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13953,plain,
% 36.77/24.60 ((~![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)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13952, 13951])).
% 36.77/24.60 tff(13954,plain,
% 36.77/24.60 (~m_counter_cell_v_carry_out(c_bit1, s50)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13953, 2887, 13950])).
% 36.77/24.60 tff(13955,plain,
% 36.77/24.60 (((~![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, s50)) | m_counter_cell_v_carry_out(c_bit1, s50))) <=> ((~![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, s50)) | m_counter_cell_v_carry_out(c_bit1, s50))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13956,plain,
% 36.77/24.60 ((~![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, s50)) | m_counter_cell_v_carry_out(c_bit1, s50))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13957,plain,
% 36.77/24.60 ((~![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, s50)) | m_counter_cell_v_carry_out(c_bit1, s50)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13956, 13955])).
% 36.77/24.60 tff(13958,plain,
% 36.77/24.60 (~m_counter_cell_v_carry_in(c_bit2, s50)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13957, 3167, 13954])).
% 36.77/24.60 tff(13959,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : (m_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, s50) | m_counter_cell_v_value(c_bit2, s50) | (~node2(c_bit2, s50)))) <=> ((~![I0: $i, X: $i] : (m_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, s50) | m_counter_cell_v_value(c_bit2, s50) | (~node2(c_bit2, s50)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13960,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_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, s50) | m_counter_cell_v_value(c_bit2, s50) | (~node2(c_bit2, s50)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13961,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_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, s50) | m_counter_cell_v_value(c_bit2, s50) | (~node2(c_bit2, s50))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13960, 13959])).
% 36.77/24.60 tff(13962,plain,
% 36.77/24.60 (m_counter_cell_v_value(c_bit2, s50) | (~node2(c_bit2, s50))),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13961, 3291, 13958])).
% 36.77/24.60 tff(13963,plain,
% 36.77/24.60 (~node2(c_bit2, s50)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13962, 13946])).
% 36.77/24.60 tff(13964,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit2, s50, s51))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit2, s50, s51))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13965,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s50, s51)) | node3(c_bit2, s50, s51))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13966,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s50, s51)) | node3(c_bit2, s50, s51)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13965, 13964])).
% 36.77/24.60 tff(13967,plain,
% 36.77/24.60 (node3(c_bit2, s50, s51)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13966, 81, 1605])).
% 36.77/24.60 tff(13968,plain,
% 36.77/24.60 (((~![Y: $i, 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, s51)) | node2(c_bit2, s50) | (~node3(c_bit2, s50, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s51)) | node2(c_bit2, s50) | (~node3(c_bit2, s50, s51)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13969,plain,
% 36.77/24.60 ((node2(c_bit2, s50) | (~node3(c_bit2, s50, s51)) | (~m_counter_cell_v_value(c_bit2, s51))) <=> ((~m_counter_cell_v_value(c_bit2, s51)) | node2(c_bit2, s50) | (~node3(c_bit2, s50, s51)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13970,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s50) | (~node3(c_bit2, s50, s51)) | (~m_counter_cell_v_value(c_bit2, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit2, s51)) | node2(c_bit2, s50) | (~node3(c_bit2, s50, s51))))),
% 36.77/24.60 inference(monotonicity,[status(thm)],[13969])).
% 36.77/24.60 tff(13971,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s50) | (~node3(c_bit2, s50, s51)) | (~m_counter_cell_v_value(c_bit2, s51)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit2, s51)) | node2(c_bit2, s50) | (~node3(c_bit2, s50, s51)))),
% 36.77/24.60 inference(transitivity,[status(thm)],[13970, 13968])).
% 36.77/24.60 tff(13972,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit2, s50) | (~node3(c_bit2, s50, s51)) | (~m_counter_cell_v_value(c_bit2, s51)))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13973,plain,
% 36.77/24.60 ((~![Y: $i, 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, s51)) | node2(c_bit2, s50) | (~node3(c_bit2, s50, s51))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13972, 13971])).
% 36.77/24.60 tff(13974,plain,
% 36.77/24.60 ((~m_counter_cell_v_value(c_bit2, s51)) | node2(c_bit2, s50)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13973, 234, 13967])).
% 36.77/24.60 tff(13975,plain,
% 36.77/24.60 (~m_counter_cell_v_value(c_bit2, s51)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13974, 13963])).
% 36.77/24.60 tff(13976,plain,
% 36.77/24.60 (((~![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, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13977,plain,
% 36.77/24.60 (((~node1(c_bit2, s51)) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13978,plain,
% 36.77/24.60 (((~![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, s51)) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51))))),
% 36.77/24.60 inference(monotonicity,[status(thm)],[13977])).
% 36.77/24.60 tff(13979,plain,
% 36.77/24.60 (((~![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, s51)) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51)))),
% 36.77/24.60 inference(transitivity,[status(thm)],[13978, 13976])).
% 36.77/24.60 tff(13980,plain,
% 36.77/24.60 ((~![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, s51)) | (~m_counter_cell_v_carry_in(c_bit2, s51)) | m_counter_cell_v_value(c_bit2, s51))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13981,plain,
% 36.77/24.60 ((~![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, s51)) | m_counter_cell_v_value(c_bit2, s51) | (~node1(c_bit2, s51))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13980, 13979])).
% 36.77/24.60 tff(13982,plain,
% 36.77/24.60 (~node1(c_bit2, s51)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13981, 170, 13975, 13864])).
% 36.77/24.60 tff(13983,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit2, s51, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit2, s51, s52))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13984,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s51, s52)) | node3(c_bit2, s51, s52))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13985,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s51, s52)) | node3(c_bit2, s51, s52)),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13984, 13983])).
% 36.77/24.60 tff(13986,plain,
% 36.77/24.60 (node3(c_bit2, s51, s52)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13985, 81, 1633])).
% 36.77/24.60 tff(13987,plain,
% 36.77/24.60 (((~![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, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13988,plain,
% 36.77/24.60 ((node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)) | m_counter_cell_v_value(c_bit2, s52)) <=> (m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13989,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)) | m_counter_cell_v_value(c_bit2, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52))))),
% 36.77/24.60 inference(monotonicity,[status(thm)],[13988])).
% 36.77/24.60 tff(13990,plain,
% 36.77/24.60 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)) | m_counter_cell_v_value(c_bit2, s52))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)))),
% 36.77/24.60 inference(transitivity,[status(thm)],[13989, 13987])).
% 36.77/24.60 tff(13991,plain,
% 36.77/24.60 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s51) | (~node3(c_bit2, s51, s52)) | m_counter_cell_v_value(c_bit2, s52))),
% 36.77/24.60 inference(quant_inst,[status(thm)],[])).
% 36.77/24.60 tff(13992,plain,
% 36.77/24.60 ((~![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, s52) | node1(c_bit2, s51) | (~node3(c_bit2, s51, s52))),
% 36.77/24.60 inference(modus_ponens,[status(thm)],[13991, 13990])).
% 36.77/24.60 tff(13993,plain,
% 36.77/24.60 (m_counter_cell_v_value(c_bit2, s52) | node1(c_bit2, s51)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13992, 199, 13986])).
% 36.77/24.60 tff(13994,plain,
% 36.77/24.60 (m_counter_cell_v_value(c_bit2, s52)),
% 36.77/24.60 inference(unit_resolution,[status(thm)],[13993, 13982])).
% 36.77/24.60 tff(13995,plain,
% 36.77/24.60 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s52) | (~node4(c_bit1, s52)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s52) | (~node4(c_bit1, s52)))),
% 36.77/24.60 inference(rewrite,[status(thm)],[])).
% 36.77/24.60 tff(13996,plain,
% 36.77/24.60 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s52) | (~node4(c_bit1, s52)))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(13997,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s52) | (~node4(c_bit1, s52))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[13996, 13995])).
% 36.77/24.61 tff(13998,plain,
% 36.77/24.61 (~node4(c_bit1, s52)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[13997, 2875, 6756])).
% 36.77/24.61 tff(13999,assumption,(m_counter_cell_v_carry_out(c_bit1, s52)), introduced(assumption)).
% 36.77/24.61 tff(14000,assumption,(~node4(c_bit1, s52)), introduced(assumption)).
% 36.77/24.61 tff(14001,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14002,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14003,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14002, 14001])).
% 36.77/24.61 tff(14004,plain,
% 36.77/24.61 ($false),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14003, 2887, 14000, 13999])).
% 36.77/24.61 tff(14005,plain,((~m_counter_cell_v_carry_out(c_bit1, s52)) | node4(c_bit1, s52)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.61 tff(14006,plain,
% 36.77/24.61 (~m_counter_cell_v_carry_out(c_bit1, s52)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14005, 13998])).
% 36.77/24.61 tff(14007,assumption,(m_counter_cell_v_carry_in(c_bit2, s52)), introduced(assumption)).
% 36.77/24.61 tff(14008,assumption,(~m_counter_cell_v_carry_out(c_bit1, s52)), introduced(assumption)).
% 36.77/24.61 tff(14009,plain,
% 36.77/24.61 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14010,plain,
% 36.77/24.61 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14011,plain,
% 36.77/24.61 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14010, 14009])).
% 36.77/24.61 tff(14012,plain,
% 36.77/24.61 ($false),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14011, 3167, 14008, 14007])).
% 36.77/24.61 tff(14013,plain,((~m_counter_cell_v_carry_in(c_bit2, s52)) | m_counter_cell_v_carry_out(c_bit1, s52)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.61 tff(14014,plain,
% 36.77/24.61 (~m_counter_cell_v_carry_in(c_bit2, s52)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14013, 14006])).
% 36.77/24.61 tff(14015,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14016,plain,
% 36.77/24.61 (((~node1(c_bit2, s52)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52))) <=> (m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14017,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s52)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52))))),
% 36.77/24.61 inference(monotonicity,[status(thm)],[14016])).
% 36.77/24.61 tff(14018,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s52)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52)))),
% 36.77/24.61 inference(transitivity,[status(thm)],[14017, 14015])).
% 36.77/24.61 tff(14019,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s52)) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14020,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s52) | (~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14019, 14018])).
% 36.77/24.61 tff(14021,plain,
% 36.77/24.61 ((~m_counter_cell_v_value(c_bit2, s52)) | (~node1(c_bit2, s52))),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14020, 3359, 14014])).
% 36.77/24.61 tff(14022,plain,
% 36.77/24.61 (~node1(c_bit2, s52)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14021, 13994])).
% 36.77/24.61 tff(14023,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit2, s52, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit2, s52, s53))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14024,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s52, s53)) | node3(c_bit2, s52, s53))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14025,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s52, s53)) | node3(c_bit2, s52, s53)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14024, 14023])).
% 36.77/24.61 tff(14026,plain,
% 36.77/24.61 (node3(c_bit2, s52, s53)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14025, 81, 1664])).
% 36.77/24.61 tff(14027,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14028,plain,
% 36.77/24.61 ((node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)) | m_counter_cell_v_value(c_bit2, s53)) <=> (m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14029,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)) | m_counter_cell_v_value(c_bit2, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53))))),
% 36.77/24.61 inference(monotonicity,[status(thm)],[14028])).
% 36.77/24.61 tff(14030,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)) | m_counter_cell_v_value(c_bit2, s53))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)))),
% 36.77/24.61 inference(transitivity,[status(thm)],[14029, 14027])).
% 36.77/24.61 tff(14031,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s52) | (~node3(c_bit2, s52, s53)) | m_counter_cell_v_value(c_bit2, s53))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14032,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52) | (~node3(c_bit2, s52, s53))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14031, 14030])).
% 36.77/24.61 tff(14033,plain,
% 36.77/24.61 (m_counter_cell_v_value(c_bit2, s53) | node1(c_bit2, s52)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14032, 199, 14026])).
% 36.77/24.61 tff(14034,plain,
% 36.77/24.61 (m_counter_cell_v_value(c_bit2, s53)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14033, 14022])).
% 36.77/24.61 tff(14035,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s53) | (~node4(c_bit1, s53)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s53) | (~node4(c_bit1, s53)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14036,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s53) | (~node4(c_bit1, s53)))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14037,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s53) | (~node4(c_bit1, s53))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14036, 14035])).
% 36.77/24.61 tff(14038,plain,
% 36.77/24.61 (~node4(c_bit1, s53)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14037, 2875, 6796])).
% 36.77/24.61 tff(14039,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s53)) | node4(c_bit1, s53))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s53)) | node4(c_bit1, s53))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14040,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s53)) | node4(c_bit1, s53))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14041,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s53)) | node4(c_bit1, s53)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14040, 14039])).
% 36.77/24.61 tff(14042,plain,
% 36.77/24.61 (~m_counter_cell_v_carry_out(c_bit1, s53)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14041, 2887, 14038])).
% 36.77/24.61 tff(14043,plain,
% 36.77/24.61 (((~![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, s53)) | m_counter_cell_v_carry_out(c_bit1, s53))) <=> ((~![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, s53)) | m_counter_cell_v_carry_out(c_bit1, s53))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14044,plain,
% 36.77/24.61 ((~![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, s53)) | m_counter_cell_v_carry_out(c_bit1, s53))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14045,plain,
% 36.77/24.61 ((~![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, s53)) | m_counter_cell_v_carry_out(c_bit1, s53)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14044, 14043])).
% 36.77/24.61 tff(14046,plain,
% 36.77/24.61 (~m_counter_cell_v_carry_in(c_bit2, s53)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14045, 3167, 14042])).
% 36.77/24.61 tff(14047,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14048,plain,
% 36.77/24.61 (((~node1(c_bit2, s53)) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53))) <=> (m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14049,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s53)) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53))))),
% 36.77/24.61 inference(monotonicity,[status(thm)],[14048])).
% 36.77/24.61 tff(14050,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s53)) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53)))),
% 36.77/24.61 inference(transitivity,[status(thm)],[14049, 14047])).
% 36.77/24.61 tff(14051,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s53)) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14052,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s53) | (~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14051, 14050])).
% 36.77/24.61 tff(14053,plain,
% 36.77/24.61 ((~m_counter_cell_v_value(c_bit2, s53)) | (~node1(c_bit2, s53))),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14052, 3359, 14046])).
% 36.77/24.61 tff(14054,plain,
% 36.77/24.61 (~node1(c_bit2, s53)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14053, 14034])).
% 36.77/24.61 tff(14055,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit2, s53, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit2, s53, s54))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14056,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s53, s54)) | node3(c_bit2, s53, s54))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14057,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s53, s54)) | node3(c_bit2, s53, s54)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14056, 14055])).
% 36.77/24.61 tff(14058,plain,
% 36.77/24.61 (node3(c_bit2, s53, s54)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14057, 81, 1692])).
% 36.77/24.61 tff(14059,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14060,plain,
% 36.77/24.61 ((node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)) | m_counter_cell_v_value(c_bit2, s54)) <=> (m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14061,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)) | m_counter_cell_v_value(c_bit2, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54))))),
% 36.77/24.61 inference(monotonicity,[status(thm)],[14060])).
% 36.77/24.61 tff(14062,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)) | m_counter_cell_v_value(c_bit2, s54))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)))),
% 36.77/24.61 inference(transitivity,[status(thm)],[14061, 14059])).
% 36.77/24.61 tff(14063,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s53) | (~node3(c_bit2, s53, s54)) | m_counter_cell_v_value(c_bit2, s54))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14064,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53) | (~node3(c_bit2, s53, s54))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14063, 14062])).
% 36.77/24.61 tff(14065,plain,
% 36.77/24.61 (m_counter_cell_v_value(c_bit2, s54) | node1(c_bit2, s53)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14064, 199, 14058])).
% 36.77/24.61 tff(14066,plain,
% 36.77/24.61 (m_counter_cell_v_value(c_bit2, s54)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14065, 14054])).
% 36.77/24.61 tff(14067,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s54) | (~node4(c_bit1, s54)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~node4(c_bit1, s54)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14068,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s54) | (~node4(c_bit1, s54)))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14069,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s54) | (~node4(c_bit1, s54))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14068, 14067])).
% 36.77/24.61 tff(14070,plain,
% 36.77/24.61 (~node4(c_bit1, s54)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14069, 3076, 6846])).
% 36.77/24.61 tff(14071,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s54)) | node4(c_bit1, s54))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s54)) | node4(c_bit1, s54))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14072,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s54)) | node4(c_bit1, s54))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14073,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s54)) | node4(c_bit1, s54)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14072, 14071])).
% 36.77/24.61 tff(14074,plain,
% 36.77/24.61 (~m_counter_cell_v_carry_out(c_bit1, s54)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14073, 2887, 14070])).
% 36.77/24.61 tff(14075,plain,
% 36.77/24.61 (((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s54)) | m_counter_cell_v_carry_out(c_bit1, s54))) <=> ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s54)) | m_counter_cell_v_carry_out(c_bit1, s54))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14076,plain,
% 36.77/24.61 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | ((~m_counter_cell_v_carry_in(c_bit2, s54)) | m_counter_cell_v_carry_out(c_bit1, s54))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14077,plain,
% 36.77/24.61 ((~![X: $i] : ((~m_counter_cell_v_carry_in(c_bit2, X)) | m_counter_cell_v_carry_out(c_bit1, X))) | (~m_counter_cell_v_carry_in(c_bit2, s54)) | m_counter_cell_v_carry_out(c_bit1, s54)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14076, 14075])).
% 36.77/24.61 tff(14078,plain,
% 36.77/24.61 (~m_counter_cell_v_carry_in(c_bit2, s54)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14077, 3167, 14074])).
% 36.77/24.61 tff(14079,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14080,plain,
% 36.77/24.61 (((~node1(c_bit2, s54)) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54))) <=> (m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14081,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s54)) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54))))),
% 36.77/24.61 inference(monotonicity,[status(thm)],[14080])).
% 36.77/24.61 tff(14082,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s54)) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54)))),
% 36.77/24.61 inference(transitivity,[status(thm)],[14081, 14079])).
% 36.77/24.61 tff(14083,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | ((~node1(c_bit2, s54)) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14084,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit2, s54) | (~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14083, 14082])).
% 36.77/24.61 tff(14085,plain,
% 36.77/24.61 ((~m_counter_cell_v_value(c_bit2, s54)) | (~node1(c_bit2, s54))),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14084, 3359, 14078])).
% 36.77/24.61 tff(14086,plain,
% 36.77/24.61 (~node1(c_bit2, s54)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14085, 14066])).
% 36.77/24.61 tff(14087,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit2, s54, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit2, s54, s55))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14088,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s54, s55)) | node3(c_bit2, s54, s55))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14089,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s54, s55)) | node3(c_bit2, s54, s55)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14088, 14087])).
% 36.77/24.61 tff(14090,plain,
% 36.77/24.61 (node3(c_bit2, s54, s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14089, 81, 1723])).
% 36.77/24.61 tff(14091,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14092,plain,
% 36.77/24.61 ((node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)) | m_counter_cell_v_value(c_bit2, s55)) <=> (m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14093,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)) | m_counter_cell_v_value(c_bit2, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55))))),
% 36.77/24.61 inference(monotonicity,[status(thm)],[14092])).
% 36.77/24.61 tff(14094,plain,
% 36.77/24.61 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)) | m_counter_cell_v_value(c_bit2, s55))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)))),
% 36.77/24.61 inference(transitivity,[status(thm)],[14093, 14091])).
% 36.77/24.61 tff(14095,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s54) | (~node3(c_bit2, s54, s55)) | m_counter_cell_v_value(c_bit2, s55))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14096,plain,
% 36.77/24.61 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54) | (~node3(c_bit2, s54, s55))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14095, 14094])).
% 36.77/24.61 tff(14097,plain,
% 36.77/24.61 (m_counter_cell_v_value(c_bit2, s55) | node1(c_bit2, s54)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14096, 199, 14090])).
% 36.77/24.61 tff(14098,plain,
% 36.77/24.61 (m_counter_cell_v_value(c_bit2, s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14097, 14086])).
% 36.77/24.61 tff(14099,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14100,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14101,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14100, 14099])).
% 36.77/24.61 tff(14102,plain,
% 36.77/24.61 ((~m_counter_cell_v_value(c_bit1, s55)) | m_counter_cell_v_carry_out(c_bit1, s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14101, 3031, 6875])).
% 36.77/24.61 tff(14103,plain,
% 36.77/24.61 (m_counter_cell_v_carry_out(c_bit1, s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14102, 6866])).
% 36.77/24.61 tff(14104,plain,
% 36.77/24.61 (((~![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))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14105,plain,
% 36.77/24.61 ((~![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))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14106,plain,
% 36.77/24.61 ((~![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)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14105, 14104])).
% 36.77/24.61 tff(14107,plain,
% 36.77/24.61 (m_counter_cell_v_carry_in(c_bit2, s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14106, 4417, 14103])).
% 36.77/24.61 tff(14108,plain,
% 36.77/24.61 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14109,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14110,plain,
% 36.77/24.61 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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)),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14109, 14108])).
% 36.77/24.61 tff(14111,plain,
% 36.77/24.61 ((~m_counter_cell_v_value(c_bit2, s55)) | m_counter_cell_v_carry_out(c_bit2, s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14110, 3031, 14107])).
% 36.77/24.61 tff(14112,plain,
% 36.77/24.61 (m_counter_cell_v_carry_out(c_bit2, s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14111, 14098])).
% 36.77/24.61 tff(14113,plain,
% 36.77/24.61 (((~![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)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14114,plain,
% 36.77/24.61 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s55)) | (~m_counter_cell_v_carry_out(c_bit2, s55)))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14115,plain,
% 36.77/24.61 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s55)) | (~m_counter_cell_v_carry_out(c_bit2, s55))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14114, 14113])).
% 36.77/24.61 tff(14116,plain,
% 36.77/24.61 (~always5(s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14115, 58, 14112])).
% 36.77/24.61 tff(14117,assumption,(~always5(s55)), introduced(assumption)).
% 36.77/24.61 tff(14118,plain,
% 36.77/24.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s55) | (~trans(s99, s55)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s55) | (~trans(s99, s55)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14119,plain,
% 36.77/24.61 (((~always5(s99)) | (~trans(s99, s55)) | always5(s55)) <=> ((~always5(s99)) | always5(s55) | (~trans(s99, s55)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14120,plain,
% 36.77/24.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s55) | (~trans(s99, s55))))),
% 36.77/24.61 inference(monotonicity,[status(thm)],[14119])).
% 36.77/24.61 tff(14121,plain,
% 36.77/24.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s55)) | always5(s55))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s55) | (~trans(s99, s55)))),
% 36.77/24.61 inference(transitivity,[status(thm)],[14120, 14118])).
% 36.77/24.61 tff(14122,plain,
% 36.77/24.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s55)) | always5(s55))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14123,plain,
% 36.77/24.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s55) | (~trans(s99, s55))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14122, 14121])).
% 36.77/24.61 tff(14124,plain,
% 36.77/24.61 ($false),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14123, 12111, 25, 13749, 14117])).
% 36.77/24.61 tff(14125,plain,((~trans(s99, s55)) | always5(s55)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.61 tff(14126,plain,
% 36.77/24.61 (~trans(s99, s55)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14125, 14116])).
% 36.77/24.61 tff(14127,plain,
% 36.77/24.61 (~always5(s54)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[9062, 14116])).
% 36.77/24.61 tff(14128,plain,
% 36.77/24.61 (~always5(s53)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[9070, 14127])).
% 36.77/24.61 tff(14129,plain,
% 36.77/24.61 (~always5(s52)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[9078, 14128])).
% 36.77/24.61 tff(14130,assumption,(~always5(s52)), introduced(assumption)).
% 36.77/24.61 tff(14131,plain,
% 36.77/24.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s52) | (~trans(s99, s52)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s52) | (~trans(s99, s52)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14132,plain,
% 36.77/24.61 (((~always5(s99)) | (~trans(s99, s52)) | always5(s52)) <=> ((~always5(s99)) | always5(s52) | (~trans(s99, s52)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14133,plain,
% 36.77/24.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s52) | (~trans(s99, s52))))),
% 36.77/24.61 inference(monotonicity,[status(thm)],[14132])).
% 36.77/24.61 tff(14134,plain,
% 36.77/24.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s52)) | always5(s52))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s52) | (~trans(s99, s52)))),
% 36.77/24.61 inference(transitivity,[status(thm)],[14133, 14131])).
% 36.77/24.61 tff(14135,plain,
% 36.77/24.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s52)) | always5(s52))),
% 36.77/24.61 inference(quant_inst,[status(thm)],[])).
% 36.77/24.61 tff(14136,plain,
% 36.77/24.61 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s52) | (~trans(s99, s52))),
% 36.77/24.61 inference(modus_ponens,[status(thm)],[14135, 14134])).
% 36.77/24.61 tff(14137,plain,
% 36.77/24.61 ($false),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14136, 12067, 25, 13749, 14130])).
% 36.77/24.61 tff(14138,plain,((~trans(s99, s52)) | always5(s52)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.61 tff(14139,plain,
% 36.77/24.61 (~trans(s99, s52)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[14138, 14129])).
% 36.77/24.61 tff(14140,plain,
% 36.77/24.61 (~always5(s51)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[9086, 14129])).
% 36.77/24.61 tff(14141,plain,
% 36.77/24.61 (~always5(s50)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[9094, 14140])).
% 36.77/24.61 tff(14142,plain,
% 36.77/24.61 (~always5(s49)),
% 36.77/24.61 inference(unit_resolution,[status(thm)],[9102, 14141])).
% 36.77/24.61 tff(14143,assumption,(~always5(s49)), introduced(assumption)).
% 36.77/24.61 tff(14144,plain,
% 36.77/24.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s49) | (~trans(s99, s49)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s49) | (~trans(s99, s49)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14145,plain,
% 36.77/24.61 (((~always5(s99)) | (~trans(s99, s49)) | always5(s49)) <=> ((~always5(s99)) | always5(s49) | (~trans(s99, s49)))),
% 36.77/24.61 inference(rewrite,[status(thm)],[])).
% 36.77/24.61 tff(14146,plain,
% 36.77/24.61 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s49) | (~trans(s99, s49))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14145])).
% 36.77/24.62 tff(14147,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s49)) | always5(s49))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s49) | (~trans(s99, s49)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14146, 14144])).
% 36.77/24.62 tff(14148,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s49)) | always5(s49))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14149,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s49) | (~trans(s99, s49))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14148, 14147])).
% 36.77/24.62 tff(14150,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14149, 11924, 25, 13749, 14143])).
% 36.77/24.62 tff(14151,plain,((~trans(s99, s49)) | always5(s49)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14152,plain,
% 36.77/24.62 (~trans(s99, s49)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14151, 14142])).
% 36.77/24.62 tff(14153,plain,
% 36.77/24.62 (~always5(s48)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9110, 14142])).
% 36.77/24.62 tff(14154,assumption,(~always5(s48)), introduced(assumption)).
% 36.77/24.62 tff(14155,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s48) | (~trans(s99, s48)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s48) | (~trans(s99, s48)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14156,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s48)) | always5(s48)) <=> ((~always5(s99)) | always5(s48) | (~trans(s99, s48)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14157,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s48) | (~trans(s99, s48))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14156])).
% 36.77/24.62 tff(14158,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s48)) | always5(s48))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s48) | (~trans(s99, s48)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14157, 14155])).
% 36.77/24.62 tff(14159,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s48)) | always5(s48))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14160,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s48) | (~trans(s99, s48))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14159, 14158])).
% 36.77/24.62 tff(14161,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14160, 12199, 25, 13749, 14154])).
% 36.77/24.62 tff(14162,plain,((~trans(s99, s48)) | always5(s48)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14163,plain,
% 36.77/24.62 (~trans(s99, s48)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14162, 14153])).
% 36.77/24.62 tff(14164,plain,
% 36.77/24.62 (((~![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_bit2, s47)) | (~m_counter_cell_v_value(c_bit2, s47)) | m_counter_cell_v_carry_out(c_bit2, 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_bit2, s47)) | (~m_counter_cell_v_value(c_bit2, s47)) | m_counter_cell_v_carry_out(c_bit2, s47))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14165,plain,
% 36.77/24.62 ((~![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_bit2, s47)) | (~m_counter_cell_v_value(c_bit2, s47)) | m_counter_cell_v_carry_out(c_bit2, s47))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14166,plain,
% 36.77/24.62 ((~![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_bit2, s47)) | (~m_counter_cell_v_value(c_bit2, s47)) | m_counter_cell_v_carry_out(c_bit2, s47)),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14165, 14164])).
% 36.77/24.62 tff(14167,plain,
% 36.77/24.62 ((~m_counter_cell_v_carry_in(c_bit2, s47)) | m_counter_cell_v_carry_out(c_bit2, s47)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14166, 3031, 13892])).
% 36.77/24.62 tff(14168,plain,
% 36.77/24.62 (m_counter_cell_v_carry_out(c_bit2, s47)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14167, 13890])).
% 36.77/24.62 tff(14169,plain,
% 36.77/24.62 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s47)) | (~m_counter_cell_v_carry_out(c_bit2, s47)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s47)) | (~m_counter_cell_v_carry_out(c_bit2, s47)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14170,plain,
% 36.77/24.62 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s47)) | (~m_counter_cell_v_carry_out(c_bit2, s47)))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14171,plain,
% 36.77/24.62 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s47)) | (~m_counter_cell_v_carry_out(c_bit2, s47))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14170, 14169])).
% 36.77/24.62 tff(14172,plain,
% 36.77/24.62 (~always5(s47)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14171, 58, 14168])).
% 36.77/24.62 tff(14173,plain,
% 36.77/24.62 (~always5(s46)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9126, 14172])).
% 36.77/24.62 tff(14174,plain,
% 36.77/24.62 (~always5(s45)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9134, 14173])).
% 36.77/24.62 tff(14175,plain,
% 36.77/24.62 (~always5(s44)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9142, 14174])).
% 36.77/24.62 tff(14176,assumption,(~always5(s44)), introduced(assumption)).
% 36.77/24.62 tff(14177,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s44) | (~trans(s99, s44)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s44) | (~trans(s99, s44)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14178,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s44)) | always5(s44)) <=> ((~always5(s99)) | always5(s44) | (~trans(s99, s44)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14179,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s44) | (~trans(s99, s44))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14178])).
% 36.77/24.62 tff(14180,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s44)) | always5(s44))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s44) | (~trans(s99, s44)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14179, 14177])).
% 36.77/24.62 tff(14181,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s44)) | always5(s44))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14182,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s44) | (~trans(s99, s44))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14181, 14180])).
% 36.77/24.62 tff(14183,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14182, 12100, 25, 13749, 14176])).
% 36.77/24.62 tff(14184,plain,((~trans(s99, s44)) | always5(s44)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14185,plain,
% 36.77/24.62 (~trans(s99, s44)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14184, 14175])).
% 36.77/24.62 tff(14186,assumption,(~always5(s46)), introduced(assumption)).
% 36.77/24.62 tff(14187,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s46) | (~trans(s99, s46)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s46) | (~trans(s99, s46)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14188,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s46)) | always5(s46)) <=> ((~always5(s99)) | always5(s46) | (~trans(s99, s46)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14189,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s46) | (~trans(s99, s46))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14188])).
% 36.77/24.62 tff(14190,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s46)) | always5(s46))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s46) | (~trans(s99, s46)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14189, 14187])).
% 36.77/24.62 tff(14191,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s46)) | always5(s46))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14192,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s46) | (~trans(s99, s46))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14191, 14190])).
% 36.77/24.62 tff(14193,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14192, 12122, 25, 13749, 14186])).
% 36.77/24.62 tff(14194,plain,((~trans(s99, s46)) | always5(s46)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14195,plain,
% 36.77/24.62 (~trans(s99, s46)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14194, 14173])).
% 36.77/24.62 tff(14196,assumption,(~always5(s47)), introduced(assumption)).
% 36.77/24.62 tff(14197,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s47) | (~trans(s99, s47)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s47) | (~trans(s99, s47)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14198,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s47)) | always5(s47)) <=> ((~always5(s99)) | always5(s47) | (~trans(s99, s47)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14199,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s47) | (~trans(s99, s47))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14198])).
% 36.77/24.62 tff(14200,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s47)) | always5(s47))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s47) | (~trans(s99, s47)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14199, 14197])).
% 36.77/24.62 tff(14201,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s47)) | always5(s47))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14202,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s47) | (~trans(s99, s47))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14201, 14200])).
% 36.77/24.62 tff(14203,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14202, 12001, 25, 13749, 14196])).
% 36.77/24.62 tff(14204,plain,((~trans(s99, s47)) | always5(s47)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14205,plain,
% 36.77/24.62 (~trans(s99, s47)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14204, 14172])).
% 36.77/24.62 tff(14206,plain,
% 36.77/24.62 (~always5(s43)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9150, 14175])).
% 36.77/24.62 tff(14207,plain,
% 36.77/24.62 (~always5(s42)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9158, 14206])).
% 36.77/24.62 tff(14208,assumption,(~always5(s42)), introduced(assumption)).
% 36.77/24.62 tff(14209,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s42) | (~trans(s99, s42)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s42) | (~trans(s99, s42)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14210,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s42)) | always5(s42)) <=> ((~always5(s99)) | always5(s42) | (~trans(s99, s42)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14211,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s42) | (~trans(s99, s42))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14210])).
% 36.77/24.62 tff(14212,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s42)) | always5(s42))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s42) | (~trans(s99, s42)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14211, 14209])).
% 36.77/24.62 tff(14213,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s42)) | always5(s42))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14214,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s42) | (~trans(s99, s42))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14213, 14212])).
% 36.77/24.62 tff(14215,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14214, 11902, 25, 13749, 14208])).
% 36.77/24.62 tff(14216,plain,((~trans(s99, s42)) | always5(s42)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14217,plain,
% 36.77/24.62 (~trans(s99, s42)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14216, 14207])).
% 36.77/24.62 tff(14218,assumption,(~always5(s43)), introduced(assumption)).
% 36.77/24.62 tff(14219,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s43) | (~trans(s99, s43)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s43) | (~trans(s99, s43)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14220,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s43)) | always5(s43)) <=> ((~always5(s99)) | always5(s43) | (~trans(s99, s43)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14221,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s43) | (~trans(s99, s43))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14220])).
% 36.77/24.62 tff(14222,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s43)) | always5(s43))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s43) | (~trans(s99, s43)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14221, 14219])).
% 36.77/24.62 tff(14223,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s43)) | always5(s43))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14224,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s43) | (~trans(s99, s43))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14223, 14222])).
% 36.77/24.62 tff(14225,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14224, 11990, 25, 13749, 14218])).
% 36.77/24.62 tff(14226,plain,((~trans(s99, s43)) | always5(s43)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14227,plain,
% 36.77/24.62 (~trans(s99, s43)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14226, 14206])).
% 36.77/24.62 tff(14228,plain,
% 36.77/24.62 (~always5(s41)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9166, 14207])).
% 36.77/24.62 tff(14229,assumption,(~always5(s41)), introduced(assumption)).
% 36.77/24.62 tff(14230,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s41) | (~trans(s99, s41)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s41) | (~trans(s99, s41)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14231,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s41)) | always5(s41)) <=> ((~always5(s99)) | always5(s41) | (~trans(s99, s41)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14232,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s41) | (~trans(s99, s41))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14231])).
% 36.77/24.62 tff(14233,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s41)) | always5(s41))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s41) | (~trans(s99, s41)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14232, 14230])).
% 36.77/24.62 tff(14234,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s41)) | always5(s41))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14235,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s41) | (~trans(s99, s41))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14234, 14233])).
% 36.77/24.62 tff(14236,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14235, 12188, 25, 13749, 14229])).
% 36.77/24.62 tff(14237,plain,((~trans(s99, s41)) | always5(s41)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14238,plain,
% 36.77/24.62 (~trans(s99, s41)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14237, 14228])).
% 36.77/24.62 tff(14239,plain,
% 36.77/24.62 (((~![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_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, 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_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, s39))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14240,plain,
% 36.77/24.62 ((~![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_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, s39))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14241,plain,
% 36.77/24.62 ((~![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_bit2, s39)) | (~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, s39)),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14240, 14239])).
% 36.77/24.62 tff(14242,plain,
% 36.77/24.62 ((~m_counter_cell_v_value(c_bit2, s39)) | m_counter_cell_v_carry_out(c_bit2, s39)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14241, 3031, 6073])).
% 36.77/24.62 tff(14243,plain,
% 36.77/24.62 (m_counter_cell_v_carry_out(c_bit2, s39)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14242, 6001])).
% 36.77/24.62 tff(14244,plain,
% 36.77/24.62 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s39)) | (~m_counter_cell_v_carry_out(c_bit2, s39)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s39)) | (~m_counter_cell_v_carry_out(c_bit2, s39)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14245,plain,
% 36.77/24.62 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s39)) | (~m_counter_cell_v_carry_out(c_bit2, s39)))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14246,plain,
% 36.77/24.62 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s39)) | (~m_counter_cell_v_carry_out(c_bit2, s39))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14245, 14244])).
% 36.77/24.62 tff(14247,plain,
% 36.77/24.62 (~always5(s39)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14246, 58, 14243])).
% 36.77/24.62 tff(14248,assumption,(~always5(s39)), introduced(assumption)).
% 36.77/24.62 tff(14249,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s39) | (~trans(s99, s39)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s39) | (~trans(s99, s39)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14250,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s39)) | always5(s39)) <=> ((~always5(s99)) | always5(s39) | (~trans(s99, s39)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14251,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s39) | (~trans(s99, s39))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14250])).
% 36.77/24.62 tff(14252,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s39)) | always5(s39))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s39) | (~trans(s99, s39)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14251, 14249])).
% 36.77/24.62 tff(14253,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s39)) | always5(s39))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14254,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s39) | (~trans(s99, s39))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14253, 14252])).
% 36.77/24.62 tff(14255,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14254, 12045, 25, 13749, 14248])).
% 36.77/24.62 tff(14256,plain,((~trans(s99, s39)) | always5(s39)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14257,plain,
% 36.77/24.62 (~trans(s99, s39)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14256, 14247])).
% 36.77/24.62 tff(14258,plain,
% 36.77/24.62 (~always5(s38)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9190, 14247])).
% 36.77/24.62 tff(14259,assumption,(~always5(s38)), introduced(assumption)).
% 36.77/24.62 tff(14260,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s38) | (~trans(s99, s38)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s38) | (~trans(s99, s38)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14261,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s38)) | always5(s38)) <=> ((~always5(s99)) | always5(s38) | (~trans(s99, s38)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14262,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s38) | (~trans(s99, s38))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14261])).
% 36.77/24.62 tff(14263,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s38)) | always5(s38))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s38) | (~trans(s99, s38)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14262, 14260])).
% 36.77/24.62 tff(14264,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s38)) | always5(s38))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14265,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s38) | (~trans(s99, s38))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14264, 14263])).
% 36.77/24.62 tff(14266,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14265, 11858, 25, 13749, 14259])).
% 36.77/24.62 tff(14267,plain,((~trans(s99, s38)) | always5(s38)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14268,plain,
% 36.77/24.62 (~trans(s99, s38)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14267, 14258])).
% 36.77/24.62 tff(14269,plain,
% 36.77/24.62 (~always5(s37)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9198, 14258])).
% 36.77/24.62 tff(14270,plain,
% 36.77/24.62 (~always5(s36)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9206, 14269])).
% 36.77/24.62 tff(14271,assumption,(~always5(s36)), introduced(assumption)).
% 36.77/24.62 tff(14272,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s36) | (~trans(s99, s36)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s36) | (~trans(s99, s36)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14273,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s36)) | always5(s36)) <=> ((~always5(s99)) | always5(s36) | (~trans(s99, s36)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14274,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s36) | (~trans(s99, s36))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14273])).
% 36.77/24.62 tff(14275,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s36)) | always5(s36))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s36) | (~trans(s99, s36)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14274, 14272])).
% 36.77/24.62 tff(14276,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s36)) | always5(s36))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14277,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s36) | (~trans(s99, s36))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14276, 14275])).
% 36.77/24.62 tff(14278,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14277, 11891, 25, 13749, 14271])).
% 36.77/24.62 tff(14279,plain,((~trans(s99, s36)) | always5(s36)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14280,plain,
% 36.77/24.62 (~trans(s99, s36)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14279, 14270])).
% 36.77/24.62 tff(14281,plain,
% 36.77/24.62 (((~![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_bit2, s31)) | (~m_counter_cell_v_value(c_bit2, s31)) | m_counter_cell_v_carry_out(c_bit2, 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_bit2, s31)) | (~m_counter_cell_v_value(c_bit2, s31)) | m_counter_cell_v_carry_out(c_bit2, s31))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14282,plain,
% 36.77/24.62 ((~![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_bit2, s31)) | (~m_counter_cell_v_value(c_bit2, s31)) | m_counter_cell_v_carry_out(c_bit2, s31))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14283,plain,
% 36.77/24.62 ((~![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_bit2, s31)) | (~m_counter_cell_v_value(c_bit2, s31)) | m_counter_cell_v_carry_out(c_bit2, s31)),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14282, 14281])).
% 36.77/24.62 tff(14284,plain,
% 36.77/24.62 (m_counter_cell_v_carry_out(c_bit2, s31)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14283, 3031, 5685, 5668])).
% 36.77/24.62 tff(14285,plain,
% 36.77/24.62 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s31)) | (~m_counter_cell_v_carry_out(c_bit2, s31)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s31)) | (~m_counter_cell_v_carry_out(c_bit2, s31)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14286,plain,
% 36.77/24.62 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s31)) | (~m_counter_cell_v_carry_out(c_bit2, s31)))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14287,plain,
% 36.77/24.62 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s31)) | (~m_counter_cell_v_carry_out(c_bit2, s31))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14286, 14285])).
% 36.77/24.62 tff(14288,plain,
% 36.77/24.62 (~always5(s31)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14287, 58, 14284])).
% 36.77/24.62 tff(14289,plain,
% 36.77/24.62 (~always5(s30)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9254, 14288])).
% 36.77/24.62 tff(14290,plain,
% 36.77/24.62 (~always5(s29)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9262, 14289])).
% 36.77/24.62 tff(14291,plain,
% 36.77/24.62 (~always5(s28)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9270, 14290])).
% 36.77/24.62 tff(14292,plain,
% 36.77/24.62 (~always5(s27)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9278, 14291])).
% 36.77/24.62 tff(14293,assumption,(~always5(s27)), introduced(assumption)).
% 36.77/24.62 tff(14294,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s27) | (~trans(s99, s27)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s27) | (~trans(s99, s27)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14295,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s27)) | always5(s27)) <=> ((~always5(s99)) | always5(s27) | (~trans(s99, s27)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14296,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s27) | (~trans(s99, s27))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14295])).
% 36.77/24.62 tff(14297,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s27)) | always5(s27))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s27) | (~trans(s99, s27)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14296, 14294])).
% 36.77/24.62 tff(14298,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s27)) | always5(s27))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14299,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s27) | (~trans(s99, s27))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14298, 14297])).
% 36.77/24.62 tff(14300,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14299, 12023, 25, 13749, 14293])).
% 36.77/24.62 tff(14301,plain,((~trans(s99, s27)) | always5(s27)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14302,plain,
% 36.77/24.62 (~trans(s99, s27)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14301, 14292])).
% 36.77/24.62 tff(14303,plain,
% 36.77/24.62 (m_counter_cell_v_carry_out(c_bit1, s23)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[5428, 3961])).
% 36.77/24.62 tff(14304,plain,
% 36.77/24.62 (m_counter_cell_v_carry_in(c_bit2, s23)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[5432, 4417, 14303])).
% 36.77/24.62 tff(14305,plain,
% 36.77/24.62 (((~![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_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14306,plain,
% 36.77/24.62 ((~![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_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14307,plain,
% 36.77/24.62 ((~![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_bit2, s23)) | (~m_counter_cell_v_value(c_bit2, s23)) | m_counter_cell_v_carry_out(c_bit2, s23)),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14306, 14305])).
% 36.77/24.62 tff(14308,plain,
% 36.77/24.62 (m_counter_cell_v_carry_out(c_bit2, s23)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14307, 3031, 5291, 14304])).
% 36.77/24.62 tff(14309,plain,
% 36.77/24.62 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s23)) | (~m_counter_cell_v_carry_out(c_bit2, s23)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s23)) | (~m_counter_cell_v_carry_out(c_bit2, s23)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14310,plain,
% 36.77/24.62 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s23)) | (~m_counter_cell_v_carry_out(c_bit2, s23)))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14311,plain,
% 36.77/24.62 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s23)) | (~m_counter_cell_v_carry_out(c_bit2, s23))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14310, 14309])).
% 36.77/24.62 tff(14312,plain,
% 36.77/24.62 (~always5(s23)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14311, 58, 14308])).
% 36.77/24.62 tff(14313,plain,
% 36.77/24.62 (~always5(s22)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9318, 14312])).
% 36.77/24.62 tff(14314,plain,
% 36.77/24.62 (~always5(s21)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9326, 14313])).
% 36.77/24.62 tff(14315,plain,
% 36.77/24.62 (~always5(s20)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9334, 14314])).
% 36.77/24.62 tff(14316,plain,
% 36.77/24.62 (~always5(s19)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9342, 14315])).
% 36.77/24.62 tff(14317,plain,
% 36.77/24.62 (~always5(s18)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9350, 14316])).
% 36.77/24.62 tff(14318,assumption,(~always5(s18)), introduced(assumption)).
% 36.77/24.62 tff(14319,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s18) | (~trans(s99, s18)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s18) | (~trans(s99, s18)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14320,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s18)) | always5(s18)) <=> ((~always5(s99)) | always5(s18) | (~trans(s99, s18)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14321,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s18) | (~trans(s99, s18))))),
% 36.77/24.62 inference(monotonicity,[status(thm)],[14320])).
% 36.77/24.62 tff(14322,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s18)) | always5(s18))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s18) | (~trans(s99, s18)))),
% 36.77/24.62 inference(transitivity,[status(thm)],[14321, 14319])).
% 36.77/24.62 tff(14323,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s18)) | always5(s18))),
% 36.77/24.62 inference(quant_inst,[status(thm)],[])).
% 36.77/24.62 tff(14324,plain,
% 36.77/24.62 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s18) | (~trans(s99, s18))),
% 36.77/24.62 inference(modus_ponens,[status(thm)],[14323, 14322])).
% 36.77/24.62 tff(14325,plain,
% 36.77/24.62 ($false),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14324, 12133, 25, 13749, 14318])).
% 36.77/24.62 tff(14326,plain,((~trans(s99, s18)) | always5(s18)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.62 tff(14327,plain,
% 36.77/24.62 (~trans(s99, s18)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[14326, 14317])).
% 36.77/24.62 tff(14328,plain,
% 36.77/24.62 (~always5(s17)),
% 36.77/24.62 inference(unit_resolution,[status(thm)],[9358, 14317])).
% 36.77/24.62 tff(14329,assumption,(~always5(s17)), introduced(assumption)).
% 36.77/24.62 tff(14330,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s17) | (~trans(s99, s17)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s17) | (~trans(s99, s17)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14331,plain,
% 36.77/24.62 (((~always5(s99)) | (~trans(s99, s17)) | always5(s17)) <=> ((~always5(s99)) | always5(s17) | (~trans(s99, s17)))),
% 36.77/24.62 inference(rewrite,[status(thm)],[])).
% 36.77/24.62 tff(14332,plain,
% 36.77/24.62 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s17) | (~trans(s99, s17))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14331])).
% 36.77/24.63 tff(14333,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s17)) | always5(s17))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s17) | (~trans(s99, s17)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14332, 14330])).
% 36.77/24.63 tff(14334,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s17)) | always5(s17))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14335,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s17) | (~trans(s99, s17))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14334, 14333])).
% 36.77/24.63 tff(14336,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14335, 12012, 25, 13749, 14329])).
% 36.77/24.63 tff(14337,plain,((~trans(s99, s17)) | always5(s17)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14338,plain,
% 36.77/24.63 (~trans(s99, s17)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14337, 14328])).
% 36.77/24.63 tff(14339,plain,
% 36.77/24.63 (m_counter_cell_v_carry_out(c_bit1, s15)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[4513, 3695])).
% 36.77/24.63 tff(14340,plain,
% 36.77/24.63 (m_counter_cell_v_carry_in(c_bit2, s15)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[4517, 4417, 14339])).
% 36.77/24.63 tff(14341,plain,
% 36.77/24.63 (~node4(c_bit1, s14)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[4524, 3207])).
% 36.77/24.63 tff(14342,plain,
% 36.77/24.63 (~m_counter_cell_v_carry_out(c_bit1, s14)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[4532, 14341])).
% 36.77/24.63 tff(14343,plain,
% 36.77/24.63 (~m_counter_cell_v_carry_in(c_bit2, s14)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[4540, 14342])).
% 36.77/24.63 tff(14344,plain,
% 36.77/24.63 (~node1(c_bit2, s14)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[5052, 14343])).
% 36.77/24.63 tff(14345,plain,
% 36.77/24.63 (m_counter_cell_v_value(c_bit2, s15)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[5064, 14344])).
% 36.77/24.63 tff(14346,plain,
% 36.77/24.63 (((~![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_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))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14347,plain,
% 36.77/24.63 ((~![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_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | m_counter_cell_v_carry_out(c_bit2, s15))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14348,plain,
% 36.77/24.63 ((~![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_bit2, s15)) | (~m_counter_cell_v_value(c_bit2, s15)) | m_counter_cell_v_carry_out(c_bit2, s15)),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14347, 14346])).
% 36.77/24.63 tff(14349,plain,
% 36.77/24.63 (m_counter_cell_v_carry_out(c_bit2, s15)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14348, 3031, 14345, 14340])).
% 36.77/24.63 tff(14350,plain,
% 36.77/24.63 (((~![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)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14351,plain,
% 36.77/24.63 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s15)) | (~m_counter_cell_v_carry_out(c_bit2, s15)))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14352,plain,
% 36.77/24.63 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s15)) | (~m_counter_cell_v_carry_out(c_bit2, s15))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14351, 14350])).
% 36.77/24.63 tff(14353,plain,
% 36.77/24.63 (~always5(s15)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14352, 58, 14349])).
% 36.77/24.63 tff(14354,plain,
% 36.77/24.63 (~always5(s14)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9383, 14353])).
% 36.77/24.63 tff(14355,plain,
% 36.77/24.63 (~always5(s13)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9437, 14354])).
% 36.77/24.63 tff(14356,plain,
% 36.77/24.63 (~always5(s12)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9458, 14355])).
% 36.77/24.63 tff(14357,plain,
% 36.77/24.63 (~always5(s11)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9479, 14356])).
% 36.77/24.63 tff(14358,plain,
% 36.77/24.63 (~always5(s10)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9500, 14357])).
% 36.77/24.63 tff(14359,plain,
% 36.77/24.63 (~always5(s9)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9521, 14358])).
% 36.77/24.63 tff(14360,assumption,(~always5(s9)), introduced(assumption)).
% 36.77/24.63 tff(14361,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s9) | (~trans(s99, s9)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s9) | (~trans(s99, s9)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14362,plain,
% 36.77/24.63 (((~always5(s99)) | (~trans(s99, s9)) | always5(s9)) <=> ((~always5(s99)) | always5(s9) | (~trans(s99, s9)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14363,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s9) | (~trans(s99, s9))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14362])).
% 36.77/24.63 tff(14364,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s9)) | always5(s9))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s9) | (~trans(s99, s9)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14363, 14361])).
% 36.77/24.63 tff(14365,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s9)) | always5(s9))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14366,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s9) | (~trans(s99, s9))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14365, 14364])).
% 36.77/24.63 tff(14367,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14366, 11946, 25, 13749, 14360])).
% 36.77/24.63 tff(14368,plain,((~trans(s99, s9)) | always5(s9)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14369,plain,
% 36.77/24.63 (~trans(s99, s9)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14368, 14359])).
% 36.77/24.63 tff(14370,plain,
% 36.77/24.63 (~always5(s8)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9542, 14359])).
% 36.77/24.63 tff(14371,assumption,(~always5(s8)), introduced(assumption)).
% 36.77/24.63 tff(14372,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s8) | (~trans(s99, s8)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s8) | (~trans(s99, s8)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14373,plain,
% 36.77/24.63 (((~always5(s99)) | (~trans(s99, s8)) | always5(s8)) <=> ((~always5(s99)) | always5(s8) | (~trans(s99, s8)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14374,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s8) | (~trans(s99, s8))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14373])).
% 36.77/24.63 tff(14375,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s8)) | always5(s8))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s8) | (~trans(s99, s8)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14374, 14372])).
% 36.77/24.63 tff(14376,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s8)) | always5(s8))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14377,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s8) | (~trans(s99, s8))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14376, 14375])).
% 36.77/24.63 tff(14378,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14377, 11935, 25, 13749, 14371])).
% 36.77/24.63 tff(14379,plain,((~trans(s99, s8)) | always5(s8)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14380,plain,
% 36.77/24.63 (~trans(s99, s8)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14379, 14370])).
% 36.77/24.63 tff(14381,assumption,(~always5(s10)), introduced(assumption)).
% 36.77/24.63 tff(14382,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s10) | (~trans(s99, s10)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s10) | (~trans(s99, s10)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14383,plain,
% 36.77/24.63 (((~always5(s99)) | (~trans(s99, s10)) | always5(s10)) <=> ((~always5(s99)) | always5(s10) | (~trans(s99, s10)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14384,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s10)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s10) | (~trans(s99, s10))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14383])).
% 36.77/24.63 tff(14385,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s10)) | always5(s10))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s10) | (~trans(s99, s10)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14384, 14382])).
% 36.77/24.63 tff(14386,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s10)) | always5(s10))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14387,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s10) | (~trans(s99, s10))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14386, 14385])).
% 36.77/24.63 tff(14388,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14387, 11957, 25, 13749, 14381])).
% 36.77/24.63 tff(14389,plain,((~trans(s99, s10)) | always5(s10)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14390,plain,
% 36.77/24.63 (~trans(s99, s10)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14389, 14358])).
% 36.77/24.63 tff(14391,assumption,(~always5(s13)), introduced(assumption)).
% 36.77/24.63 tff(14392,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s13) | (~trans(s99, s13)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s13) | (~trans(s99, s13)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14393,plain,
% 36.77/24.63 (((~always5(s99)) | (~trans(s99, s13)) | always5(s13)) <=> ((~always5(s99)) | always5(s13) | (~trans(s99, s13)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14394,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s13) | (~trans(s99, s13))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14393])).
% 36.77/24.63 tff(14395,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s13)) | always5(s13))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s13) | (~trans(s99, s13)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14394, 14392])).
% 36.77/24.63 tff(14396,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s13)) | always5(s13))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14397,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s13) | (~trans(s99, s13))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14396, 14395])).
% 36.77/24.63 tff(14398,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14397, 12078, 25, 13749, 14391])).
% 36.77/24.63 tff(14399,plain,((~trans(s99, s13)) | always5(s13)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14400,plain,
% 36.77/24.63 (~trans(s99, s13)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14399, 14355])).
% 36.77/24.63 tff(14401,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s15) | (~trans(s99, s15)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s15) | (~trans(s99, s15)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14402,plain,
% 36.77/24.63 (((~always5(s99)) | (~trans(s99, s15)) | always5(s15)) <=> ((~always5(s99)) | always5(s15) | (~trans(s99, s15)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14403,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s15) | (~trans(s99, s15))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14402])).
% 36.77/24.63 tff(14404,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s15)) | always5(s15))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s15) | (~trans(s99, s15)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14403, 14401])).
% 36.77/24.63 tff(14405,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s15)) | always5(s15))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14406,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s15) | (~trans(s99, s15))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14405, 14404])).
% 36.77/24.63 tff(14407,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14406, 11979, 25, 13749, 9376])).
% 36.77/24.63 tff(14408,plain,((~trans(s99, s15)) | always5(s15)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14409,plain,
% 36.77/24.63 (~trans(s99, s15)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14408, 14353])).
% 36.77/24.63 tff(14410,plain,
% 36.77/24.63 (((~![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_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))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14411,plain,
% 36.77/24.63 ((~![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_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | m_counter_cell_v_carry_out(c_bit2, s7))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14412,plain,
% 36.77/24.63 ((~![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_bit2, s7)) | (~m_counter_cell_v_value(c_bit2, s7)) | m_counter_cell_v_carry_out(c_bit2, s7)),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14411, 14410])).
% 36.77/24.63 tff(14413,plain,
% 36.77/24.63 ((~m_counter_cell_v_carry_in(c_bit2, s7)) | m_counter_cell_v_carry_out(c_bit2, s7)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14412, 3031, 4837])).
% 36.77/24.63 tff(14414,plain,
% 36.77/24.63 (m_counter_cell_v_carry_out(c_bit2, s7)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14413, 4551])).
% 36.77/24.63 tff(14415,plain,
% 36.77/24.63 (((~![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)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14416,plain,
% 36.77/24.63 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s7)) | (~m_counter_cell_v_carry_out(c_bit2, s7)))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14417,plain,
% 36.77/24.63 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s7)) | (~m_counter_cell_v_carry_out(c_bit2, s7))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14416, 14415])).
% 36.77/24.63 tff(14418,plain,
% 36.77/24.63 (~always5(s7)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14417, 58, 14414])).
% 36.77/24.63 tff(14419,plain,
% 36.77/24.63 (~always5(s6)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9566, 14418])).
% 36.77/24.63 tff(14420,plain,
% 36.77/24.63 (~always5(s5)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9574, 14419])).
% 36.77/24.63 tff(14421,plain,
% 36.77/24.63 (~always5(s4)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9582, 14420])).
% 36.77/24.63 tff(14422,plain,
% 36.77/24.63 (~always5(s3)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[9590, 14421])).
% 36.77/24.63 tff(14423,assumption,(~always5(s3)), introduced(assumption)).
% 36.77/24.63 tff(14424,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s3) | (~trans(s99, s3)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s3) | (~trans(s99, s3)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14425,plain,
% 36.77/24.63 (((~always5(s99)) | (~trans(s99, s3)) | always5(s3)) <=> ((~always5(s99)) | always5(s3) | (~trans(s99, s3)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14426,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s3) | (~trans(s99, s3))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14425])).
% 36.77/24.63 tff(14427,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s3)) | always5(s3))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s3) | (~trans(s99, s3)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14426, 14424])).
% 36.77/24.63 tff(14428,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s3)) | always5(s3))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14429,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s3) | (~trans(s99, s3))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14428, 14427])).
% 36.77/24.63 tff(14430,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14429, 12166, 25, 13749, 14423])).
% 36.77/24.63 tff(14431,plain,((~trans(s99, s3)) | always5(s3)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14432,plain,
% 36.77/24.63 (~trans(s99, s3)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14431, 14422])).
% 36.77/24.63 tff(14433,assumption,(~always5(s5)), introduced(assumption)).
% 36.77/24.63 tff(14434,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s5) | (~trans(s99, s5)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s5) | (~trans(s99, s5)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14435,plain,
% 36.77/24.63 (((~always5(s99)) | (~trans(s99, s5)) | always5(s5)) <=> ((~always5(s99)) | always5(s5) | (~trans(s99, s5)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14436,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s5) | (~trans(s99, s5))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14435])).
% 36.77/24.63 tff(14437,plain,
% 36.77/24.63 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s5)) | always5(s5))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s5) | (~trans(s99, s5)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14436, 14434])).
% 36.77/24.63 tff(14438,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s5)) | always5(s5))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14439,plain,
% 36.77/24.63 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s5) | (~trans(s99, s5))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14438, 14437])).
% 36.77/24.63 tff(14440,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14439, 11968, 25, 13749, 14433])).
% 36.77/24.63 tff(14441,plain,((~trans(s99, s5)) | always5(s5)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14442,plain,
% 36.77/24.63 (~trans(s99, s5)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14441, 14420])).
% 36.77/24.63 tff(14443,assumption,(~m_counter_cell_v_carry_in(c_bit1, s98)), introduced(assumption)).
% 36.77/24.63 tff(14444,plain,
% 36.77/24.63 (((~![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, s98)) | m_counter_cell_v_carry_in(c_bit1, s98))) <=> ((~![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, s98)) | m_counter_cell_v_carry_in(c_bit1, s98))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14445,plain,
% 36.77/24.63 ((~![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, s98)) | m_counter_cell_v_carry_in(c_bit1, s98))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14446,plain,
% 36.77/24.63 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit0, X)) | m_counter_cell_v_carry_in(c_bit1, X))) | (~m_counter_cell_v_carry_out(c_bit0, s98)) | m_counter_cell_v_carry_in(c_bit1, s98)),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14445, 14444])).
% 36.77/24.63 tff(14447,plain,
% 36.77/24.63 ($false),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14446, 3046, 8583, 14443])).
% 36.77/24.63 tff(14448,plain,((~m_counter_cell_v_carry_out(c_bit0, s98)) | m_counter_cell_v_carry_in(c_bit1, s98)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.63 tff(14449,plain,
% 36.77/24.63 (~m_counter_cell_v_carry_out(c_bit0, s98)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14448, 14443])).
% 36.77/24.63 tff(14450,plain,
% 36.77/24.63 (((~![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_bit0, s98)) | (~m_counter_cell_v_value(c_bit0, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s98)) | (~m_counter_cell_v_value(c_bit0, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14451,plain,
% 36.77/24.63 ((~![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_bit0, s98)) | (~m_counter_cell_v_value(c_bit0, s98)) | m_counter_cell_v_carry_out(c_bit0, s98))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14452,plain,
% 36.77/24.63 ((~![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_bit0, s98)) | (~m_counter_cell_v_value(c_bit0, s98)) | m_counter_cell_v_carry_out(c_bit0, s98)),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14451, 14450])).
% 36.77/24.63 tff(14453,plain,
% 36.77/24.63 ((~m_counter_cell_v_value(c_bit0, s98)) | m_counter_cell_v_carry_out(c_bit0, s98)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14452, 3031, 8614])).
% 36.77/24.63 tff(14454,plain,
% 36.77/24.63 (~m_counter_cell_v_value(c_bit0, s98)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14453, 14449])).
% 36.77/24.63 tff(14455,plain,
% 36.77/24.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s97) | (~node3(c_bit0, s97, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14456,plain,
% 36.77/24.63 ((node1(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | m_counter_cell_v_value(c_bit0, s98)) <=> (m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14457,plain,
% 36.77/24.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | m_counter_cell_v_value(c_bit0, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s97) | (~node3(c_bit0, s97, s98))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14456])).
% 36.77/24.63 tff(14458,plain,
% 36.77/24.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | m_counter_cell_v_value(c_bit0, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s97) | (~node3(c_bit0, s97, s98)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14457, 14455])).
% 36.77/24.63 tff(14459,plain,
% 36.77/24.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s97) | (~node3(c_bit0, s97, s98)) | m_counter_cell_v_value(c_bit0, s98))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14460,plain,
% 36.77/24.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s97) | (~node3(c_bit0, s97, s98))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14459, 14458])).
% 36.77/24.63 tff(14461,plain,
% 36.77/24.63 (m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s97)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14460, 199, 8569])).
% 36.77/24.63 tff(14462,plain,
% 36.77/24.63 (node1(c_bit0, s97)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14461, 14454])).
% 36.77/24.63 tff(14463,plain,
% 36.77/24.63 (((~![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_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97) | (~node1(c_bit0, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97) | (~node1(c_bit0, s97)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14464,plain,
% 36.77/24.63 (((~node1(c_bit0, s97)) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97) | (~node1(c_bit0, s97)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14465,plain,
% 36.77/24.63 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s97)) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97) | (~node1(c_bit0, s97))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14464])).
% 36.77/24.63 tff(14466,plain,
% 36.77/24.63 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s97)) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97) | (~node1(c_bit0, s97)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14465, 14463])).
% 36.77/24.63 tff(14467,plain,
% 36.77/24.63 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s97)) | (~m_counter_cell_v_carry_in(c_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14468,plain,
% 36.77/24.63 ((~![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_bit0, s97)) | m_counter_cell_v_value(c_bit0, s97) | (~node1(c_bit0, s97))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14467, 14466])).
% 36.77/24.63 tff(14469,plain,
% 36.77/24.63 (m_counter_cell_v_value(c_bit0, s97) | (~node1(c_bit0, s97))),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14468, 170, 8381])).
% 36.77/24.63 tff(14470,plain,
% 36.77/24.63 (m_counter_cell_v_value(c_bit0, s97)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14469, 14462])).
% 36.77/24.63 tff(14471,plain,
% 36.77/24.63 (m_counter_cell_v_carry_out(c_bit0, s97)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[8385, 14470])).
% 36.77/24.63 tff(14472,plain,
% 36.77/24.63 (m_counter_cell_v_carry_in(c_bit1, s97)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[8389, 3046, 14471])).
% 36.77/24.63 tff(14473,assumption,(~m_counter_cell_v_carry_in(c_bit1, s94)), introduced(assumption)).
% 36.77/24.63 tff(14474,plain,
% 36.77/24.63 (((~![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_bit0, s97)) | node2(c_bit0, s96) | (~node3(c_bit0, s96, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14475,plain,
% 36.77/24.63 ((node2(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | (~m_counter_cell_v_value(c_bit0, s97))) <=> ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14476,plain,
% 36.77/24.63 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s96) | (~node3(c_bit0, s96, s97))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14475])).
% 36.77/24.63 tff(14477,plain,
% 36.77/24.63 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s96) | (~node3(c_bit0, s96, s97)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14476, 14474])).
% 36.77/24.63 tff(14478,plain,
% 36.77/24.63 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s96) | (~node3(c_bit0, s96, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14479,plain,
% 36.77/24.63 ((~![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_bit0, s97)) | node2(c_bit0, s96) | (~node3(c_bit0, s96, s97))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14478, 14477])).
% 36.77/24.63 tff(14480,plain,
% 36.77/24.63 ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s96)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14479, 234, 8369])).
% 36.77/24.63 tff(14481,plain,
% 36.77/24.63 (node2(c_bit0, s96)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14480, 14470])).
% 36.77/24.63 tff(14482,plain,
% 36.77/24.63 (((~![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_bit0, s96)) | (~m_counter_cell_v_value(c_bit0, s96)) | (~node2(c_bit0, s96)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s96)) | (~m_counter_cell_v_value(c_bit0, s96)) | (~node2(c_bit0, s96)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14483,plain,
% 36.77/24.63 ((~![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_bit0, s96)) | (~m_counter_cell_v_value(c_bit0, s96)) | (~node2(c_bit0, s96)))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14484,plain,
% 36.77/24.63 ((~![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_bit0, s96)) | (~m_counter_cell_v_value(c_bit0, s96)) | (~node2(c_bit0, s96))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14483, 14482])).
% 36.77/24.63 tff(14485,plain,
% 36.77/24.63 ((~m_counter_cell_v_value(c_bit0, s96)) | (~node2(c_bit0, s96))),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14484, 219, 8357])).
% 36.77/24.63 tff(14486,plain,
% 36.77/24.63 (~m_counter_cell_v_value(c_bit0, s96)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14485, 14481])).
% 36.77/24.63 tff(14487,plain,
% 36.77/24.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s96) | node1(c_bit0, s95) | (~node3(c_bit0, s95, s96)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s96) | node1(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14488,plain,
% 36.77/24.63 ((node1(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | m_counter_cell_v_value(c_bit0, s96)) <=> (m_counter_cell_v_value(c_bit0, s96) | node1(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14489,plain,
% 36.77/24.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | m_counter_cell_v_value(c_bit0, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s96) | node1(c_bit0, s95) | (~node3(c_bit0, s95, s96))))),
% 36.77/24.63 inference(monotonicity,[status(thm)],[14488])).
% 36.77/24.63 tff(14490,plain,
% 36.77/24.63 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | m_counter_cell_v_value(c_bit0, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s96) | node1(c_bit0, s95) | (~node3(c_bit0, s95, s96)))),
% 36.77/24.63 inference(transitivity,[status(thm)],[14489, 14487])).
% 36.77/24.63 tff(14491,plain,
% 36.77/24.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s95) | (~node3(c_bit0, s95, s96)) | m_counter_cell_v_value(c_bit0, s96))),
% 36.77/24.63 inference(quant_inst,[status(thm)],[])).
% 36.77/24.63 tff(14492,plain,
% 36.77/24.63 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s96) | node1(c_bit0, s95) | (~node3(c_bit0, s95, s96))),
% 36.77/24.63 inference(modus_ponens,[status(thm)],[14491, 14490])).
% 36.77/24.63 tff(14493,plain,
% 36.77/24.63 (m_counter_cell_v_value(c_bit0, s96) | node1(c_bit0, s95)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14492, 199, 8345])).
% 36.77/24.63 tff(14494,plain,
% 36.77/24.63 (node1(c_bit0, s95)),
% 36.77/24.63 inference(unit_resolution,[status(thm)],[14493, 14486])).
% 36.77/24.63 tff(14495,plain,
% 36.77/24.63 (((~![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_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95) | (~node1(c_bit0, s95)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95) | (~node1(c_bit0, s95)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14496,plain,
% 36.77/24.63 (((~node1(c_bit0, s95)) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95) | (~node1(c_bit0, s95)))),
% 36.77/24.63 inference(rewrite,[status(thm)],[])).
% 36.77/24.63 tff(14497,plain,
% 36.77/24.63 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s95)) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95) | (~node1(c_bit0, s95))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14496])).
% 36.77/24.64 tff(14498,plain,
% 36.77/24.64 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s95)) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95) | (~node1(c_bit0, s95)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14497, 14495])).
% 36.77/24.64 tff(14499,plain,
% 36.77/24.64 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s95)) | (~m_counter_cell_v_carry_in(c_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14500,plain,
% 36.77/24.64 ((~![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_bit0, s95)) | m_counter_cell_v_value(c_bit0, s95) | (~node1(c_bit0, s95))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14499, 14498])).
% 36.77/24.64 tff(14501,plain,
% 36.77/24.64 (m_counter_cell_v_value(c_bit0, s95) | (~node1(c_bit0, s95))),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14500, 170, 8282])).
% 36.77/24.64 tff(14502,plain,
% 36.77/24.64 (m_counter_cell_v_value(c_bit0, s95)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14501, 14494])).
% 36.77/24.64 tff(14503,plain,
% 36.77/24.64 (m_counter_cell_v_carry_out(c_bit0, s95)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8286, 14502])).
% 36.77/24.64 tff(14504,plain,
% 36.77/24.64 (m_counter_cell_v_carry_in(c_bit1, s95)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8290, 3046, 14503])).
% 36.77/24.64 tff(14505,assumption,(~trans(s99, s5)), introduced(assumption)).
% 36.77/24.64 tff(14506,assumption,(~trans(s99, s95)), introduced(assumption)).
% 36.77/24.64 tff(14507,assumption,(~trans(s99, s75)), introduced(assumption)).
% 36.77/24.64 tff(14508,assumption,(~trans(s99, s87)), introduced(assumption)).
% 36.77/24.64 tff(14509,assumption,(~trans(s99, s70)), introduced(assumption)).
% 36.77/24.64 tff(14510,assumption,(~trans(s99, s86)), introduced(assumption)).
% 36.77/24.64 tff(14511,assumption,(~trans(s99, s44)), introduced(assumption)).
% 36.77/24.64 tff(14512,assumption,(~trans(s99, s63)), introduced(assumption)).
% 36.77/24.64 tff(14513,assumption,(~trans(s99, s57)), introduced(assumption)).
% 36.77/24.64 tff(14514,assumption,(~trans(s99, s55)), introduced(assumption)).
% 36.77/24.64 tff(14515,assumption,(~trans(s99, s76)), introduced(assumption)).
% 36.77/24.64 tff(14516,assumption,(~trans(s99, s68)), introduced(assumption)).
% 36.77/24.64 tff(14517,assumption,(~trans(s99, s39)), introduced(assumption)).
% 36.77/24.64 tff(14518,assumption,(~trans(s99, s8)), introduced(assumption)).
% 36.77/24.64 tff(14519,assumption,(~trans(s99, s52)), introduced(assumption)).
% 36.77/24.64 tff(14520,assumption,(~trans(s99, s46)), introduced(assumption)).
% 36.77/24.64 tff(14521,assumption,(~trans(s99, s49)), introduced(assumption)).
% 36.77/24.64 tff(14522,assumption,(~trans(s99, s48)), introduced(assumption)).
% 36.77/24.64 tff(14523,assumption,(~trans(s99, s9)), introduced(assumption)).
% 36.77/24.64 tff(14524,assumption,(~trans(s99, s47)), introduced(assumption)).
% 36.77/24.64 tff(14525,assumption,(~trans(s99, s38)), introduced(assumption)).
% 36.77/24.64 tff(14526,assumption,(~trans(s99, s36)), introduced(assumption)).
% 36.77/24.64 tff(14527,assumption,(~trans(s99, s42)), introduced(assumption)).
% 36.77/24.64 tff(14528,assumption,(~trans(s99, s43)), introduced(assumption)).
% 36.77/24.64 tff(14529,assumption,(~trans(s99, s41)), introduced(assumption)).
% 36.77/24.64 tff(14530,assumption,(~trans(s99, s27)), introduced(assumption)).
% 36.77/24.64 tff(14531,assumption,(~trans(s99, s10)), introduced(assumption)).
% 36.77/24.64 tff(14532,assumption,(~trans(s99, s13)), introduced(assumption)).
% 36.77/24.64 tff(14533,assumption,(~trans(s99, s15)), introduced(assumption)).
% 36.77/24.64 tff(14534,assumption,(~trans(s99, s18)), introduced(assumption)).
% 36.77/24.64 tff(14535,assumption,(~trans(s99, s17)), introduced(assumption)).
% 36.77/24.64 tff(14536,assumption,(~trans(s99, s3)), introduced(assumption)).
% 36.77/24.64 tff(14537,plain,
% 36.77/24.64 (~node1(c_bit0, s98)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8621, 14454])).
% 36.77/24.64 tff(14538,plain,
% 36.77/24.64 (m_counter_cell_v_value(c_bit0, s99)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8640, 14537])).
% 36.77/24.64 tff(14539,plain,
% 36.77/24.64 (((~![I0: $i, X: $i] : ((~m_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, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14540,plain,
% 36.77/24.64 ((~![I0: $i, X: $i] : ((~m_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, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99)))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14541,plain,
% 36.77/24.64 ((~![I0: $i, X: $i] : ((~m_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, s99)) | (~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14540, 14539])).
% 36.77/24.64 tff(14542,plain,
% 36.77/24.64 ((~m_counter_cell_v_value(c_bit0, s99)) | (~node2(c_bit0, s99))),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14541, 219, 8645])).
% 36.77/24.64 tff(14543,plain,
% 36.77/24.64 (~node2(c_bit0, s99)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14542, 14538])).
% 36.77/24.64 tff(14544,assumption,(node3(c_bit0, s99, s97)), introduced(assumption)).
% 36.77/24.64 tff(14545,assumption,(~node2(c_bit0, s99)), introduced(assumption)).
% 36.77/24.64 tff(14546,assumption,(m_counter_cell_v_value(c_bit0, s97)), introduced(assumption)).
% 36.77/24.64 tff(14547,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14548,plain,
% 36.77/24.64 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97))) <=> ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14549,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14548])).
% 36.77/24.64 tff(14550,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14549, 14547])).
% 36.77/24.64 tff(14551,plain,
% 36.77/24.64 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97)))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14552,plain,
% 36.77/24.64 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s97))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14551, 14550])).
% 36.77/24.64 tff(14553,plain,
% 36.77/24.64 ($false),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14552, 234, 14546, 14545, 14544])).
% 36.77/24.64 tff(14554,plain,((~node3(c_bit0, s99, s97)) | (~m_counter_cell_v_value(c_bit0, s97)) | node2(c_bit0, s99)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.64 tff(14555,plain,
% 36.77/24.64 (~m_counter_cell_v_value(c_bit0, s97)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14554, 14544, 14545])).
% 36.77/24.64 tff(14556,plain,
% 36.77/24.64 (~node1(c_bit0, s97)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14469, 14555])).
% 36.77/24.64 tff(14557,plain,
% 36.77/24.64 (m_counter_cell_v_value(c_bit0, s98)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14461, 14556])).
% 36.77/24.64 tff(14558,plain,
% 36.77/24.64 (((~![I0: $i, X: $i] : ((~m_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, s98)) | (~m_counter_cell_v_value(c_bit0, s98)) | (~node2(c_bit0, s98)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s98)) | (~m_counter_cell_v_value(c_bit0, s98)) | (~node2(c_bit0, s98)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14559,plain,
% 36.77/24.64 ((~![I0: $i, X: $i] : ((~m_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, s98)) | (~m_counter_cell_v_value(c_bit0, s98)) | (~node2(c_bit0, s98)))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14560,plain,
% 36.77/24.64 ((~![I0: $i, X: $i] : ((~m_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, s98)) | (~m_counter_cell_v_value(c_bit0, s98)) | (~node2(c_bit0, s98))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14559, 14558])).
% 36.77/24.64 tff(14561,plain,
% 36.77/24.64 ((~m_counter_cell_v_value(c_bit0, s98)) | (~node2(c_bit0, s98))),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14560, 219, 8614])).
% 36.77/24.64 tff(14562,plain,
% 36.77/24.64 (~node2(c_bit0, s98)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14561, 14557])).
% 36.77/24.64 tff(14563,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s98) | (~node3(c_bit0, s98, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14564,plain,
% 36.77/24.64 ((node2(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | (~m_counter_cell_v_value(c_bit0, s99))) <=> ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14565,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s98) | (~node3(c_bit0, s98, s99))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14564])).
% 36.77/24.64 tff(14566,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s98) | (~node3(c_bit0, s98, s99)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14565, 14563])).
% 36.77/24.64 tff(14567,plain,
% 36.77/24.64 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s98) | (~node3(c_bit0, s98, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14568,plain,
% 36.77/24.64 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s98) | (~node3(c_bit0, s98, s99))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14567, 14566])).
% 36.77/24.64 tff(14569,plain,
% 36.77/24.64 ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s98)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14568, 234, 8633])).
% 36.77/24.64 tff(14570,plain,
% 36.77/24.64 (~m_counter_cell_v_value(c_bit0, s99)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14569, 14562])).
% 36.77/24.64 tff(14571,plain,
% 36.77/24.64 (((~![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_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14572,plain,
% 36.77/24.64 (((~node1(c_bit0, s99)) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14573,plain,
% 36.77/24.64 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s99)) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14572])).
% 36.77/24.64 tff(14574,plain,
% 36.77/24.64 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s99)) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14573, 14571])).
% 36.77/24.64 tff(14575,plain,
% 36.77/24.64 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~node1(c_bit0, s99)) | (~m_counter_cell_v_carry_in(c_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14576,plain,
% 36.77/24.64 ((~![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_bit0, s99)) | m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14575, 14574])).
% 36.77/24.64 tff(14577,plain,
% 36.77/24.64 (m_counter_cell_v_value(c_bit0, s99) | (~node1(c_bit0, s99))),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14576, 170, 8645])).
% 36.77/24.64 tff(14578,plain,
% 36.77/24.64 (~node1(c_bit0, s99)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14577, 14570])).
% 36.77/24.64 tff(14579,plain,
% 36.77/24.64 (((~![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_bit0, s97) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s97)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14580,plain,
% 36.77/24.64 ((node1(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | m_counter_cell_v_value(c_bit0, s97)) <=> (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14581,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | m_counter_cell_v_value(c_bit0, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s97))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14580])).
% 36.77/24.64 tff(14582,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | m_counter_cell_v_value(c_bit0, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s97)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14581, 14579])).
% 36.77/24.64 tff(14583,plain,
% 36.77/24.64 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s97)) | m_counter_cell_v_value(c_bit0, s97))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14584,plain,
% 36.77/24.64 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s97) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s97))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14583, 14582])).
% 36.77/24.64 tff(14585,plain,
% 36.77/24.64 ($false),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14584, 199, 14555, 14578, 14544])).
% 36.77/24.64 tff(14586,plain,((~node3(c_bit0, s99, s97)) | node2(c_bit0, s99)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.64 tff(14587,plain,
% 36.77/24.64 (~node3(c_bit0, s99, s97)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14586, 14543])).
% 36.77/24.64 tff(14588,plain,
% 36.77/24.64 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s97)) | node3(c_bit0, s99, s97))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s97)) | node3(c_bit0, s99, s97))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14589,plain,
% 36.77/24.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s97)) | node3(c_bit0, s99, s97))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14590,plain,
% 36.77/24.64 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s97)) | node3(c_bit0, s99, s97)),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14589, 14588])).
% 36.77/24.64 tff(14591,plain,
% 36.77/24.64 ((~trans(s99, s97)) | node3(c_bit0, s99, s97)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14590, 81])).
% 36.77/24.64 tff(14592,plain,
% 36.77/24.64 (~trans(s99, s97)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14591, 14587])).
% 36.77/24.64 tff(14593,assumption,(~trans(s99, s89)), introduced(assumption)).
% 36.77/24.64 tff(14594,assumption,(~always5(s96)), introduced(assumption)).
% 36.77/24.64 tff(14595,plain,
% 36.77/24.64 (~always5(s95)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[32, 14594])).
% 36.77/24.64 tff(14596,plain,
% 36.77/24.64 (~always5(s94)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8686, 14595])).
% 36.77/24.64 tff(14597,plain,
% 36.77/24.64 (~always5(s93)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8694, 14596])).
% 36.77/24.64 tff(14598,plain,
% 36.77/24.64 (~always5(s92)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8702, 14597])).
% 36.77/24.64 tff(14599,plain,
% 36.77/24.64 (~always5(s91)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8710, 14598])).
% 36.77/24.64 tff(14600,plain,
% 36.77/24.64 (~always5(s90)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8718, 14599])).
% 36.77/24.64 tff(14601,plain,
% 36.77/24.64 (~always5(s89)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8726, 14600])).
% 36.77/24.64 tff(14602,plain,
% 36.77/24.64 (~always5(s88)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8734, 14601])).
% 36.77/24.64 tff(14603,assumption,(~always5(s88)), introduced(assumption)).
% 36.77/24.64 tff(14604,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s88) | (~trans(s99, s88)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s88) | (~trans(s99, s88)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14605,plain,
% 36.77/24.64 (((~always5(s99)) | (~trans(s99, s88)) | always5(s88)) <=> ((~always5(s99)) | always5(s88) | (~trans(s99, s88)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14606,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s88)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s88) | (~trans(s99, s88))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14605])).
% 36.77/24.64 tff(14607,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s88)) | always5(s88))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s88) | (~trans(s99, s88)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14606, 14604])).
% 36.77/24.64 tff(14608,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s88)) | always5(s88))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14609,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s88) | (~trans(s99, s88))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14608, 14607])).
% 36.77/24.64 tff(14610,plain,
% 36.77/24.64 ($false),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14609, 12386, 25, 13749, 14603])).
% 36.77/24.64 tff(14611,plain,((~trans(s99, s88)) | always5(s88)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.64 tff(14612,plain,
% 36.77/24.64 (~trans(s99, s88)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14611, 14602])).
% 36.77/24.64 tff(14613,plain,
% 36.77/24.64 (~always5(s87)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8742, 14602])).
% 36.77/24.64 tff(14614,plain,
% 36.77/24.64 (~always5(s86)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8750, 14613])).
% 36.77/24.64 tff(14615,plain,
% 36.77/24.64 (~always5(s85)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8758, 14614])).
% 36.77/24.64 tff(14616,plain,
% 36.77/24.64 (~always5(s84)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8766, 14615])).
% 36.77/24.64 tff(14617,plain,
% 36.77/24.64 (~always5(s83)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8774, 14616])).
% 36.77/24.64 tff(14618,plain,
% 36.77/24.64 (~always5(s82)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8782, 14617])).
% 36.77/24.64 tff(14619,plain,
% 36.77/24.64 (~always5(s81)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8790, 14618])).
% 36.77/24.64 tff(14620,plain,
% 36.77/24.64 (~always5(s80)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8798, 14619])).
% 36.77/24.64 tff(14621,plain,
% 36.77/24.64 (~always5(s79)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8806, 14620])).
% 36.77/24.64 tff(14622,plain,
% 36.77/24.64 (~always5(s78)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[8814, 14621])).
% 36.77/24.64 tff(14623,assumption,(~always5(s78)), introduced(assumption)).
% 36.77/24.64 tff(14624,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s78) | (~trans(s99, s78)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s78) | (~trans(s99, s78)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14625,plain,
% 36.77/24.64 (((~always5(s99)) | (~trans(s99, s78)) | always5(s78)) <=> ((~always5(s99)) | always5(s78) | (~trans(s99, s78)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14626,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s78)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s78) | (~trans(s99, s78))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14625])).
% 36.77/24.64 tff(14627,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s78)) | always5(s78))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s78) | (~trans(s99, s78)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14626, 14624])).
% 36.77/24.64 tff(14628,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s78)) | always5(s78))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14629,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s78) | (~trans(s99, s78))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14628, 14627])).
% 36.77/24.64 tff(14630,plain,
% 36.77/24.64 ($false),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14629, 12837, 25, 13749, 14623])).
% 36.77/24.64 tff(14631,plain,((~trans(s99, s78)) | always5(s78)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.64 tff(14632,plain,
% 36.77/24.64 (~trans(s99, s78)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14631, 14622])).
% 36.77/24.64 tff(14633,assumption,(~always5(s80)), introduced(assumption)).
% 36.77/24.64 tff(14634,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s80) | (~trans(s99, s80)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s80) | (~trans(s99, s80)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14635,plain,
% 36.77/24.64 (((~always5(s99)) | (~trans(s99, s80)) | always5(s80)) <=> ((~always5(s99)) | always5(s80) | (~trans(s99, s80)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14636,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s80)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s80) | (~trans(s99, s80))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14635])).
% 36.77/24.64 tff(14637,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s80)) | always5(s80))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s80) | (~trans(s99, s80)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14636, 14634])).
% 36.77/24.64 tff(14638,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s80)) | always5(s80))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14639,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s80) | (~trans(s99, s80))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14638, 14637])).
% 36.77/24.64 tff(14640,plain,
% 36.77/24.64 ($false),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14639, 12672, 25, 13749, 14633])).
% 36.77/24.64 tff(14641,plain,((~trans(s99, s80)) | always5(s80)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.64 tff(14642,plain,
% 36.77/24.64 (~trans(s99, s80)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14641, 14620])).
% 36.77/24.64 tff(14643,assumption,(~always5(s81)), introduced(assumption)).
% 36.77/24.64 tff(14644,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s81) | (~trans(s99, s81)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s81) | (~trans(s99, s81)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14645,plain,
% 36.77/24.64 (((~always5(s99)) | (~trans(s99, s81)) | always5(s81)) <=> ((~always5(s99)) | always5(s81) | (~trans(s99, s81)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14646,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s81)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s81) | (~trans(s99, s81))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14645])).
% 36.77/24.64 tff(14647,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s81)) | always5(s81))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s81) | (~trans(s99, s81)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14646, 14644])).
% 36.77/24.64 tff(14648,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s81)) | always5(s81))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14649,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s81) | (~trans(s99, s81))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14648, 14647])).
% 36.77/24.64 tff(14650,plain,
% 36.77/24.64 ($false),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14649, 12518, 25, 13749, 14643])).
% 36.77/24.64 tff(14651,plain,((~trans(s99, s81)) | always5(s81)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.64 tff(14652,plain,
% 36.77/24.64 (~trans(s99, s81)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14651, 14619])).
% 36.77/24.64 tff(14653,assumption,(~always5(s82)), introduced(assumption)).
% 36.77/24.64 tff(14654,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s82) | (~trans(s99, s82)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s82) | (~trans(s99, s82)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14655,plain,
% 36.77/24.64 (((~always5(s99)) | (~trans(s99, s82)) | always5(s82)) <=> ((~always5(s99)) | always5(s82) | (~trans(s99, s82)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14656,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s82)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s82) | (~trans(s99, s82))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14655])).
% 36.77/24.64 tff(14657,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s82)) | always5(s82))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s82) | (~trans(s99, s82)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14656, 14654])).
% 36.77/24.64 tff(14658,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s82)) | always5(s82))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14659,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s82) | (~trans(s99, s82))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14658, 14657])).
% 36.77/24.64 tff(14660,plain,
% 36.77/24.64 ($false),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14659, 12551, 25, 13749, 14653])).
% 36.77/24.64 tff(14661,plain,((~trans(s99, s82)) | always5(s82)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.64 tff(14662,plain,
% 36.77/24.64 (~trans(s99, s82)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14661, 14618])).
% 36.77/24.64 tff(14663,assumption,(~always5(s83)), introduced(assumption)).
% 36.77/24.64 tff(14664,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s83) | (~trans(s99, s83)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s83) | (~trans(s99, s83)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14665,plain,
% 36.77/24.64 (((~always5(s99)) | (~trans(s99, s83)) | always5(s83)) <=> ((~always5(s99)) | always5(s83) | (~trans(s99, s83)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14666,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s83)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s83) | (~trans(s99, s83))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14665])).
% 36.77/24.64 tff(14667,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s83)) | always5(s83))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s83) | (~trans(s99, s83)))),
% 36.77/24.64 inference(transitivity,[status(thm)],[14666, 14664])).
% 36.77/24.64 tff(14668,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s83)) | always5(s83))),
% 36.77/24.64 inference(quant_inst,[status(thm)],[])).
% 36.77/24.64 tff(14669,plain,
% 36.77/24.64 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s83) | (~trans(s99, s83))),
% 36.77/24.64 inference(modus_ponens,[status(thm)],[14668, 14667])).
% 36.77/24.64 tff(14670,plain,
% 36.77/24.64 ($false),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14669, 12859, 25, 13749, 14663])).
% 36.77/24.64 tff(14671,plain,((~trans(s99, s83)) | always5(s83)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.64 tff(14672,plain,
% 36.77/24.64 (~trans(s99, s83)),
% 36.77/24.64 inference(unit_resolution,[status(thm)],[14671, 14617])).
% 36.77/24.64 tff(14673,assumption,(~always5(s84)), introduced(assumption)).
% 36.77/24.64 tff(14674,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s84) | (~trans(s99, s84)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s84) | (~trans(s99, s84)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14675,plain,
% 36.77/24.64 (((~always5(s99)) | (~trans(s99, s84)) | always5(s84)) <=> ((~always5(s99)) | always5(s84) | (~trans(s99, s84)))),
% 36.77/24.64 inference(rewrite,[status(thm)],[])).
% 36.77/24.64 tff(14676,plain,
% 36.77/24.64 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s84)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s84) | (~trans(s99, s84))))),
% 36.77/24.64 inference(monotonicity,[status(thm)],[14675])).
% 36.77/24.65 tff(14677,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s84)) | always5(s84))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s84) | (~trans(s99, s84)))),
% 36.77/24.65 inference(transitivity,[status(thm)],[14676, 14674])).
% 36.77/24.65 tff(14678,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s84)) | always5(s84))),
% 36.77/24.65 inference(quant_inst,[status(thm)],[])).
% 36.77/24.65 tff(14679,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s84) | (~trans(s99, s84))),
% 36.77/24.65 inference(modus_ponens,[status(thm)],[14678, 14677])).
% 36.77/24.65 tff(14680,plain,
% 36.77/24.65 ($false),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[14679, 12342, 25, 13749, 14673])).
% 36.77/24.65 tff(14681,plain,((~trans(s99, s84)) | always5(s84)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.65 tff(14682,plain,
% 36.77/24.65 (~trans(s99, s84)),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[14681, 14616])).
% 36.77/24.65 tff(14683,assumption,(~always5(s85)), introduced(assumption)).
% 36.77/24.65 tff(14684,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s85) | (~trans(s99, s85)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s85) | (~trans(s99, s85)))),
% 36.77/24.65 inference(rewrite,[status(thm)],[])).
% 36.77/24.65 tff(14685,plain,
% 36.77/24.65 (((~always5(s99)) | (~trans(s99, s85)) | always5(s85)) <=> ((~always5(s99)) | always5(s85) | (~trans(s99, s85)))),
% 36.77/24.65 inference(rewrite,[status(thm)],[])).
% 36.77/24.65 tff(14686,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s85)) | always5(s85))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s85) | (~trans(s99, s85))))),
% 36.77/24.65 inference(monotonicity,[status(thm)],[14685])).
% 36.77/24.65 tff(14687,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s85)) | always5(s85))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s85) | (~trans(s99, s85)))),
% 36.77/24.65 inference(transitivity,[status(thm)],[14686, 14684])).
% 36.77/24.65 tff(14688,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s85)) | always5(s85))),
% 36.77/24.65 inference(quant_inst,[status(thm)],[])).
% 36.77/24.65 tff(14689,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s85) | (~trans(s99, s85))),
% 36.77/24.65 inference(modus_ponens,[status(thm)],[14688, 14687])).
% 36.77/24.65 tff(14690,plain,
% 36.77/24.65 ($false),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[14689, 12496, 25, 13749, 14683])).
% 36.77/24.65 tff(14691,plain,((~trans(s99, s85)) | always5(s85)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.65 tff(14692,plain,
% 36.77/24.65 (~trans(s99, s85)),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[14691, 14615])).
% 36.77/24.65 tff(14693,assumption,(~always5(s90)), introduced(assumption)).
% 36.77/24.65 tff(14694,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s90) | (~trans(s99, s90)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s90) | (~trans(s99, s90)))),
% 36.77/24.65 inference(rewrite,[status(thm)],[])).
% 36.77/24.65 tff(14695,plain,
% 36.77/24.65 (((~always5(s99)) | (~trans(s99, s90)) | always5(s90)) <=> ((~always5(s99)) | always5(s90) | (~trans(s99, s90)))),
% 36.77/24.65 inference(rewrite,[status(thm)],[])).
% 36.77/24.65 tff(14696,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s90)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s90) | (~trans(s99, s90))))),
% 36.77/24.65 inference(monotonicity,[status(thm)],[14695])).
% 36.77/24.65 tff(14697,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s90)) | always5(s90))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s90) | (~trans(s99, s90)))),
% 36.77/24.65 inference(transitivity,[status(thm)],[14696, 14694])).
% 36.77/24.65 tff(14698,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s90)) | always5(s90))),
% 36.77/24.65 inference(quant_inst,[status(thm)],[])).
% 36.77/24.65 tff(14699,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s90) | (~trans(s99, s90))),
% 36.77/24.65 inference(modus_ponens,[status(thm)],[14698, 14697])).
% 36.77/24.65 tff(14700,plain,
% 36.77/24.65 ($false),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[14699, 12870, 25, 13749, 14693])).
% 36.77/24.65 tff(14701,plain,((~trans(s99, s90)) | always5(s90)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.65 tff(14702,plain,
% 36.77/24.65 (~trans(s99, s90)),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[14701, 14600])).
% 36.77/24.65 tff(14703,plain,
% 36.77/24.65 (~trans(s99, s91)),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[13827, 14599])).
% 36.77/24.65 tff(14704,assumption,(~trans(s99, s97)), introduced(assumption)).
% 36.77/24.65 tff(14705,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s96) | (~trans(s99, s96)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s96) | (~trans(s99, s96)))),
% 36.77/24.65 inference(rewrite,[status(thm)],[])).
% 36.77/24.65 tff(14706,plain,
% 36.77/24.65 (((~always5(s99)) | (~trans(s99, s96)) | always5(s96)) <=> ((~always5(s99)) | always5(s96) | (~trans(s99, s96)))),
% 36.77/24.65 inference(rewrite,[status(thm)],[])).
% 36.77/24.65 tff(14707,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s96)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s96) | (~trans(s99, s96))))),
% 36.77/24.65 inference(monotonicity,[status(thm)],[14706])).
% 36.77/24.65 tff(14708,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s96)) | always5(s96))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s96) | (~trans(s99, s96)))),
% 36.77/24.65 inference(transitivity,[status(thm)],[14707, 14705])).
% 36.77/24.65 tff(14709,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s96)) | always5(s96))),
% 36.77/24.65 inference(quant_inst,[status(thm)],[])).
% 36.77/24.65 tff(14710,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s96) | (~trans(s99, s96))),
% 36.77/24.65 inference(modus_ponens,[status(thm)],[14709, 14708])).
% 36.77/24.65 tff(14711,plain,
% 36.77/24.65 ($false),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[14710, 12177, 25, 13749, 14594])).
% 36.77/24.65 tff(14712,plain,((~trans(s99, s96)) | always5(s96)), inference(lemma,lemma(discharge,[]))).
% 36.77/24.65 tff(14713,plain,
% 36.77/24.65 (~trans(s99, s96)),
% 36.77/24.65 inference(unit_resolution,[status(thm)],[14712, 14594])).
% 36.77/24.65 tff(14714,assumption,(~always5(s79)), introduced(assumption)).
% 36.77/24.65 tff(14715,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s79) | (~trans(s99, s79)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s79) | (~trans(s99, s79)))),
% 36.77/24.65 inference(rewrite,[status(thm)],[])).
% 36.77/24.65 tff(14716,plain,
% 36.77/24.65 (((~always5(s99)) | (~trans(s99, s79)) | always5(s79)) <=> ((~always5(s99)) | always5(s79) | (~trans(s99, s79)))),
% 36.77/24.65 inference(rewrite,[status(thm)],[])).
% 36.77/24.65 tff(14717,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s79)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s79) | (~trans(s99, s79))))),
% 36.77/24.65 inference(monotonicity,[status(thm)],[14716])).
% 36.77/24.65 tff(14718,plain,
% 36.77/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s79)) | always5(s79))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s79) | (~trans(s99, s79)))),
% 36.77/24.65 inference(transitivity,[status(thm)],[14717, 14715])).
% 36.77/24.65 tff(14719,plain,
% 36.77/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s79)) | always5(s79))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14720,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s79) | (~trans(s99, s79))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14719, 14718])).
% 36.84/24.65 tff(14721,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14720, 12639, 25, 13749, 14714])).
% 36.84/24.65 tff(14722,plain,((~trans(s99, s79)) | always5(s79)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14723,plain,
% 36.84/24.65 (~trans(s99, s79)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14722, 14621])).
% 36.84/24.65 tff(14724,plain,
% 36.84/24.65 (~always5(s77)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8822, 14622])).
% 36.84/24.65 tff(14725,assumption,(~always5(s94)), introduced(assumption)).
% 36.84/24.65 tff(14726,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s94) | (~trans(s99, s94)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s94) | (~trans(s99, s94)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14727,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s94)) | always5(s94)) <=> ((~always5(s99)) | always5(s94) | (~trans(s99, s94)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14728,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s94)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s94) | (~trans(s99, s94))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14727])).
% 36.84/24.65 tff(14729,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s94)) | always5(s94))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s94) | (~trans(s99, s94)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14728, 14726])).
% 36.84/24.65 tff(14730,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s94)) | always5(s94))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14731,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s94) | (~trans(s99, s94))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14730, 14729])).
% 36.84/24.65 tff(14732,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14731, 12892, 25, 13749, 14725])).
% 36.84/24.65 tff(14733,plain,((~trans(s99, s94)) | always5(s94)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14734,plain,
% 36.84/24.65 (~trans(s99, s94)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14733, 14725])).
% 36.84/24.65 tff(14735,assumption,(~always5(s77)), introduced(assumption)).
% 36.84/24.65 tff(14736,plain,
% 36.84/24.65 (~always5(s76)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8830, 14735])).
% 36.84/24.65 tff(14737,plain,
% 36.84/24.65 (~always5(s75)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8838, 14736])).
% 36.84/24.65 tff(14738,plain,
% 36.84/24.65 (~always5(s74)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8846, 14737])).
% 36.84/24.65 tff(14739,plain,
% 36.84/24.65 (~always5(s73)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8854, 14738])).
% 36.84/24.65 tff(14740,plain,
% 36.84/24.65 (~always5(s72)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8862, 14739])).
% 36.84/24.65 tff(14741,plain,
% 36.84/24.65 (~always5(s71)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8870, 14740])).
% 36.84/24.65 tff(14742,plain,
% 36.84/24.65 (~always5(s70)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8878, 14741])).
% 36.84/24.65 tff(14743,plain,
% 36.84/24.65 (~always5(s69)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8886, 14742])).
% 36.84/24.65 tff(14744,plain,
% 36.84/24.65 (~always5(s68)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8894, 14743])).
% 36.84/24.65 tff(14745,plain,
% 36.84/24.65 (~always5(s67)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8902, 14744])).
% 36.84/24.65 tff(14746,plain,
% 36.84/24.65 (~always5(s66)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8910, 14745])).
% 36.84/24.65 tff(14747,plain,
% 36.84/24.65 (~always5(s65)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8918, 14746])).
% 36.84/24.65 tff(14748,plain,
% 36.84/24.65 (~always5(s64)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8926, 14747])).
% 36.84/24.65 tff(14749,plain,
% 36.84/24.65 (~always5(s63)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8934, 14748])).
% 36.84/24.65 tff(14750,plain,
% 36.84/24.65 (~always5(s62)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8942, 14749])).
% 36.84/24.65 tff(14751,plain,
% 36.84/24.65 (~always5(s61)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8950, 14750])).
% 36.84/24.65 tff(14752,plain,
% 36.84/24.65 (~always5(s60)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8958, 14751])).
% 36.84/24.65 tff(14753,plain,
% 36.84/24.65 (~always5(s59)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[8966, 14752])).
% 36.84/24.65 tff(14754,plain,
% 36.84/24.65 (~always5(s58)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9030, 14753])).
% 36.84/24.65 tff(14755,plain,
% 36.84/24.65 (~always5(s57)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9038, 14754])).
% 36.84/24.65 tff(14756,plain,
% 36.84/24.65 (~always5(s56)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9046, 14755])).
% 36.84/24.65 tff(14757,plain,
% 36.84/24.65 (~always5(s55)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9054, 14756])).
% 36.84/24.65 tff(14758,plain,
% 36.84/24.65 (~always5(s54)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9062, 14757])).
% 36.84/24.65 tff(14759,plain,
% 36.84/24.65 (~always5(s53)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9070, 14758])).
% 36.84/24.65 tff(14760,plain,
% 36.84/24.65 (~always5(s52)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9078, 14759])).
% 36.84/24.65 tff(14761,plain,
% 36.84/24.65 (~always5(s51)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9086, 14760])).
% 36.84/24.65 tff(14762,plain,
% 36.84/24.65 (~always5(s50)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9094, 14761])).
% 36.84/24.65 tff(14763,plain,
% 36.84/24.65 (~always5(s49)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9102, 14762])).
% 36.84/24.65 tff(14764,plain,
% 36.84/24.65 (~always5(s48)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9110, 14763])).
% 36.84/24.65 tff(14765,plain,
% 36.84/24.65 (~always5(s47)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9118, 14764])).
% 36.84/24.65 tff(14766,plain,
% 36.84/24.65 (~always5(s46)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9126, 14765])).
% 36.84/24.65 tff(14767,plain,
% 36.84/24.65 (~always5(s45)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9134, 14766])).
% 36.84/24.65 tff(14768,plain,
% 36.84/24.65 (~always5(s44)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9142, 14767])).
% 36.84/24.65 tff(14769,plain,
% 36.84/24.65 (~always5(s43)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9150, 14768])).
% 36.84/24.65 tff(14770,plain,
% 36.84/24.65 (~always5(s42)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9158, 14769])).
% 36.84/24.65 tff(14771,plain,
% 36.84/24.65 (~always5(s41)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9166, 14770])).
% 36.84/24.65 tff(14772,plain,
% 36.84/24.65 (~always5(s40)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9174, 14771])).
% 36.84/24.65 tff(14773,plain,
% 36.84/24.65 (~always5(s39)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9182, 14772])).
% 36.84/24.65 tff(14774,plain,
% 36.84/24.65 (~always5(s38)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9190, 14773])).
% 36.84/24.65 tff(14775,plain,
% 36.84/24.65 (~always5(s37)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9198, 14774])).
% 36.84/24.65 tff(14776,plain,
% 36.84/24.65 (~always5(s36)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9206, 14775])).
% 36.84/24.65 tff(14777,plain,
% 36.84/24.65 (~always5(s35)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9214, 14776])).
% 36.84/24.65 tff(14778,plain,
% 36.84/24.65 (~always5(s34)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9222, 14777])).
% 36.84/24.65 tff(14779,plain,
% 36.84/24.65 (~always5(s33)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9230, 14778])).
% 36.84/24.65 tff(14780,plain,
% 36.84/24.65 (~always5(s32)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9238, 14779])).
% 36.84/24.65 tff(14781,plain,
% 36.84/24.65 (~always5(s31)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9246, 14780])).
% 36.84/24.65 tff(14782,assumption,(~always5(s31)), introduced(assumption)).
% 36.84/24.65 tff(14783,assumption,(always5(s99)), introduced(assumption)).
% 36.84/24.65 tff(14784,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s31) | (~trans(s99, s31)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s31) | (~trans(s99, s31)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14785,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s31)) | always5(s31)) <=> ((~always5(s99)) | always5(s31) | (~trans(s99, s31)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14786,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s31) | (~trans(s99, s31))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14785])).
% 36.84/24.65 tff(14787,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s31)) | always5(s31))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s31) | (~trans(s99, s31)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14786, 14784])).
% 36.84/24.65 tff(14788,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s31)) | always5(s31))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14789,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s31) | (~trans(s99, s31))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14788, 14787])).
% 36.84/24.65 tff(14790,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14789, 12936, 25, 14783, 14782])).
% 36.84/24.65 tff(14791,plain,((~trans(s99, s31)) | (~always5(s99)) | always5(s31)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14792,plain,
% 36.84/24.65 ((~trans(s99, s31)) | always5(s31)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14791, 13749])).
% 36.84/24.65 tff(14793,plain,
% 36.84/24.65 (~trans(s99, s31)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14792, 14781])).
% 36.84/24.65 tff(14794,plain,
% 36.84/24.65 (~always5(s30)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9254, 14781])).
% 36.84/24.65 tff(14795,plain,
% 36.84/24.65 (~always5(s29)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9262, 14794])).
% 36.84/24.65 tff(14796,plain,
% 36.84/24.65 (~always5(s28)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9270, 14795])).
% 36.84/24.65 tff(14797,plain,
% 36.84/24.65 (~always5(s27)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9278, 14796])).
% 36.84/24.65 tff(14798,plain,
% 36.84/24.65 (~always5(s26)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9286, 14797])).
% 36.84/24.65 tff(14799,plain,
% 36.84/24.65 (~always5(s25)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9294, 14798])).
% 36.84/24.65 tff(14800,plain,
% 36.84/24.65 (~always5(s24)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9302, 14799])).
% 36.84/24.65 tff(14801,plain,
% 36.84/24.65 (~always5(s23)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9310, 14800])).
% 36.84/24.65 tff(14802,plain,
% 36.84/24.65 (~always5(s22)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9318, 14801])).
% 36.84/24.65 tff(14803,plain,
% 36.84/24.65 (~always5(s21)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9326, 14802])).
% 36.84/24.65 tff(14804,plain,
% 36.84/24.65 (~always5(s20)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9334, 14803])).
% 36.84/24.65 tff(14805,plain,
% 36.84/24.65 (~always5(s19)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9342, 14804])).
% 36.84/24.65 tff(14806,plain,
% 36.84/24.65 (~always5(s18)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9350, 14805])).
% 36.84/24.65 tff(14807,plain,
% 36.84/24.65 (~always5(s17)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9358, 14806])).
% 36.84/24.65 tff(14808,plain,
% 36.84/24.65 (~always5(s16)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9366, 14807])).
% 36.84/24.65 tff(14809,plain,
% 36.84/24.65 (~always5(s15)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9374, 14808])).
% 36.84/24.65 tff(14810,plain,
% 36.84/24.65 (~always5(s14)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9383, 14809])).
% 36.84/24.65 tff(14811,plain,
% 36.84/24.65 (~always5(s13)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9437, 14810])).
% 36.84/24.65 tff(14812,plain,
% 36.84/24.65 (~always5(s12)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9458, 14811])).
% 36.84/24.65 tff(14813,plain,
% 36.84/24.65 (~always5(s11)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9479, 14812])).
% 36.84/24.65 tff(14814,plain,
% 36.84/24.65 (~always5(s10)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9500, 14813])).
% 36.84/24.65 tff(14815,plain,
% 36.84/24.65 (~always5(s9)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9521, 14814])).
% 36.84/24.65 tff(14816,plain,
% 36.84/24.65 (~always5(s8)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9542, 14815])).
% 36.84/24.65 tff(14817,plain,
% 36.84/24.65 (~always5(s7)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9558, 14816])).
% 36.84/24.65 tff(14818,plain,
% 36.84/24.65 (~always5(s6)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9566, 14817])).
% 36.84/24.65 tff(14819,plain,
% 36.84/24.65 (~always5(s5)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9574, 14818])).
% 36.84/24.65 tff(14820,plain,
% 36.84/24.65 (~always5(s4)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9582, 14819])).
% 36.84/24.65 tff(14821,plain,
% 36.84/24.65 (~always5(s3)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9590, 14820])).
% 36.84/24.65 tff(14822,plain,
% 36.84/24.65 (~always5(s2)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9598, 14821])).
% 36.84/24.65 tff(14823,plain,
% 36.84/24.65 (~always5(s1)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9606, 14822])).
% 36.84/24.65 tff(14824,assumption,(trans(s99, s1)), introduced(assumption)).
% 36.84/24.65 tff(14825,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s1) | (~trans(s99, s1)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s1) | (~trans(s99, s1)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14826,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s1)) | always5(s1)) <=> ((~always5(s99)) | always5(s1) | (~trans(s99, s1)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14827,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s1) | (~trans(s99, s1))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14826])).
% 36.84/24.65 tff(14828,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s1)) | always5(s1))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s1) | (~trans(s99, s1)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14827, 14825])).
% 36.84/24.65 tff(14829,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s1)) | always5(s1))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14830,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s1) | (~trans(s99, s1))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14829, 14828])).
% 36.84/24.65 tff(14831,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14830, 14824, 25, 14783, 11840])).
% 36.84/24.65 tff(14832,plain,((~trans(s99, s1)) | (~always5(s99)) | always5(s1)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14833,plain,
% 36.84/24.65 ((~trans(s99, s1)) | always5(s1)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14832, 13749])).
% 36.84/24.65 tff(14834,plain,
% 36.84/24.65 (~trans(s99, s1)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14833, 14823])).
% 36.84/24.65 tff(14835,assumption,(~trans(s99, s88)), introduced(assumption)).
% 36.84/24.65 tff(14836,assumption,(~always5(s74)), introduced(assumption)).
% 36.84/24.65 tff(14837,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s74) | (~trans(s99, s74)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s74) | (~trans(s99, s74)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14838,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s74)) | always5(s74)) <=> ((~always5(s99)) | always5(s74) | (~trans(s99, s74)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14839,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s74)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s74) | (~trans(s99, s74))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14838])).
% 36.84/24.65 tff(14840,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s74)) | always5(s74))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s74) | (~trans(s99, s74)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14839, 14837])).
% 36.84/24.65 tff(14841,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s74)) | always5(s74))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14842,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s74) | (~trans(s99, s74))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14841, 14840])).
% 36.84/24.65 tff(14843,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14842, 12397, 25, 13749, 14836])).
% 36.84/24.65 tff(14844,plain,((~trans(s99, s74)) | always5(s74)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14845,plain,
% 36.84/24.65 (~trans(s99, s74)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14844, 14738])).
% 36.84/24.65 tff(14846,plain,
% 36.84/24.65 (~always5(s0)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[9614, 14823])).
% 36.84/24.65 tff(14847,assumption,(~always5(s0)), introduced(assumption)).
% 36.84/24.65 tff(14848,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s0) | (~trans(s99, s0)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s0) | (~trans(s99, s0)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14849,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s0)) | always5(s0)) <=> ((~always5(s99)) | always5(s0) | (~trans(s99, s0)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14850,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s0)) | always5(s0))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s0) | (~trans(s99, s0))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14849])).
% 36.84/24.65 tff(14851,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s0)) | always5(s0))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s0) | (~trans(s99, s0)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14850, 14848])).
% 36.84/24.65 tff(14852,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s0)) | always5(s0))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14853,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s0) | (~trans(s99, s0))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14852, 14851])).
% 36.84/24.65 tff(14854,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14853, 12254, 25, 13749, 14847])).
% 36.84/24.65 tff(14855,plain,((~trans(s99, s0)) | always5(s0)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14856,plain,
% 36.84/24.65 (~trans(s99, s0)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14855, 14846])).
% 36.84/24.65 tff(14857,assumption,(~always5(s71)), introduced(assumption)).
% 36.84/24.65 tff(14858,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s71) | (~trans(s99, s71)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s71) | (~trans(s99, s71)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14859,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s71)) | always5(s71)) <=> ((~always5(s99)) | always5(s71) | (~trans(s99, s71)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14860,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s71)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s71) | (~trans(s99, s71))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14859])).
% 36.84/24.65 tff(14861,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s71)) | always5(s71))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s71) | (~trans(s99, s71)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14860, 14858])).
% 36.84/24.65 tff(14862,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s71)) | always5(s71))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14863,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s71) | (~trans(s99, s71))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14862, 14861])).
% 36.84/24.65 tff(14864,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14863, 12452, 25, 13749, 14857])).
% 36.84/24.65 tff(14865,plain,((~trans(s99, s71)) | always5(s71)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14866,plain,
% 36.84/24.65 (~trans(s99, s71)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14865, 14741])).
% 36.84/24.65 tff(14867,assumption,(~trans(s99, s78)), introduced(assumption)).
% 36.84/24.65 tff(14868,assumption,(~trans(s99, s80)), introduced(assumption)).
% 36.84/24.65 tff(14869,assumption,(~trans(s99, s79)), introduced(assumption)).
% 36.84/24.65 tff(14870,assumption,(~trans(s99, s82)), introduced(assumption)).
% 36.84/24.65 tff(14871,assumption,(~trans(s99, s81)), introduced(assumption)).
% 36.84/24.65 tff(14872,assumption,(~trans(s99, s84)), introduced(assumption)).
% 36.84/24.65 tff(14873,assumption,(~trans(s99, s85)), introduced(assumption)).
% 36.84/24.65 tff(14874,assumption,(~always5(s72)), introduced(assumption)).
% 36.84/24.65 tff(14875,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s72) | (~trans(s99, s72)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s72) | (~trans(s99, s72)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14876,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s72)) | always5(s72)) <=> ((~always5(s99)) | always5(s72) | (~trans(s99, s72)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14877,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s72)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s72) | (~trans(s99, s72))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14876])).
% 36.84/24.65 tff(14878,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s72)) | always5(s72))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s72) | (~trans(s99, s72)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14877, 14875])).
% 36.84/24.65 tff(14879,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s72)) | always5(s72))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14880,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s72) | (~trans(s99, s72))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14879, 14878])).
% 36.84/24.65 tff(14881,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14880, 12320, 25, 13749, 14874])).
% 36.84/24.65 tff(14882,plain,((~trans(s99, s72)) | always5(s72)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14883,plain,
% 36.84/24.65 (~trans(s99, s72)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14882, 14740])).
% 36.84/24.65 tff(14884,assumption,(~always5(s58)), introduced(assumption)).
% 36.84/24.65 tff(14885,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s58) | (~trans(s99, s58)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s58) | (~trans(s99, s58)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14886,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s58)) | always5(s58)) <=> ((~always5(s99)) | always5(s58) | (~trans(s99, s58)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14887,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s58)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s58) | (~trans(s99, s58))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14886])).
% 36.84/24.65 tff(14888,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s58)) | always5(s58))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s58) | (~trans(s99, s58)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14887, 14885])).
% 36.84/24.65 tff(14889,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s58)) | always5(s58))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14890,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s58) | (~trans(s99, s58))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14889, 14888])).
% 36.84/24.65 tff(14891,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14890, 12595, 25, 13749, 14884])).
% 36.84/24.65 tff(14892,plain,((~trans(s99, s58)) | always5(s58)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14893,plain,
% 36.84/24.65 (~trans(s99, s58)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14892, 14754])).
% 36.84/24.65 tff(14894,assumption,(~always5(s59)), introduced(assumption)).
% 36.84/24.65 tff(14895,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s59) | (~trans(s99, s59)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s59) | (~trans(s99, s59)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14896,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s59)) | always5(s59)) <=> ((~always5(s99)) | always5(s59) | (~trans(s99, s59)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14897,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s59)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s59) | (~trans(s99, s59))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14896])).
% 36.84/24.65 tff(14898,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s59)) | always5(s59))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s59) | (~trans(s99, s59)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14897, 14895])).
% 36.84/24.65 tff(14899,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s59)) | always5(s59))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14900,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s59) | (~trans(s99, s59))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14899, 14898])).
% 36.84/24.65 tff(14901,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14900, 12771, 25, 13749, 14894])).
% 36.84/24.65 tff(14902,plain,((~trans(s99, s59)) | always5(s59)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14903,plain,
% 36.84/24.65 (~trans(s99, s59)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14902, 14753])).
% 36.84/24.65 tff(14904,assumption,(~always5(s53)), introduced(assumption)).
% 36.84/24.65 tff(14905,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s53) | (~trans(s99, s53)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s53) | (~trans(s99, s53)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14906,plain,
% 36.84/24.65 (((~always5(s99)) | (~trans(s99, s53)) | always5(s53)) <=> ((~always5(s99)) | always5(s53) | (~trans(s99, s53)))),
% 36.84/24.65 inference(rewrite,[status(thm)],[])).
% 36.84/24.65 tff(14907,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s53) | (~trans(s99, s53))))),
% 36.84/24.65 inference(monotonicity,[status(thm)],[14906])).
% 36.84/24.65 tff(14908,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s53)) | always5(s53))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s53) | (~trans(s99, s53)))),
% 36.84/24.65 inference(transitivity,[status(thm)],[14907, 14905])).
% 36.84/24.65 tff(14909,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s53)) | always5(s53))),
% 36.84/24.65 inference(quant_inst,[status(thm)],[])).
% 36.84/24.65 tff(14910,plain,
% 36.84/24.65 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s53) | (~trans(s99, s53))),
% 36.84/24.65 inference(modus_ponens,[status(thm)],[14909, 14908])).
% 36.84/24.65 tff(14911,plain,
% 36.84/24.65 ($false),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14910, 12705, 25, 13749, 14904])).
% 36.84/24.65 tff(14912,plain,((~trans(s99, s53)) | always5(s53)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.65 tff(14913,plain,
% 36.84/24.65 (~trans(s99, s53)),
% 36.84/24.65 inference(unit_resolution,[status(thm)],[14912, 14759])).
% 36.84/24.65 tff(14914,assumption,(~always5(s54)), introduced(assumption)).
% 36.84/24.65 tff(14915,plain,
% 36.84/24.65 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s54) | (~trans(s99, s54)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s54) | (~trans(s99, s54)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14916,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s54)) | always5(s54)) <=> ((~always5(s99)) | always5(s54) | (~trans(s99, s54)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14917,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s54) | (~trans(s99, s54))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14916])).
% 36.84/24.66 tff(14918,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s54)) | always5(s54))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s54) | (~trans(s99, s54)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14917, 14915])).
% 36.84/24.66 tff(14919,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s54)) | always5(s54))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(14920,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s54) | (~trans(s99, s54))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14919, 14918])).
% 36.84/24.66 tff(14921,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14920, 12298, 25, 13749, 14914])).
% 36.84/24.66 tff(14922,plain,((~trans(s99, s54)) | always5(s54)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(14923,plain,
% 36.84/24.66 (~trans(s99, s54)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14922, 14758])).
% 36.84/24.66 tff(14924,assumption,(~always5(s56)), introduced(assumption)).
% 36.84/24.66 tff(14925,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s56) | (~trans(s99, s56)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s56) | (~trans(s99, s56)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14926,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s56)) | always5(s56)) <=> ((~always5(s99)) | always5(s56) | (~trans(s99, s56)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14927,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s56)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s56) | (~trans(s99, s56))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14926])).
% 36.84/24.66 tff(14928,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s56)) | always5(s56))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s56) | (~trans(s99, s56)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14927, 14925])).
% 36.84/24.66 tff(14929,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s56)) | always5(s56))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(14930,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s56) | (~trans(s99, s56))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14929, 14928])).
% 36.84/24.66 tff(14931,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14930, 12694, 25, 13749, 14924])).
% 36.84/24.66 tff(14932,plain,((~trans(s99, s56)) | always5(s56)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(14933,plain,
% 36.84/24.66 (~trans(s99, s56)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14932, 14756])).
% 36.84/24.66 tff(14934,assumption,(~always5(s60)), introduced(assumption)).
% 36.84/24.66 tff(14935,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s60) | (~trans(s99, s60)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s60) | (~trans(s99, s60)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14936,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s60)) | always5(s60)) <=> ((~always5(s99)) | always5(s60) | (~trans(s99, s60)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14937,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s60)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s60) | (~trans(s99, s60))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14936])).
% 36.84/24.66 tff(14938,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s60)) | always5(s60))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s60) | (~trans(s99, s60)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14937, 14935])).
% 36.84/24.66 tff(14939,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s60)) | always5(s60))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(14940,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s60) | (~trans(s99, s60))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14939, 14938])).
% 36.84/24.66 tff(14941,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14940, 12540, 25, 13749, 14934])).
% 36.84/24.66 tff(14942,plain,((~trans(s99, s60)) | always5(s60)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(14943,plain,
% 36.84/24.66 (~trans(s99, s60)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14942, 14752])).
% 36.84/24.66 tff(14944,assumption,(~always5(s62)), introduced(assumption)).
% 36.84/24.66 tff(14945,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s62) | (~trans(s99, s62)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s62) | (~trans(s99, s62)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14946,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s62)) | always5(s62)) <=> ((~always5(s99)) | always5(s62) | (~trans(s99, s62)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14947,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s62)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s62) | (~trans(s99, s62))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14946])).
% 36.84/24.66 tff(14948,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s62)) | always5(s62))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s62) | (~trans(s99, s62)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14947, 14945])).
% 36.84/24.66 tff(14949,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s62)) | always5(s62))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(14950,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s62) | (~trans(s99, s62))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14949, 14948])).
% 36.84/24.66 tff(14951,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14950, 12529, 25, 13749, 14944])).
% 36.84/24.66 tff(14952,plain,((~trans(s99, s62)) | always5(s62)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(14953,plain,
% 36.84/24.66 (~trans(s99, s62)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14952, 14750])).
% 36.84/24.66 tff(14954,assumption,(~always5(s61)), introduced(assumption)).
% 36.84/24.66 tff(14955,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s61) | (~trans(s99, s61)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s61) | (~trans(s99, s61)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14956,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s61)) | always5(s61)) <=> ((~always5(s99)) | always5(s61) | (~trans(s99, s61)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14957,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s61)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s61) | (~trans(s99, s61))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14956])).
% 36.84/24.66 tff(14958,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s61)) | always5(s61))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s61) | (~trans(s99, s61)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14957, 14955])).
% 36.84/24.66 tff(14959,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s61)) | always5(s61))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(14960,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s61) | (~trans(s99, s61))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14959, 14958])).
% 36.84/24.66 tff(14961,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14960, 12826, 25, 13749, 14954])).
% 36.84/24.66 tff(14962,plain,((~trans(s99, s61)) | always5(s61)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(14963,plain,
% 36.84/24.66 (~trans(s99, s61)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14962, 14751])).
% 36.84/24.66 tff(14964,assumption,(~always5(s64)), introduced(assumption)).
% 36.84/24.66 tff(14965,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s64) | (~trans(s99, s64)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s64) | (~trans(s99, s64)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14966,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s64)) | always5(s64)) <=> ((~always5(s99)) | always5(s64) | (~trans(s99, s64)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14967,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s64)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s64) | (~trans(s99, s64))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14966])).
% 36.84/24.66 tff(14968,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s64)) | always5(s64))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s64) | (~trans(s99, s64)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14967, 14965])).
% 36.84/24.66 tff(14969,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s64)) | always5(s64))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(14970,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s64) | (~trans(s99, s64))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14969, 14968])).
% 36.84/24.66 tff(14971,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14970, 12606, 25, 13749, 14964])).
% 36.84/24.66 tff(14972,plain,((~trans(s99, s64)) | always5(s64)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(14973,plain,
% 36.84/24.66 (~trans(s99, s64)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14972, 14748])).
% 36.84/24.66 tff(14974,assumption,(~always5(s65)), introduced(assumption)).
% 36.84/24.66 tff(14975,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s65) | (~trans(s99, s65)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s65) | (~trans(s99, s65)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14976,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s65)) | always5(s65)) <=> ((~always5(s99)) | always5(s65) | (~trans(s99, s65)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14977,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s65)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s65) | (~trans(s99, s65))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14976])).
% 36.84/24.66 tff(14978,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s65)) | always5(s65))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s65) | (~trans(s99, s65)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14977, 14975])).
% 36.84/24.66 tff(14979,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s65)) | always5(s65))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(14980,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s65) | (~trans(s99, s65))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14979, 14978])).
% 36.84/24.66 tff(14981,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14980, 12584, 25, 13749, 14974])).
% 36.84/24.66 tff(14982,plain,((~trans(s99, s65)) | always5(s65)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(14983,plain,
% 36.84/24.66 (~trans(s99, s65)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14982, 14747])).
% 36.84/24.66 tff(14984,assumption,(~always5(s66)), introduced(assumption)).
% 36.84/24.66 tff(14985,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s66) | (~trans(s99, s66)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s66) | (~trans(s99, s66)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14986,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s66)) | always5(s66)) <=> ((~always5(s99)) | always5(s66) | (~trans(s99, s66)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14987,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s66)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s66) | (~trans(s99, s66))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14986])).
% 36.84/24.66 tff(14988,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s66)) | always5(s66))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s66) | (~trans(s99, s66)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14987, 14985])).
% 36.84/24.66 tff(14989,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s66)) | always5(s66))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(14990,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s66) | (~trans(s99, s66))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14989, 14988])).
% 36.84/24.66 tff(14991,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14990, 12353, 25, 13749, 14984])).
% 36.84/24.66 tff(14992,plain,((~trans(s99, s66)) | always5(s66)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(14993,plain,
% 36.84/24.66 (~trans(s99, s66)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[14992, 14746])).
% 36.84/24.66 tff(14994,assumption,(~always5(s67)), introduced(assumption)).
% 36.84/24.66 tff(14995,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s67) | (~trans(s99, s67)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s67) | (~trans(s99, s67)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14996,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s67)) | always5(s67)) <=> ((~always5(s99)) | always5(s67) | (~trans(s99, s67)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(14997,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s67)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s67) | (~trans(s99, s67))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[14996])).
% 36.84/24.66 tff(14998,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s67)) | always5(s67))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s67) | (~trans(s99, s67)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[14997, 14995])).
% 36.84/24.66 tff(14999,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s67)) | always5(s67))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15000,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s67) | (~trans(s99, s67))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[14999, 14998])).
% 36.84/24.66 tff(15001,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15000, 12661, 25, 13749, 14994])).
% 36.84/24.66 tff(15002,plain,((~trans(s99, s67)) | always5(s67)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15003,plain,
% 36.84/24.66 (~trans(s99, s67)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15002, 14745])).
% 36.84/24.66 tff(15004,assumption,(~always5(s69)), introduced(assumption)).
% 36.84/24.66 tff(15005,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s69) | (~trans(s99, s69)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s69) | (~trans(s99, s69)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15006,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s69)) | always5(s69)) <=> ((~always5(s99)) | always5(s69) | (~trans(s99, s69)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15007,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s69)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s69) | (~trans(s99, s69))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[15006])).
% 36.84/24.66 tff(15008,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s69)) | always5(s69))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s69) | (~trans(s99, s69)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[15007, 15005])).
% 36.84/24.66 tff(15009,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s69)) | always5(s69))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15010,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s69) | (~trans(s99, s69))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[15009, 15008])).
% 36.84/24.66 tff(15011,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15010, 12738, 25, 13749, 15004])).
% 36.84/24.66 tff(15012,plain,((~trans(s99, s69)) | always5(s69)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15013,plain,
% 36.84/24.66 (~trans(s99, s69)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15012, 14743])).
% 36.84/24.66 tff(15014,assumption,(~always5(s73)), introduced(assumption)).
% 36.84/24.66 tff(15015,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s73) | (~trans(s99, s73)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s73) | (~trans(s99, s73)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15016,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s73)) | always5(s73)) <=> ((~always5(s99)) | always5(s73) | (~trans(s99, s73)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15017,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s73)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s73) | (~trans(s99, s73))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[15016])).
% 36.84/24.66 tff(15018,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s73)) | always5(s73))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s73) | (~trans(s99, s73)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[15017, 15015])).
% 36.84/24.66 tff(15019,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s73)) | always5(s73))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15020,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s73) | (~trans(s99, s73))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[15019, 15018])).
% 36.84/24.66 tff(15021,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15020, 12287, 25, 13749, 15014])).
% 36.84/24.66 tff(15022,plain,((~trans(s99, s73)) | always5(s73)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15023,plain,
% 36.84/24.66 (~trans(s99, s73)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15022, 14739])).
% 36.84/24.66 tff(15024,assumption,(~trans(s99, s83)), introduced(assumption)).
% 36.84/24.66 tff(15025,assumption,(~always5(s6)), introduced(assumption)).
% 36.84/24.66 tff(15026,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s6) | (~trans(s99, s6)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s6) | (~trans(s99, s6)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15027,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s6)) | always5(s6)) <=> ((~always5(s99)) | always5(s6) | (~trans(s99, s6)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15028,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s6) | (~trans(s99, s6))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[15027])).
% 36.84/24.66 tff(15029,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s6)) | always5(s6))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s6) | (~trans(s99, s6)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[15028, 15026])).
% 36.84/24.66 tff(15030,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s6)) | always5(s6))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15031,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s6) | (~trans(s99, s6))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[15030, 15029])).
% 36.84/24.66 tff(15032,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15031, 12650, 25, 13749, 15025])).
% 36.84/24.66 tff(15033,plain,((~trans(s99, s6)) | always5(s6)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15034,plain,
% 36.84/24.66 (~trans(s99, s6)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15033, 14818])).
% 36.84/24.66 tff(15035,assumption,(~always5(s51)), introduced(assumption)).
% 36.84/24.66 tff(15036,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s51) | (~trans(s99, s51)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s51) | (~trans(s99, s51)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15037,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s51)) | always5(s51)) <=> ((~always5(s99)) | always5(s51) | (~trans(s99, s51)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15038,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s51) | (~trans(s99, s51))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[15037])).
% 36.84/24.66 tff(15039,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s51)) | always5(s51))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s51) | (~trans(s99, s51)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[15038, 15036])).
% 36.84/24.66 tff(15040,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s51)) | always5(s51))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15041,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s51) | (~trans(s99, s51))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[15040, 15039])).
% 36.84/24.66 tff(15042,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15041, 12232, 25, 13749, 15035])).
% 36.84/24.66 tff(15043,plain,((~trans(s99, s51)) | always5(s51)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15044,plain,
% 36.84/24.66 (~trans(s99, s51)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15043, 14761])).
% 36.84/24.66 tff(15045,assumption,(~always5(s50)), introduced(assumption)).
% 36.84/24.66 tff(15046,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s50) | (~trans(s99, s50)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s50) | (~trans(s99, s50)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15047,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s50)) | always5(s50)) <=> ((~always5(s99)) | always5(s50) | (~trans(s99, s50)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15048,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s50) | (~trans(s99, s50))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[15047])).
% 36.84/24.66 tff(15049,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s50)) | always5(s50))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s50) | (~trans(s99, s50)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[15048, 15046])).
% 36.84/24.66 tff(15050,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s50)) | always5(s50))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15051,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s50) | (~trans(s99, s50))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[15050, 15049])).
% 36.84/24.66 tff(15052,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15051, 12276, 25, 13749, 15045])).
% 36.84/24.66 tff(15053,plain,((~trans(s99, s50)) | always5(s50)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15054,plain,
% 36.84/24.66 (~trans(s99, s50)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15053, 14762])).
% 36.84/24.66 tff(15055,assumption,(~always5(s32)), introduced(assumption)).
% 36.84/24.66 tff(15056,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s32) | (~trans(s99, s32)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s32) | (~trans(s99, s32)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15057,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s32)) | always5(s32)) <=> ((~always5(s99)) | always5(s32) | (~trans(s99, s32)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15058,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s32) | (~trans(s99, s32))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[15057])).
% 36.84/24.66 tff(15059,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s32)) | always5(s32))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s32) | (~trans(s99, s32)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[15058, 15056])).
% 36.84/24.66 tff(15060,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s32)) | always5(s32))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15061,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s32) | (~trans(s99, s32))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[15060, 15059])).
% 36.84/24.66 tff(15062,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15061, 12408, 25, 13749, 15055])).
% 36.84/24.66 tff(15063,plain,((~trans(s99, s32)) | always5(s32)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15064,plain,
% 36.84/24.66 (~trans(s99, s32)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15063, 14780])).
% 36.84/24.66 tff(15065,assumption,(~always5(s45)), introduced(assumption)).
% 36.84/24.66 tff(15066,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s45) | (~trans(s99, s45)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s45) | (~trans(s99, s45)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15067,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s45)) | always5(s45)) <=> ((~always5(s99)) | always5(s45) | (~trans(s99, s45)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15068,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s45) | (~trans(s99, s45))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[15067])).
% 36.84/24.66 tff(15069,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s45)) | always5(s45))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s45) | (~trans(s99, s45)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[15068, 15066])).
% 36.84/24.66 tff(15070,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s45)) | always5(s45))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15071,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s45) | (~trans(s99, s45))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[15070, 15069])).
% 36.84/24.66 tff(15072,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15071, 12507, 25, 13749, 15065])).
% 36.84/24.66 tff(15073,plain,((~trans(s99, s45)) | always5(s45)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15074,plain,
% 36.84/24.66 (~trans(s99, s45)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15073, 14767])).
% 36.84/24.66 tff(15075,assumption,(~always5(s37)), introduced(assumption)).
% 36.84/24.66 tff(15076,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s37) | (~trans(s99, s37)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s37) | (~trans(s99, s37)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15077,plain,
% 36.84/24.66 (((~always5(s99)) | (~trans(s99, s37)) | always5(s37)) <=> ((~always5(s99)) | always5(s37) | (~trans(s99, s37)))),
% 36.84/24.66 inference(rewrite,[status(thm)],[])).
% 36.84/24.66 tff(15078,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s37) | (~trans(s99, s37))))),
% 36.84/24.66 inference(monotonicity,[status(thm)],[15077])).
% 36.84/24.66 tff(15079,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s37)) | always5(s37))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s37) | (~trans(s99, s37)))),
% 36.84/24.66 inference(transitivity,[status(thm)],[15078, 15076])).
% 36.84/24.66 tff(15080,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s37)) | always5(s37))),
% 36.84/24.66 inference(quant_inst,[status(thm)],[])).
% 36.84/24.66 tff(15081,plain,
% 36.84/24.66 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s37) | (~trans(s99, s37))),
% 36.84/24.66 inference(modus_ponens,[status(thm)],[15080, 15079])).
% 36.84/24.66 tff(15082,plain,
% 36.84/24.66 ($false),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15081, 12364, 25, 13749, 15075])).
% 36.84/24.66 tff(15083,plain,((~trans(s99, s37)) | always5(s37)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.66 tff(15084,plain,
% 36.84/24.66 (~trans(s99, s37)),
% 36.84/24.66 inference(unit_resolution,[status(thm)],[15083, 14775])).
% 36.84/24.66 tff(15085,assumption,(~always5(s34)), introduced(assumption)).
% 36.84/24.66 tff(15086,plain,
% 36.84/24.66 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s34) | (~trans(s99, s34)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s34) | (~trans(s99, s34)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15087,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s34)) | always5(s34)) <=> ((~always5(s99)) | always5(s34) | (~trans(s99, s34)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15088,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s34) | (~trans(s99, s34))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15087])).
% 36.84/24.67 tff(15089,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s34)) | always5(s34))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s34) | (~trans(s99, s34)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15088, 15086])).
% 36.84/24.67 tff(15090,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s34)) | always5(s34))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15091,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s34) | (~trans(s99, s34))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15090, 15089])).
% 36.84/24.67 tff(15092,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15091, 12441, 25, 13749, 15085])).
% 36.84/24.67 tff(15093,plain,((~trans(s99, s34)) | always5(s34)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15094,plain,
% 36.84/24.67 (~trans(s99, s34)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15093, 14778])).
% 36.84/24.67 tff(15095,assumption,(~always5(s40)), introduced(assumption)).
% 36.84/24.67 tff(15096,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s40) | (~trans(s99, s40)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s40) | (~trans(s99, s40)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15097,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s40)) | always5(s40)) <=> ((~always5(s99)) | always5(s40) | (~trans(s99, s40)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15098,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s40) | (~trans(s99, s40))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15097])).
% 36.84/24.67 tff(15099,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s40)) | always5(s40))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s40) | (~trans(s99, s40)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15098, 15096])).
% 36.84/24.67 tff(15100,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s40)) | always5(s40))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15101,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s40) | (~trans(s99, s40))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15100, 15099])).
% 36.84/24.67 tff(15102,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15101, 12716, 25, 13749, 15095])).
% 36.84/24.67 tff(15103,plain,((~trans(s99, s40)) | always5(s40)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15104,plain,
% 36.84/24.67 (~trans(s99, s40)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15103, 14772])).
% 36.84/24.67 tff(15105,assumption,(~always5(s26)), introduced(assumption)).
% 36.84/24.67 tff(15106,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s26) | (~trans(s99, s26)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s26) | (~trans(s99, s26)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15107,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s26)) | always5(s26)) <=> ((~always5(s99)) | always5(s26) | (~trans(s99, s26)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15108,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s26) | (~trans(s99, s26))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15107])).
% 36.84/24.67 tff(15109,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s26)) | always5(s26))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s26) | (~trans(s99, s26)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15108, 15106])).
% 36.84/24.67 tff(15110,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s26)) | always5(s26))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15111,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s26) | (~trans(s99, s26))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15110, 15109])).
% 36.84/24.67 tff(15112,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15111, 12474, 25, 13749, 15105])).
% 36.84/24.67 tff(15113,plain,((~trans(s99, s26)) | always5(s26)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15114,plain,
% 36.84/24.67 (~trans(s99, s26)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15113, 14798])).
% 36.84/24.67 tff(15115,assumption,(~always5(s25)), introduced(assumption)).
% 36.84/24.67 tff(15116,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s25) | (~trans(s99, s25)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s25) | (~trans(s99, s25)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15117,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s25)) | always5(s25)) <=> ((~always5(s99)) | always5(s25) | (~trans(s99, s25)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15118,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s25) | (~trans(s99, s25))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15117])).
% 36.84/24.67 tff(15119,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s25)) | always5(s25))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s25) | (~trans(s99, s25)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15118, 15116])).
% 36.84/24.67 tff(15120,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s25)) | always5(s25))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15121,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s25) | (~trans(s99, s25))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15120, 15119])).
% 36.84/24.67 tff(15122,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15121, 12562, 25, 13749, 15115])).
% 36.84/24.67 tff(15123,plain,((~trans(s99, s25)) | always5(s25)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15124,plain,
% 36.84/24.67 (~trans(s99, s25)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15123, 14799])).
% 36.84/24.67 tff(15125,assumption,(~always5(s28)), introduced(assumption)).
% 36.84/24.67 tff(15126,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s28) | (~trans(s99, s28)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s28) | (~trans(s99, s28)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15127,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s28)) | always5(s28)) <=> ((~always5(s99)) | always5(s28) | (~trans(s99, s28)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15128,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s28) | (~trans(s99, s28))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15127])).
% 36.84/24.67 tff(15129,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s28)) | always5(s28))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s28) | (~trans(s99, s28)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15128, 15126])).
% 36.84/24.67 tff(15130,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s28)) | always5(s28))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15131,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s28) | (~trans(s99, s28))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15130, 15129])).
% 36.84/24.67 tff(15132,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15131, 12265, 25, 13749, 15125])).
% 36.84/24.67 tff(15133,plain,((~trans(s99, s28)) | always5(s28)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15134,plain,
% 36.84/24.67 (~trans(s99, s28)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15133, 14796])).
% 36.84/24.67 tff(15135,assumption,(~always5(s29)), introduced(assumption)).
% 36.84/24.67 tff(15136,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s29) | (~trans(s99, s29)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s29) | (~trans(s99, s29)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15137,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s29)) | always5(s29)) <=> ((~always5(s99)) | always5(s29) | (~trans(s99, s29)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15138,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s29) | (~trans(s99, s29))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15137])).
% 36.84/24.67 tff(15139,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s29)) | always5(s29))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s29) | (~trans(s99, s29)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15138, 15136])).
% 36.84/24.67 tff(15140,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s29)) | always5(s29))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15141,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s29) | (~trans(s99, s29))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15140, 15139])).
% 36.84/24.67 tff(15142,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15141, 12628, 25, 13749, 15135])).
% 36.84/24.67 tff(15143,plain,((~trans(s99, s29)) | always5(s29)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15144,plain,
% 36.84/24.67 (~trans(s99, s29)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15143, 14795])).
% 36.84/24.67 tff(15145,assumption,(~always5(s30)), introduced(assumption)).
% 36.84/24.67 tff(15146,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s30) | (~trans(s99, s30)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s30) | (~trans(s99, s30)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15147,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s30)) | always5(s30)) <=> ((~always5(s99)) | always5(s30) | (~trans(s99, s30)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15148,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s30) | (~trans(s99, s30))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15147])).
% 36.84/24.67 tff(15149,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s30)) | always5(s30))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s30) | (~trans(s99, s30)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15148, 15146])).
% 36.84/24.67 tff(15150,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s30)) | always5(s30))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15151,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s30) | (~trans(s99, s30))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15150, 15149])).
% 36.84/24.67 tff(15152,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15151, 12221, 25, 13749, 15145])).
% 36.84/24.67 tff(15153,plain,((~trans(s99, s30)) | always5(s30)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15154,plain,
% 36.84/24.67 (~trans(s99, s30)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15153, 14794])).
% 36.84/24.67 tff(15155,assumption,(~always5(s7)), introduced(assumption)).
% 36.84/24.67 tff(15156,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s7) | (~trans(s99, s7)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s7) | (~trans(s99, s7)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15157,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s7)) | always5(s7)) <=> ((~always5(s99)) | always5(s7) | (~trans(s99, s7)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15158,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s7) | (~trans(s99, s7))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15157])).
% 36.84/24.67 tff(15159,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s7)) | always5(s7))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s7) | (~trans(s99, s7)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15158, 15156])).
% 36.84/24.67 tff(15160,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s7)) | always5(s7))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15161,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s7) | (~trans(s99, s7))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15160, 15159])).
% 36.84/24.67 tff(15162,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15161, 12573, 25, 13749, 15155])).
% 36.84/24.67 tff(15163,plain,((~trans(s99, s7)) | always5(s7)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15164,plain,
% 36.84/24.67 (~trans(s99, s7)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15163, 14817])).
% 36.84/24.67 tff(15165,assumption,(~always5(s23)), introduced(assumption)).
% 36.84/24.67 tff(15166,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s23) | (~trans(s99, s23)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s23) | (~trans(s99, s23)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15167,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s23)) | always5(s23)) <=> ((~always5(s99)) | always5(s23) | (~trans(s99, s23)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15168,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s23) | (~trans(s99, s23))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15167])).
% 36.84/24.67 tff(15169,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s23)) | always5(s23))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s23) | (~trans(s99, s23)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15168, 15166])).
% 36.84/24.67 tff(15170,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s23)) | always5(s23))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15171,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s23) | (~trans(s99, s23))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15170, 15169])).
% 36.84/24.67 tff(15172,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15171, 12760, 25, 13749, 15165])).
% 36.84/24.67 tff(15173,plain,((~trans(s99, s23)) | always5(s23)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15174,plain,
% 36.84/24.67 (~trans(s99, s23)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15173, 14801])).
% 36.84/24.67 tff(15175,assumption,(~always5(s12)), introduced(assumption)).
% 36.84/24.67 tff(15176,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s12) | (~trans(s99, s12)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s12) | (~trans(s99, s12)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15177,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s12)) | always5(s12)) <=> ((~always5(s99)) | always5(s12) | (~trans(s99, s12)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15178,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s12)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s12) | (~trans(s99, s12))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15177])).
% 36.84/24.67 tff(15179,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s12)) | always5(s12))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s12) | (~trans(s99, s12)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15178, 15176])).
% 36.84/24.67 tff(15180,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s12)) | always5(s12))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15181,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s12) | (~trans(s99, s12))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15180, 15179])).
% 36.84/24.67 tff(15182,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15181, 12485, 25, 13749, 15175])).
% 36.84/24.67 tff(15183,plain,((~trans(s99, s12)) | always5(s12)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15184,plain,
% 36.84/24.67 (~trans(s99, s12)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15183, 14812])).
% 36.84/24.67 tff(15185,assumption,(~always5(s24)), introduced(assumption)).
% 36.84/24.67 tff(15186,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s24) | (~trans(s99, s24)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s24) | (~trans(s99, s24)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15187,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s24)) | always5(s24)) <=> ((~always5(s99)) | always5(s24) | (~trans(s99, s24)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15188,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s24) | (~trans(s99, s24))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15187])).
% 36.84/24.67 tff(15189,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s24)) | always5(s24))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s24) | (~trans(s99, s24)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15188, 15186])).
% 36.84/24.67 tff(15190,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s24)) | always5(s24))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15191,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s24) | (~trans(s99, s24))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15190, 15189])).
% 36.84/24.67 tff(15192,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15191, 12331, 25, 13749, 15185])).
% 36.84/24.67 tff(15193,plain,((~trans(s99, s24)) | always5(s24)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15194,plain,
% 36.84/24.67 (~trans(s99, s24)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15193, 14800])).
% 36.84/24.67 tff(15195,assumption,(~always5(s11)), introduced(assumption)).
% 36.84/24.67 tff(15196,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s11) | (~trans(s99, s11)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s11) | (~trans(s99, s11)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15197,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s11)) | always5(s11)) <=> ((~always5(s99)) | always5(s11) | (~trans(s99, s11)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15198,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s11)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s11) | (~trans(s99, s11))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15197])).
% 36.84/24.67 tff(15199,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s11)) | always5(s11))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s11) | (~trans(s99, s11)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15198, 15196])).
% 36.84/24.67 tff(15200,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s11)) | always5(s11))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15201,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s11) | (~trans(s99, s11))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15200, 15199])).
% 36.84/24.67 tff(15202,plain,
% 36.84/24.67 ($false),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15201, 12375, 25, 13749, 15195])).
% 36.84/24.67 tff(15203,plain,((~trans(s99, s11)) | always5(s11)), inference(lemma,lemma(discharge,[]))).
% 36.84/24.67 tff(15204,plain,
% 36.84/24.67 (~trans(s99, s11)),
% 36.84/24.67 inference(unit_resolution,[status(thm)],[15203, 14813])).
% 36.84/24.67 tff(15205,assumption,(~always5(s14)), introduced(assumption)).
% 36.84/24.67 tff(15206,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s14) | (~trans(s99, s14)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s14) | (~trans(s99, s14)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15207,plain,
% 36.84/24.67 (((~always5(s99)) | (~trans(s99, s14)) | always5(s14)) <=> ((~always5(s99)) | always5(s14) | (~trans(s99, s14)))),
% 36.84/24.67 inference(rewrite,[status(thm)],[])).
% 36.84/24.67 tff(15208,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s14) | (~trans(s99, s14))))),
% 36.84/24.67 inference(monotonicity,[status(thm)],[15207])).
% 36.84/24.67 tff(15209,plain,
% 36.84/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s14)) | always5(s14))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s14) | (~trans(s99, s14)))),
% 36.84/24.67 inference(transitivity,[status(thm)],[15208, 15206])).
% 36.84/24.67 tff(15210,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s14)) | always5(s14))),
% 36.84/24.67 inference(quant_inst,[status(thm)],[])).
% 36.84/24.67 tff(15211,plain,
% 36.84/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s14) | (~trans(s99, s14))),
% 36.84/24.67 inference(modus_ponens,[status(thm)],[15210, 15209])).
% 36.87/24.67 tff(15212,plain,
% 36.87/24.67 ($false),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15211, 12617, 25, 13749, 15205])).
% 36.87/24.67 tff(15213,plain,((~trans(s99, s14)) | always5(s14)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.67 tff(15214,plain,
% 36.87/24.67 (~trans(s99, s14)),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15213, 14810])).
% 36.87/24.67 tff(15215,assumption,(~always5(s19)), introduced(assumption)).
% 36.87/24.67 tff(15216,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s19) | (~trans(s99, s19)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s19) | (~trans(s99, s19)))),
% 36.87/24.67 inference(rewrite,[status(thm)],[])).
% 36.87/24.67 tff(15217,plain,
% 36.87/24.67 (((~always5(s99)) | (~trans(s99, s19)) | always5(s19)) <=> ((~always5(s99)) | always5(s19) | (~trans(s99, s19)))),
% 36.87/24.67 inference(rewrite,[status(thm)],[])).
% 36.87/24.67 tff(15218,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s19) | (~trans(s99, s19))))),
% 36.87/24.67 inference(monotonicity,[status(thm)],[15217])).
% 36.87/24.67 tff(15219,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s19)) | always5(s19))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s19) | (~trans(s99, s19)))),
% 36.87/24.67 inference(transitivity,[status(thm)],[15218, 15216])).
% 36.87/24.67 tff(15220,plain,
% 36.87/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s19)) | always5(s19))),
% 36.87/24.67 inference(quant_inst,[status(thm)],[])).
% 36.87/24.67 tff(15221,plain,
% 36.87/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s19) | (~trans(s99, s19))),
% 36.87/24.67 inference(modus_ponens,[status(thm)],[15220, 15219])).
% 36.87/24.67 tff(15222,plain,
% 36.87/24.67 ($false),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15221, 12463, 25, 13749, 15215])).
% 36.87/24.67 tff(15223,plain,((~trans(s99, s19)) | always5(s19)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.67 tff(15224,plain,
% 36.87/24.67 (~trans(s99, s19)),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15223, 14805])).
% 36.87/24.67 tff(15225,assumption,(~always5(s16)), introduced(assumption)).
% 36.87/24.67 tff(15226,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s16) | (~trans(s99, s16)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s16) | (~trans(s99, s16)))),
% 36.87/24.67 inference(rewrite,[status(thm)],[])).
% 36.87/24.67 tff(15227,plain,
% 36.87/24.67 (((~always5(s99)) | (~trans(s99, s16)) | always5(s16)) <=> ((~always5(s99)) | always5(s16) | (~trans(s99, s16)))),
% 36.87/24.67 inference(rewrite,[status(thm)],[])).
% 36.87/24.67 tff(15228,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s16) | (~trans(s99, s16))))),
% 36.87/24.67 inference(monotonicity,[status(thm)],[15227])).
% 36.87/24.67 tff(15229,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s16)) | always5(s16))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s16) | (~trans(s99, s16)))),
% 36.87/24.67 inference(transitivity,[status(thm)],[15228, 15226])).
% 36.87/24.67 tff(15230,plain,
% 36.87/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s16)) | always5(s16))),
% 36.87/24.67 inference(quant_inst,[status(thm)],[])).
% 36.87/24.67 tff(15231,plain,
% 36.87/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s16) | (~trans(s99, s16))),
% 36.87/24.67 inference(modus_ponens,[status(thm)],[15230, 15229])).
% 36.87/24.67 tff(15232,plain,
% 36.87/24.67 ($false),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15231, 12683, 25, 13749, 15225])).
% 36.87/24.67 tff(15233,plain,((~trans(s99, s16)) | always5(s16)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.67 tff(15234,plain,
% 36.87/24.67 (~trans(s99, s16)),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15233, 14808])).
% 36.87/24.67 tff(15235,assumption,(~always5(s20)), introduced(assumption)).
% 36.87/24.67 tff(15236,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s20) | (~trans(s99, s20)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s20) | (~trans(s99, s20)))),
% 36.87/24.67 inference(rewrite,[status(thm)],[])).
% 36.87/24.67 tff(15237,plain,
% 36.87/24.67 (((~always5(s99)) | (~trans(s99, s20)) | always5(s20)) <=> ((~always5(s99)) | always5(s20) | (~trans(s99, s20)))),
% 36.87/24.67 inference(rewrite,[status(thm)],[])).
% 36.87/24.67 tff(15238,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s20) | (~trans(s99, s20))))),
% 36.87/24.67 inference(monotonicity,[status(thm)],[15237])).
% 36.87/24.67 tff(15239,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s20)) | always5(s20))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s20) | (~trans(s99, s20)))),
% 36.87/24.67 inference(transitivity,[status(thm)],[15238, 15236])).
% 36.87/24.67 tff(15240,plain,
% 36.87/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s20)) | always5(s20))),
% 36.87/24.67 inference(quant_inst,[status(thm)],[])).
% 36.87/24.67 tff(15241,plain,
% 36.87/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s20) | (~trans(s99, s20))),
% 36.87/24.67 inference(modus_ponens,[status(thm)],[15240, 15239])).
% 36.87/24.67 tff(15242,plain,
% 36.87/24.67 ($false),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15241, 12727, 25, 13749, 15235])).
% 36.87/24.67 tff(15243,plain,((~trans(s99, s20)) | always5(s20)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.67 tff(15244,plain,
% 36.87/24.67 (~trans(s99, s20)),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15243, 14804])).
% 36.87/24.67 tff(15245,assumption,(~always5(s21)), introduced(assumption)).
% 36.87/24.67 tff(15246,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s21) | (~trans(s99, s21)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s21) | (~trans(s99, s21)))),
% 36.87/24.67 inference(rewrite,[status(thm)],[])).
% 36.87/24.67 tff(15247,plain,
% 36.87/24.67 (((~always5(s99)) | (~trans(s99, s21)) | always5(s21)) <=> ((~always5(s99)) | always5(s21) | (~trans(s99, s21)))),
% 36.87/24.67 inference(rewrite,[status(thm)],[])).
% 36.87/24.67 tff(15248,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s21)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s21) | (~trans(s99, s21))))),
% 36.87/24.67 inference(monotonicity,[status(thm)],[15247])).
% 36.87/24.67 tff(15249,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s21)) | always5(s21))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s21) | (~trans(s99, s21)))),
% 36.87/24.67 inference(transitivity,[status(thm)],[15248, 15246])).
% 36.87/24.67 tff(15250,plain,
% 36.87/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s21)) | always5(s21))),
% 36.87/24.67 inference(quant_inst,[status(thm)],[])).
% 36.87/24.67 tff(15251,plain,
% 36.87/24.67 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s21) | (~trans(s99, s21))),
% 36.87/24.67 inference(modus_ponens,[status(thm)],[15250, 15249])).
% 36.87/24.67 tff(15252,plain,
% 36.87/24.67 ($false),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15251, 12881, 25, 13749, 15245])).
% 36.87/24.67 tff(15253,plain,((~trans(s99, s21)) | always5(s21)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.67 tff(15254,plain,
% 36.87/24.67 (~trans(s99, s21)),
% 36.87/24.67 inference(unit_resolution,[status(thm)],[15253, 14803])).
% 36.87/24.67 tff(15255,assumption,(~always5(s22)), introduced(assumption)).
% 36.87/24.67 tff(15256,plain,
% 36.87/24.67 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s22) | (~trans(s99, s22)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s22) | (~trans(s99, s22)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15257,plain,
% 36.87/24.68 (((~always5(s99)) | (~trans(s99, s22)) | always5(s22)) <=> ((~always5(s99)) | always5(s22) | (~trans(s99, s22)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15258,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s22) | (~trans(s99, s22))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15257])).
% 36.87/24.68 tff(15259,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s22)) | always5(s22))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s22) | (~trans(s99, s22)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15258, 15256])).
% 36.87/24.68 tff(15260,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s22)) | always5(s22))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15261,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s22) | (~trans(s99, s22))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15260, 15259])).
% 36.87/24.68 tff(15262,plain,
% 36.87/24.68 ($false),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15261, 12749, 25, 13749, 15255])).
% 36.87/24.68 tff(15263,plain,((~trans(s99, s22)) | always5(s22)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.68 tff(15264,plain,
% 36.87/24.68 (~trans(s99, s22)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15263, 14802])).
% 36.87/24.68 tff(15265,assumption,(~trans(s99, s90)), introduced(assumption)).
% 36.87/24.68 tff(15266,assumption,(~always5(s2)), introduced(assumption)).
% 36.87/24.68 tff(15267,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s2) | (~trans(s99, s2)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s2) | (~trans(s99, s2)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15268,plain,
% 36.87/24.68 (((~always5(s99)) | (~trans(s99, s2)) | always5(s2)) <=> ((~always5(s99)) | always5(s2) | (~trans(s99, s2)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15269,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s2) | (~trans(s99, s2))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15268])).
% 36.87/24.68 tff(15270,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s2)) | always5(s2))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s2) | (~trans(s99, s2)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15269, 15267])).
% 36.87/24.68 tff(15271,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s2)) | always5(s2))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15272,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s2) | (~trans(s99, s2))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15271, 15270])).
% 36.87/24.68 tff(15273,plain,
% 36.87/24.68 ($false),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15272, 12793, 25, 13749, 15266])).
% 36.87/24.68 tff(15274,plain,((~trans(s99, s2)) | always5(s2)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.68 tff(15275,plain,
% 36.87/24.68 (~trans(s99, s2)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15274, 14822])).
% 36.87/24.68 tff(15276,assumption,(~always5(s4)), introduced(assumption)).
% 36.87/24.68 tff(15277,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s4) | (~trans(s99, s4)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s4) | (~trans(s99, s4)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15278,plain,
% 36.87/24.68 (((~always5(s99)) | (~trans(s99, s4)) | always5(s4)) <=> ((~always5(s99)) | always5(s4) | (~trans(s99, s4)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15279,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s4) | (~trans(s99, s4))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15278])).
% 36.87/24.68 tff(15280,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s4)) | always5(s4))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s4) | (~trans(s99, s4)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15279, 15277])).
% 36.87/24.68 tff(15281,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s4)) | always5(s4))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15282,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s4) | (~trans(s99, s4))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15281, 15280])).
% 36.87/24.68 tff(15283,plain,
% 36.87/24.68 ($false),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15282, 12419, 25, 13749, 15276])).
% 36.87/24.68 tff(15284,plain,((~trans(s99, s4)) | always5(s4)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.68 tff(15285,plain,
% 36.87/24.68 (~trans(s99, s4)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15284, 14820])).
% 36.87/24.68 tff(15286,assumption,(~trans(s99, s91)), introduced(assumption)).
% 36.87/24.68 tff(15287,plain,
% 36.87/24.68 (~always5(s93)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[8694, 14725])).
% 36.87/24.68 tff(15288,assumption,(~always5(s93)), introduced(assumption)).
% 36.87/24.68 tff(15289,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s93) | (~trans(s99, s93)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s93) | (~trans(s99, s93)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15290,plain,
% 36.87/24.68 (((~always5(s99)) | (~trans(s99, s93)) | always5(s93)) <=> ((~always5(s99)) | always5(s93) | (~trans(s99, s93)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15291,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s93)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s93) | (~trans(s99, s93))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15290])).
% 36.87/24.68 tff(15292,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s93)) | always5(s93))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s93) | (~trans(s99, s93)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15291, 15289])).
% 36.87/24.68 tff(15293,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s93)) | always5(s93))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15294,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s93) | (~trans(s99, s93))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15293, 15292])).
% 36.87/24.68 tff(15295,plain,
% 36.87/24.68 ($false),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15294, 12782, 25, 13749, 15288])).
% 36.87/24.68 tff(15296,plain,((~trans(s99, s93)) | always5(s93)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.68 tff(15297,plain,
% 36.87/24.68 (~trans(s99, s93)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15296, 15287])).
% 36.87/24.68 tff(15298,plain,
% 36.87/24.68 (~always5(s92)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[8702, 15287])).
% 36.87/24.68 tff(15299,assumption,(~always5(s92)), introduced(assumption)).
% 36.87/24.68 tff(15300,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s92) | (~trans(s99, s92)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s92) | (~trans(s99, s92)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15301,plain,
% 36.87/24.68 (((~always5(s99)) | (~trans(s99, s92)) | always5(s92)) <=> ((~always5(s99)) | always5(s92) | (~trans(s99, s92)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15302,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s92)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s92) | (~trans(s99, s92))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15301])).
% 36.87/24.68 tff(15303,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s92)) | always5(s92))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s92) | (~trans(s99, s92)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15302, 15300])).
% 36.87/24.68 tff(15304,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s92)) | always5(s92))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15305,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s92) | (~trans(s99, s92))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15304, 15303])).
% 36.87/24.68 tff(15306,plain,
% 36.87/24.68 ($false),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15305, 12804, 25, 13749, 15299])).
% 36.87/24.68 tff(15307,plain,((~trans(s99, s92)) | always5(s92)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.68 tff(15308,plain,
% 36.87/24.68 (~trans(s99, s92)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15307, 15298])).
% 36.87/24.68 tff(15309,assumption,(~trans(s99, s93)), introduced(assumption)).
% 36.87/24.68 tff(15310,assumption,(~trans(s99, s92)), introduced(assumption)).
% 36.87/24.68 tff(15311,assumption,(~trans(s99, s94)), introduced(assumption)).
% 36.87/24.68 tff(15312,assumption,(~trans(s99, s71)), introduced(assumption)).
% 36.87/24.68 tff(15313,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s77) | (~trans(s99, s77)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s77) | (~trans(s99, s77)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15314,plain,
% 36.87/24.68 (((~always5(s99)) | (~trans(s99, s77)) | always5(s77)) <=> ((~always5(s99)) | always5(s77) | (~trans(s99, s77)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15315,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s77)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s77) | (~trans(s99, s77))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15314])).
% 36.87/24.68 tff(15316,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s77)) | always5(s77))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s77) | (~trans(s99, s77)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15315, 15313])).
% 36.87/24.68 tff(15317,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s77)) | always5(s77))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15318,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s77) | (~trans(s99, s77))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15317, 15316])).
% 36.87/24.68 tff(15319,plain,
% 36.87/24.68 ($false),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15318, 12914, 25, 13749, 14735])).
% 36.87/24.68 tff(15320,plain,((~trans(s99, s77)) | always5(s77)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.68 tff(15321,plain,
% 36.87/24.68 (~trans(s99, s77)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15320, 14735])).
% 36.87/24.68 tff(15322,assumption,(~trans(s99, s58)), introduced(assumption)).
% 36.87/24.68 tff(15323,assumption,(~trans(s99, s59)), introduced(assumption)).
% 36.87/24.68 tff(15324,assumption,(~trans(s99, s53)), introduced(assumption)).
% 36.87/24.68 tff(15325,assumption,(~trans(s99, s54)), introduced(assumption)).
% 36.87/24.68 tff(15326,assumption,(~trans(s99, s56)), introduced(assumption)).
% 36.87/24.68 tff(15327,assumption,(~trans(s99, s60)), introduced(assumption)).
% 36.87/24.68 tff(15328,assumption,(~trans(s99, s62)), introduced(assumption)).
% 36.87/24.68 tff(15329,assumption,(~trans(s99, s61)), introduced(assumption)).
% 36.87/24.68 tff(15330,assumption,(~trans(s99, s64)), introduced(assumption)).
% 36.87/24.68 tff(15331,assumption,(~trans(s99, s65)), introduced(assumption)).
% 36.87/24.68 tff(15332,assumption,(~trans(s99, s66)), introduced(assumption)).
% 36.87/24.68 tff(15333,assumption,(~trans(s99, s67)), introduced(assumption)).
% 36.87/24.68 tff(15334,assumption,(~trans(s99, s69)), introduced(assumption)).
% 36.87/24.68 tff(15335,assumption,(~trans(s99, s73)), introduced(assumption)).
% 36.87/24.68 tff(15336,assumption,(~trans(s99, s74)), introduced(assumption)).
% 36.87/24.68 tff(15337,assumption,(~trans(s99, s72)), introduced(assumption)).
% 36.87/24.68 tff(15338,assumption,(~trans(s99, s51)), introduced(assumption)).
% 36.87/24.68 tff(15339,assumption,(~trans(s99, s50)), introduced(assumption)).
% 36.87/24.68 tff(15340,assumption,(~trans(s99, s32)), introduced(assumption)).
% 36.87/24.68 tff(15341,assumption,(~trans(s99, s21)), introduced(assumption)).
% 36.87/24.68 tff(15342,assumption,(~trans(s99, s45)), introduced(assumption)).
% 36.87/24.68 tff(15343,assumption,(~trans(s99, s37)), introduced(assumption)).
% 36.87/24.68 tff(15344,assumption,(~trans(s99, s2)), introduced(assumption)).
% 36.87/24.68 tff(15345,assumption,(~trans(s99, s34)), introduced(assumption)).
% 36.87/24.68 tff(15346,assumption,(~trans(s99, s40)), introduced(assumption)).
% 36.87/24.68 tff(15347,assumption,(~trans(s99, s26)), introduced(assumption)).
% 36.87/24.68 tff(15348,assumption,(~trans(s99, s25)), introduced(assumption)).
% 36.87/24.68 tff(15349,assumption,(~trans(s99, s28)), introduced(assumption)).
% 36.87/24.68 tff(15350,assumption,(~trans(s99, s29)), introduced(assumption)).
% 36.87/24.68 tff(15351,assumption,(~trans(s99, s30)), introduced(assumption)).
% 36.87/24.68 tff(15352,assumption,(~trans(s99, s4)), introduced(assumption)).
% 36.87/24.68 tff(15353,assumption,(~trans(s99, s23)), introduced(assumption)).
% 36.87/24.68 tff(15354,assumption,(~trans(s99, s24)), introduced(assumption)).
% 36.87/24.68 tff(15355,assumption,(~trans(s99, s11)), introduced(assumption)).
% 36.87/24.68 tff(15356,assumption,(~trans(s99, s6)), introduced(assumption)).
% 36.87/24.68 tff(15357,assumption,(~trans(s99, s19)), introduced(assumption)).
% 36.87/24.68 tff(15358,assumption,(~trans(s99, s12)), introduced(assumption)).
% 36.87/24.68 tff(15359,assumption,(~trans(s99, s7)), introduced(assumption)).
% 36.87/24.68 tff(15360,assumption,(~trans(s99, s14)), introduced(assumption)).
% 36.87/24.68 tff(15361,assumption,(~trans(s99, s16)), introduced(assumption)).
% 36.87/24.68 tff(15362,assumption,(~trans(s99, s22)), introduced(assumption)).
% 36.87/24.68 tff(15363,assumption,(~trans(s99, s20)), introduced(assumption)).
% 36.87/24.68 tff(15364,assumption,(~trans(s99, s0)), introduced(assumption)).
% 36.87/24.68 tff(15365,assumption,(~trans(s99, s1)), introduced(assumption)).
% 36.87/24.68 tff(15366,assumption,(~trans(s99, s31)), introduced(assumption)).
% 36.87/24.68 tff(15367,assumption,(~always5(s35)), introduced(assumption)).
% 36.87/24.68 tff(15368,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s35) | (~trans(s99, s35)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s35) | (~trans(s99, s35)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15369,plain,
% 36.87/24.68 (((~always5(s99)) | (~trans(s99, s35)) | always5(s35)) <=> ((~always5(s99)) | always5(s35) | (~trans(s99, s35)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15370,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s35) | (~trans(s99, s35))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15369])).
% 36.87/24.68 tff(15371,plain,
% 36.87/24.68 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s35)) | always5(s35))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s35) | (~trans(s99, s35)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15370, 15368])).
% 36.87/24.68 tff(15372,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s35)) | always5(s35))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15373,plain,
% 36.87/24.68 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s35) | (~trans(s99, s35))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15372, 15371])).
% 36.87/24.68 tff(15374,plain,
% 36.87/24.68 ($false),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15373, 12925, 25, 13749, 15367])).
% 36.87/24.68 tff(15375,plain,((~trans(s99, s35)) | always5(s35)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.68 tff(15376,plain,
% 36.87/24.68 (~trans(s99, s35)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15375, 14777])).
% 36.87/24.68 tff(15377,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s98)) | node3(c_bit1, s99, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s98)) | node3(c_bit1, s99, s98))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15378,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s98)) | node3(c_bit1, s99, s98))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15379,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s98)) | node3(c_bit1, s99, s98)),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15378, 15377])).
% 36.87/24.68 tff(15380,plain,
% 36.87/24.68 ((~trans(s99, s98)) | node3(c_bit1, s99, s98)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15379, 81])).
% 36.87/24.68 tff(15381,plain,
% 36.87/24.68 (node3(c_bit1, s99, s98)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15380, 12210])).
% 36.87/24.68 tff(15382,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s98)) | node3(c_bit0, s99, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s98)) | node3(c_bit0, s99, s98))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15383,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s98)) | node3(c_bit0, s99, s98))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15384,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s98)) | node3(c_bit0, s99, s98)),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15383, 15382])).
% 36.87/24.68 tff(15385,plain,
% 36.87/24.68 ((~trans(s99, s98)) | node3(c_bit0, s99, s98)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15384, 81])).
% 36.87/24.68 tff(15386,plain,
% 36.87/24.68 (node3(c_bit0, s99, s98)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15385, 12210])).
% 36.87/24.68 tff(15387,assumption,(node3(c_bit1, s99, s98)), introduced(assumption)).
% 36.87/24.68 tff(15388,assumption,(~m_counter_cell_v_value(c_bit0, s99)), introduced(assumption)).
% 36.87/24.68 tff(15389,plain,
% 36.87/24.68 (~node1(c_bit0, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[14577, 15388])).
% 36.87/24.68 tff(15390,assumption,(node3(c_bit0, s99, s98)), introduced(assumption)).
% 36.87/24.68 tff(15391,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s98)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15392,plain,
% 36.87/24.68 ((node1(c_bit0, s99) | (~node3(c_bit0, s99, s98)) | m_counter_cell_v_value(c_bit0, s98)) <=> (m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s98)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15393,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s98)) | m_counter_cell_v_value(c_bit0, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s98))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15392])).
% 36.87/24.68 tff(15394,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s98)) | m_counter_cell_v_value(c_bit0, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s98)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15393, 15391])).
% 36.87/24.68 tff(15395,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s98)) | m_counter_cell_v_value(c_bit0, s98))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15396,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s98))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15395, 15394])).
% 36.87/24.68 tff(15397,plain,
% 36.87/24.68 (m_counter_cell_v_value(c_bit0, s98) | node1(c_bit0, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15396, 199, 15390])).
% 36.87/24.68 tff(15398,plain,
% 36.87/24.68 (m_counter_cell_v_value(c_bit0, s98)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15397, 15389])).
% 36.87/24.68 tff(15399,plain,
% 36.87/24.68 (m_counter_cell_v_carry_out(c_bit0, s98)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[14453, 15398])).
% 36.87/24.68 tff(15400,plain,
% 36.87/24.68 (m_counter_cell_v_carry_in(c_bit1, s98)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[14446, 3046, 15399])).
% 36.87/24.68 tff(15401,plain,
% 36.87/24.68 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s99) | (~node4(c_bit0, s99)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s99) | (~node4(c_bit0, s99)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15402,plain,
% 36.87/24.68 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit0, s99) | (~node4(c_bit0, s99)))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15403,plain,
% 36.87/24.68 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit0, s99) | (~node4(c_bit0, s99))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15402, 15401])).
% 36.87/24.68 tff(15404,plain,
% 36.87/24.68 (~node4(c_bit0, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15403, 2875, 15388])).
% 36.87/24.68 tff(15405,plain,
% 36.87/24.68 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s99)) | node4(c_bit0, s99))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s99)) | node4(c_bit0, s99))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15406,plain,
% 36.87/24.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit0, s99)) | node4(c_bit0, s99))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15407,plain,
% 36.87/24.68 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit0, s99)) | node4(c_bit0, s99)),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15406, 15405])).
% 36.87/24.68 tff(15408,plain,
% 36.87/24.68 (~m_counter_cell_v_carry_out(c_bit0, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15407, 2887, 15404])).
% 36.87/24.68 tff(15409,plain,
% 36.87/24.68 (((~![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, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))) <=> ((~![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, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15410,plain,
% 36.87/24.68 ((~![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, s99)) | m_counter_cell_v_carry_out(c_bit0, s99))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15411,plain,
% 36.87/24.68 ((~![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, s99)) | m_counter_cell_v_carry_out(c_bit0, s99)),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15410, 15409])).
% 36.87/24.68 tff(15412,plain,
% 36.87/24.68 (~m_counter_cell_v_carry_in(c_bit1, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15411, 2901, 15408])).
% 36.87/24.68 tff(15413,assumption,(m_counter_cell_v_value(c_bit1, s98)), introduced(assumption)).
% 36.87/24.68 tff(15414,plain,
% 36.87/24.68 (((~![I0: $i, X: $i] : ((~m_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, s98)) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node2(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s98)) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node2(c_bit1, s98)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15415,plain,
% 36.87/24.68 ((~![I0: $i, X: $i] : ((~m_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, s98)) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node2(c_bit1, s98)))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15416,plain,
% 36.87/24.68 ((~![I0: $i, X: $i] : ((~m_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, s98)) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node2(c_bit1, s98))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15415, 15414])).
% 36.87/24.68 tff(15417,plain,
% 36.87/24.68 ((~m_counter_cell_v_value(c_bit1, s98)) | (~node2(c_bit1, s98))),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15416, 219, 8590])).
% 36.87/24.68 tff(15418,plain,
% 36.87/24.68 (~node2(c_bit1, s98)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15417, 15413])).
% 36.87/24.68 tff(15419,plain,
% 36.87/24.68 (((~![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_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15420,plain,
% 36.87/24.68 ((node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | (~m_counter_cell_v_value(c_bit1, s98))) <=> ((~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15421,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | (~m_counter_cell_v_value(c_bit1, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15420])).
% 36.87/24.68 tff(15422,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | (~m_counter_cell_v_value(c_bit1, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15421, 15419])).
% 36.87/24.68 tff(15423,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | (~m_counter_cell_v_value(c_bit1, s98)))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15424,plain,
% 36.87/24.68 ((~![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_bit1, s98)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s98))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15423, 15422])).
% 36.87/24.68 tff(15425,plain,
% 36.87/24.68 ((~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15424, 234, 15387])).
% 36.87/24.68 tff(15426,plain,
% 36.87/24.68 (node2(c_bit1, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15425, 15413])).
% 36.87/24.68 tff(15427,assumption,(~m_counter_cell_v_carry_in(c_bit1, s99)), introduced(assumption)).
% 36.87/24.68 tff(15428,plain,
% 36.87/24.68 (((~![I0: $i, X: $i] : (m_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, s99) | m_counter_cell_v_value(c_bit1, s99) | (~node2(c_bit1, s99)))) <=> ((~![I0: $i, X: $i] : (m_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, s99) | m_counter_cell_v_value(c_bit1, s99) | (~node2(c_bit1, s99)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15429,plain,
% 36.87/24.68 ((~![I0: $i, X: $i] : (m_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, s99) | m_counter_cell_v_value(c_bit1, s99) | (~node2(c_bit1, s99)))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15430,plain,
% 36.87/24.68 ((~![I0: $i, X: $i] : (m_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, s99) | m_counter_cell_v_value(c_bit1, s99) | (~node2(c_bit1, s99))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15429, 15428])).
% 36.87/24.68 tff(15431,plain,
% 36.87/24.68 (m_counter_cell_v_value(c_bit1, s99) | (~node2(c_bit1, s99))),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15430, 3291, 15427])).
% 36.87/24.68 tff(15432,plain,
% 36.87/24.68 (m_counter_cell_v_value(c_bit1, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15431, 15426])).
% 36.87/24.68 tff(15433,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit1, s98, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit1, s98, s99))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15434,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit1, s98, s99))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15435,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit1, s98, s99)),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15434, 15433])).
% 36.87/24.68 tff(15436,plain,
% 36.87/24.68 (node3(c_bit1, s98, s99)),
% 36.87/24.68 inference(unit_resolution,[status(thm)],[15435, 81, 8629])).
% 36.87/24.68 tff(15437,plain,
% 36.87/24.68 (((~![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_bit1, s99)) | node2(c_bit1, s98) | (~node3(c_bit1, s98, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s99)) | node2(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15438,plain,
% 36.87/24.68 ((node2(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | (~m_counter_cell_v_value(c_bit1, s99))) <=> ((~m_counter_cell_v_value(c_bit1, s99)) | node2(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 36.87/24.68 inference(rewrite,[status(thm)],[])).
% 36.87/24.68 tff(15439,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | (~m_counter_cell_v_value(c_bit1, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s99)) | node2(c_bit1, s98) | (~node3(c_bit1, s98, s99))))),
% 36.87/24.68 inference(monotonicity,[status(thm)],[15438])).
% 36.87/24.68 tff(15440,plain,
% 36.87/24.68 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | (~m_counter_cell_v_value(c_bit1, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s99)) | node2(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 36.87/24.68 inference(transitivity,[status(thm)],[15439, 15437])).
% 36.87/24.68 tff(15441,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | (~m_counter_cell_v_value(c_bit1, s99)))),
% 36.87/24.68 inference(quant_inst,[status(thm)],[])).
% 36.87/24.68 tff(15442,plain,
% 36.87/24.68 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s99)) | node2(c_bit1, s98) | (~node3(c_bit1, s98, s99))),
% 36.87/24.68 inference(modus_ponens,[status(thm)],[15441, 15440])).
% 36.87/24.69 tff(15443,plain,
% 36.87/24.69 ((~m_counter_cell_v_value(c_bit1, s99)) | node2(c_bit1, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15442, 234, 15436])).
% 36.87/24.69 tff(15444,plain,
% 36.87/24.69 ($false),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15443, 15432, 15418])).
% 36.87/24.69 tff(15445,plain,((~m_counter_cell_v_value(c_bit1, s98)) | m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | (~node3(c_bit1, s99, s98))), inference(lemma,lemma(discharge,[]))).
% 36.87/24.69 tff(15446,plain,
% 36.87/24.69 (~m_counter_cell_v_value(c_bit1, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15445, 15412, 15400, 15387])).
% 36.87/24.69 tff(15447,plain,
% 36.87/24.69 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98) | (~node1(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98) | (~node1(c_bit1, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15448,plain,
% 36.87/24.69 (((~node1(c_bit1, s98)) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98) | (~node1(c_bit1, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15449,plain,
% 36.87/24.69 (((~![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, s98)) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98) | (~node1(c_bit1, s98))))),
% 36.87/24.69 inference(monotonicity,[status(thm)],[15448])).
% 36.87/24.69 tff(15450,plain,
% 36.87/24.69 (((~![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, s98)) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98) | (~node1(c_bit1, s98)))),
% 36.87/24.69 inference(transitivity,[status(thm)],[15449, 15447])).
% 36.87/24.69 tff(15451,plain,
% 36.87/24.69 ((~![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, s98)) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15452,plain,
% 36.87/24.69 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s98)) | m_counter_cell_v_value(c_bit1, s98) | (~node1(c_bit1, s98))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15451, 15450])).
% 36.87/24.69 tff(15453,plain,
% 36.87/24.69 (m_counter_cell_v_value(c_bit1, s98) | (~node1(c_bit1, s98))),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15452, 170, 15400])).
% 36.87/24.69 tff(15454,plain,
% 36.87/24.69 (~node1(c_bit1, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15453, 15446])).
% 36.87/24.69 tff(15455,plain,
% 36.87/24.69 (((~![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_bit1, s98) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15456,plain,
% 36.87/24.69 ((node1(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | m_counter_cell_v_value(c_bit1, s98)) <=> (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15457,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | m_counter_cell_v_value(c_bit1, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s98))))),
% 36.87/24.69 inference(monotonicity,[status(thm)],[15456])).
% 36.87/24.69 tff(15458,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | m_counter_cell_v_value(c_bit1, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s98)))),
% 36.87/24.69 inference(transitivity,[status(thm)],[15457, 15455])).
% 36.87/24.69 tff(15459,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s99) | (~node3(c_bit1, s99, s98)) | m_counter_cell_v_value(c_bit1, s98))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15460,plain,
% 36.87/24.69 ((~![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_bit1, s98) | node1(c_bit1, s99) | (~node3(c_bit1, s99, s98))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15459, 15458])).
% 36.87/24.69 tff(15461,plain,
% 36.87/24.69 (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15460, 199, 15387])).
% 36.87/24.69 tff(15462,plain,
% 36.87/24.69 (node1(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15461, 15446])).
% 36.87/24.69 tff(15463,plain,
% 36.87/24.69 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node1(c_bit1, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node1(c_bit1, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15464,plain,
% 36.87/24.69 (((~node1(c_bit1, s99)) | m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99))) <=> (m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node1(c_bit1, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15465,plain,
% 36.87/24.69 (((~![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, s99)) | m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node1(c_bit1, s99))))),
% 36.87/24.69 inference(monotonicity,[status(thm)],[15464])).
% 36.87/24.69 tff(15466,plain,
% 36.87/24.69 (((~![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, s99)) | m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node1(c_bit1, s99)))),
% 36.87/24.69 inference(transitivity,[status(thm)],[15465, 15463])).
% 36.87/24.69 tff(15467,plain,
% 36.87/24.69 ((~![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, s99)) | m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15468,plain,
% 36.87/24.69 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s99) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node1(c_bit1, s99))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15467, 15466])).
% 36.87/24.69 tff(15469,plain,
% 36.87/24.69 ((~m_counter_cell_v_value(c_bit1, s99)) | (~node1(c_bit1, s99))),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15468, 3359, 15412])).
% 36.87/24.69 tff(15470,plain,
% 36.87/24.69 (~m_counter_cell_v_value(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15469, 15462])).
% 36.87/24.69 tff(15471,plain,
% 36.87/24.69 (((~![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_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15472,plain,
% 36.87/24.69 ((node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | m_counter_cell_v_value(c_bit1, s99)) <=> (m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15473,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | m_counter_cell_v_value(c_bit1, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99))))),
% 36.87/24.69 inference(monotonicity,[status(thm)],[15472])).
% 36.87/24.69 tff(15474,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | m_counter_cell_v_value(c_bit1, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)))),
% 36.87/24.69 inference(transitivity,[status(thm)],[15473, 15471])).
% 36.87/24.69 tff(15475,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s98) | (~node3(c_bit1, s98, s99)) | m_counter_cell_v_value(c_bit1, s99))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15476,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98) | (~node3(c_bit1, s98, s99))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15475, 15474])).
% 36.87/24.69 tff(15477,plain,
% 36.87/24.69 (m_counter_cell_v_value(c_bit1, s99) | node1(c_bit1, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15476, 199, 15436])).
% 36.87/24.69 tff(15478,plain,
% 36.87/24.69 ($false),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15477, 15470, 15454])).
% 36.87/24.69 tff(15479,plain,(m_counter_cell_v_value(c_bit0, s99) | (~node3(c_bit1, s99, s98)) | (~node3(c_bit0, s99, s98))), inference(lemma,lemma(discharge,[]))).
% 36.87/24.69 tff(15480,plain,
% 36.87/24.69 (m_counter_cell_v_value(c_bit0, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15479, 15381, 15386])).
% 36.87/24.69 tff(15481,plain,
% 36.87/24.69 (~node2(c_bit0, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[14542, 15480])).
% 36.87/24.69 tff(15482,plain,
% 36.87/24.69 (((~![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_bit0, s98)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15483,plain,
% 36.87/24.69 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s98)) | (~m_counter_cell_v_value(c_bit0, s98))) <=> ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15484,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s98))))),
% 36.87/24.69 inference(monotonicity,[status(thm)],[15483])).
% 36.87/24.69 tff(15485,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s98)))),
% 36.87/24.69 inference(transitivity,[status(thm)],[15484, 15482])).
% 36.87/24.69 tff(15486,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s98)) | (~m_counter_cell_v_value(c_bit0, s98)))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15487,plain,
% 36.87/24.69 ((~![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_bit0, s98)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s98))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15486, 15485])).
% 36.87/24.69 tff(15488,plain,
% 36.87/24.69 ((~m_counter_cell_v_value(c_bit0, s98)) | node2(c_bit0, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15487, 234, 15386])).
% 36.87/24.69 tff(15489,plain,
% 36.87/24.69 (~m_counter_cell_v_value(c_bit0, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15488, 15481])).
% 36.87/24.69 tff(15490,plain,
% 36.87/24.69 (~node4(c_bit0, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[8580, 2875, 15489])).
% 36.87/24.69 tff(15491,plain,
% 36.87/24.69 (~m_counter_cell_v_carry_out(c_bit0, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[8588, 15490])).
% 36.87/24.69 tff(15492,plain,
% 36.87/24.69 (~m_counter_cell_v_carry_in(c_bit1, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[8596, 15491])).
% 36.87/24.69 tff(15493,plain,
% 36.87/24.69 (m_counter_cell_v_carry_out(c_bit0, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[8649, 15480])).
% 36.87/24.69 tff(15494,plain,
% 36.87/24.69 (m_counter_cell_v_carry_in(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[8653, 3046, 15493])).
% 36.87/24.69 tff(15495,assumption,(~m_counter_cell_v_value(c_bit1, s98)), introduced(assumption)).
% 36.87/24.69 tff(15496,plain,
% 36.87/24.69 (((~![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_bit1, s98) | m_counter_cell_v_value(c_bit1, s98) | (~node2(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : (m_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, s98) | m_counter_cell_v_value(c_bit1, s98) | (~node2(c_bit1, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15497,plain,
% 36.87/24.69 ((~![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_bit1, s98) | m_counter_cell_v_value(c_bit1, s98) | (~node2(c_bit1, s98)))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15498,plain,
% 36.87/24.69 ((~![I0: $i, X: $i] : (m_counter_cell_v_carry_in(I0, X) | m_counter_cell_v_value(I0, X) | (~node2(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | m_counter_cell_v_value(c_bit1, s98) | (~node2(c_bit1, s98))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15497, 15496])).
% 36.87/24.69 tff(15499,plain,
% 36.87/24.69 (m_counter_cell_v_value(c_bit1, s98) | (~node2(c_bit1, s98))),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15498, 3291, 14443])).
% 36.87/24.69 tff(15500,plain,
% 36.87/24.69 (~node2(c_bit1, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15499, 15495])).
% 36.87/24.69 tff(15501,plain,
% 36.87/24.69 (node1(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15461, 15495])).
% 36.87/24.69 tff(15502,assumption,(m_counter_cell_v_carry_in(c_bit1, s99)), introduced(assumption)).
% 36.87/24.69 tff(15503,plain,
% 36.87/24.69 (m_counter_cell_v_value(c_bit1, s99) | (~node1(c_bit1, s99))),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[8660, 170, 15502])).
% 36.87/24.69 tff(15504,plain,
% 36.87/24.69 (m_counter_cell_v_value(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15503, 15501])).
% 36.87/24.69 tff(15505,plain,
% 36.87/24.69 ($false),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15443, 15504, 15500])).
% 36.87/24.69 tff(15506,plain,(m_counter_cell_v_value(c_bit1, s98) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~node3(c_bit1, s99, s98))), inference(lemma,lemma(discharge,[]))).
% 36.87/24.69 tff(15507,plain,
% 36.87/24.69 (m_counter_cell_v_value(c_bit1, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15506, 15494, 15492, 15381])).
% 36.87/24.69 tff(15508,plain,
% 36.87/24.69 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15509,plain,
% 36.87/24.69 (((~node1(c_bit1, s98)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98))) <=> (m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15510,plain,
% 36.87/24.69 (((~![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, s98)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | (m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98))))),
% 36.87/24.69 inference(monotonicity,[status(thm)],[15509])).
% 36.87/24.69 tff(15511,plain,
% 36.87/24.69 (((~![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, s98)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98)))),
% 36.87/24.69 inference(transitivity,[status(thm)],[15510, 15508])).
% 36.87/24.69 tff(15512,plain,
% 36.87/24.69 ((~![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, s98)) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15513,plain,
% 36.87/24.69 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | m_counter_cell_v_carry_in(I0, X) | (~m_counter_cell_v_value(I0, X)))) | m_counter_cell_v_carry_in(c_bit1, s98) | (~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15512, 15511])).
% 36.87/24.69 tff(15514,plain,
% 36.87/24.69 ((~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98))),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15513, 3359, 15492])).
% 36.87/24.69 tff(15515,plain,
% 36.87/24.69 (~node1(c_bit1, s98)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15514, 15507])).
% 36.87/24.69 tff(15516,plain,
% 36.87/24.69 ((~m_counter_cell_v_value(c_bit1, s98)) | node2(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15424, 234, 15381])).
% 36.87/24.69 tff(15517,plain,
% 36.87/24.69 (node2(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15516, 15507])).
% 36.87/24.69 tff(15518,plain,
% 36.87/24.69 (((~![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_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15519,plain,
% 36.87/24.69 ((~![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_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99)))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15520,plain,
% 36.87/24.69 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | (~node2(I0, X)))) | (~m_counter_cell_v_carry_in(c_bit1, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15519, 15518])).
% 36.87/24.69 tff(15521,plain,
% 36.87/24.69 ((~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99))),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15520, 219, 15494])).
% 36.87/24.69 tff(15522,plain,
% 36.87/24.69 (~m_counter_cell_v_value(c_bit1, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15521, 15517])).
% 36.87/24.69 tff(15523,plain,
% 36.87/24.69 ($false),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15477, 15522, 15515])).
% 36.87/24.69 tff(15524,plain,(~trans(s99, s98)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.69 tff(15525,assumption,(node3(c_bit0, s99, s99)), introduced(assumption)).
% 36.87/24.69 tff(15526,assumption,(m_counter_cell_v_value(c_bit0, s99)), introduced(assumption)).
% 36.87/24.69 tff(15527,plain,
% 36.87/24.69 (~node2(c_bit0, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[14542, 15526])).
% 36.87/24.69 tff(15528,plain,
% 36.87/24.69 (((~![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_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15529,plain,
% 36.87/24.69 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99))) <=> ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15530,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99))))),
% 36.87/24.69 inference(monotonicity,[status(thm)],[15529])).
% 36.87/24.69 tff(15531,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 36.87/24.69 inference(transitivity,[status(thm)],[15530, 15528])).
% 36.87/24.69 tff(15532,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99)))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15533,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s99)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s99))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15532, 15531])).
% 36.87/24.69 tff(15534,plain,
% 36.87/24.69 ($false),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15533, 234, 15526, 15527, 15525])).
% 36.87/24.69 tff(15535,plain,((~node3(c_bit0, s99, s99)) | (~m_counter_cell_v_value(c_bit0, s99))), inference(lemma,lemma(discharge,[]))).
% 36.87/24.69 tff(15536,plain,
% 36.87/24.69 (~m_counter_cell_v_value(c_bit0, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15535, 15525])).
% 36.87/24.69 tff(15537,plain,
% 36.87/24.69 (~node1(c_bit0, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[14577, 15536])).
% 36.87/24.69 tff(15538,plain,
% 36.87/24.69 (((~![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_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15539,plain,
% 36.87/24.69 ((node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | m_counter_cell_v_value(c_bit0, s99)) <=> (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15540,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99))))),
% 36.87/24.69 inference(monotonicity,[status(thm)],[15539])).
% 36.87/24.69 tff(15541,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | m_counter_cell_v_value(c_bit0, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)))),
% 36.87/24.69 inference(transitivity,[status(thm)],[15540, 15538])).
% 36.87/24.69 tff(15542,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s99) | (~node3(c_bit0, s99, s99)) | m_counter_cell_v_value(c_bit0, s99))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15543,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s99) | node1(c_bit0, s99) | (~node3(c_bit0, s99, s99))),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15542, 15541])).
% 36.87/24.69 tff(15544,plain,
% 36.87/24.69 ($false),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15543, 199, 15536, 15537, 15525])).
% 36.87/24.69 tff(15545,plain,(~node3(c_bit0, s99, s99)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.69 tff(15546,plain,
% 36.87/24.69 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s99)) | node3(c_bit0, s99, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s99)) | node3(c_bit0, s99, s99))),
% 36.87/24.69 inference(rewrite,[status(thm)],[])).
% 36.87/24.69 tff(15547,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s99)) | node3(c_bit0, s99, s99))),
% 36.87/24.69 inference(quant_inst,[status(thm)],[])).
% 36.87/24.69 tff(15548,plain,
% 36.87/24.69 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s99)) | node3(c_bit0, s99, s99)),
% 36.87/24.69 inference(modus_ponens,[status(thm)],[15547, 15546])).
% 36.87/24.69 tff(15549,plain,
% 36.87/24.69 ((~trans(s99, s99)) | node3(c_bit0, s99, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15548, 81])).
% 36.87/24.69 tff(15550,plain,
% 36.87/24.69 (~trans(s99, s99)),
% 36.87/24.69 inference(unit_resolution,[status(thm)],[15549, 15545])).
% 36.87/24.69 tff(15551,plain,
% 36.87/24.69 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97) | trans(s99, s98)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[13689, 15550])).
% 36.87/24.70 tff(15552,plain,
% 36.87/24.70 (trans(s99, s0) | trans(s99, s1) | trans(s99, s2) | trans(s99, s3) | trans(s99, s4) | trans(s99, s5) | trans(s99, s6) | trans(s99, s7) | trans(s99, s8) | trans(s99, s9) | trans(s99, s10) | trans(s99, s11) | trans(s99, s12) | trans(s99, s13) | trans(s99, s14) | trans(s99, s15) | trans(s99, s16) | trans(s99, s17) | trans(s99, s18) | trans(s99, s19) | trans(s99, s20) | trans(s99, s21) | trans(s99, s22) | trans(s99, s23) | trans(s99, s24) | trans(s99, s25) | trans(s99, s26) | trans(s99, s27) | trans(s99, s28) | trans(s99, s29) | trans(s99, s30) | trans(s99, s31) | trans(s99, s32) | trans(s99, s33) | trans(s99, s34) | trans(s99, s35) | trans(s99, s36) | trans(s99, s37) | trans(s99, s38) | trans(s99, s39) | trans(s99, s40) | trans(s99, s41) | trans(s99, s42) | trans(s99, s43) | trans(s99, s44) | trans(s99, s45) | trans(s99, s46) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s50) | trans(s99, s51) | trans(s99, s52) | trans(s99, s53) | trans(s99, s54) | trans(s99, s55) | trans(s99, s56) | trans(s99, s57) | trans(s99, s58) | trans(s99, s59) | trans(s99, s60) | trans(s99, s61) | trans(s99, s62) | trans(s99, s63) | trans(s99, s64) | trans(s99, s65) | trans(s99, s66) | trans(s99, s67) | trans(s99, s68) | trans(s99, s69) | trans(s99, s70) | trans(s99, s71) | trans(s99, s72) | trans(s99, s73) | trans(s99, s74) | trans(s99, s75) | trans(s99, s76) | trans(s99, s77) | trans(s99, s78) | trans(s99, s79) | trans(s99, s80) | trans(s99, s81) | trans(s99, s82) | trans(s99, s83) | trans(s99, s84) | trans(s99, s85) | trans(s99, s86) | trans(s99, s87) | trans(s99, s88) | trans(s99, s89) | trans(s99, s90) | trans(s99, s91) | trans(s99, s92) | trans(s99, s93) | trans(s99, s94) | trans(s99, s95) | trans(s99, s96) | trans(s99, s97)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15551, 15524])).
% 36.87/24.70 tff(15553,plain,
% 36.87/24.70 (trans(s99, s33)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15552, 15376, 15366, 15365, 14704, 15364, 15363, 15362, 15361, 14536, 15360, 15359, 14534, 15358, 14532, 15357, 15356, 15355, 15354, 14535, 14533, 14505, 14531, 14523, 14518, 15353, 15352, 15351, 15350, 14530, 15349, 14529, 15348, 14528, 15347, 14527, 14526, 14525, 14524, 15346, 15345, 15344, 15343, 15342, 14522, 14521, 14520, 14519, 15341, 15340, 15339, 15338, 14517, 14507, 15337, 15336, 15335, 15334, 14516, 15333, 15332, 15331, 15330, 15329, 14515, 15328, 15327, 15326, 15325, 14514, 15324, 14513, 15323, 15322, 14512, 14511, 14873, 15024, 14872, 14871, 14870, 14869, 14868, 15321, 14867, 14510, 14509, 15312, 14508, 15265, 15286, 14835, 14593, 14506, 13838, 15311, 15310, 15309])).
% 36.87/24.70 tff(15554,assumption,(~always5(s33)), introduced(assumption)).
% 36.87/24.70 tff(15555,plain,
% 36.87/24.70 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s33) | (~trans(s99, s33)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s33) | (~trans(s99, s33)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15556,plain,
% 36.87/24.70 (((~always5(s99)) | (~trans(s99, s33)) | always5(s33)) <=> ((~always5(s99)) | always5(s33) | (~trans(s99, s33)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15557,plain,
% 36.87/24.70 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s33) | (~trans(s99, s33))))),
% 36.87/24.70 inference(monotonicity,[status(thm)],[15556])).
% 36.87/24.70 tff(15558,plain,
% 36.87/24.70 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s33)) | always5(s33))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s33) | (~trans(s99, s33)))),
% 36.87/24.70 inference(transitivity,[status(thm)],[15557, 15555])).
% 36.87/24.70 tff(15559,plain,
% 36.87/24.70 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s33)) | always5(s33))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15560,plain,
% 36.87/24.70 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s33) | (~trans(s99, s33))),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15559, 15558])).
% 36.87/24.70 tff(15561,plain,
% 36.87/24.70 ($false),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15560, 12903, 25, 13749, 15554])).
% 36.87/24.70 tff(15562,plain,((~trans(s99, s33)) | always5(s33)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.70 tff(15563,plain,
% 36.87/24.70 ($false),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15562, 15553, 14779])).
% 36.87/24.70 tff(15564,plain,(always5(s77) | trans(s99, s31) | trans(s99, s1) | trans(s99, s97) | trans(s99, s0) | trans(s99, s20) | trans(s99, s22) | trans(s99, s16) | trans(s99, s3) | trans(s99, s14) | trans(s99, s7) | trans(s99, s18) | trans(s99, s12) | trans(s99, s13) | trans(s99, s19) | trans(s99, s6) | trans(s99, s11) | trans(s99, s24) | trans(s99, s17) | trans(s99, s15) | trans(s99, s5) | trans(s99, s10) | trans(s99, s9) | trans(s99, s8) | trans(s99, s23) | trans(s99, s4) | trans(s99, s30) | trans(s99, s29) | trans(s99, s27) | trans(s99, s28) | trans(s99, s41) | trans(s99, s25) | trans(s99, s43) | trans(s99, s26) | trans(s99, s42) | trans(s99, s36) | trans(s99, s38) | trans(s99, s47) | trans(s99, s40) | trans(s99, s34) | trans(s99, s2) | trans(s99, s37) | trans(s99, s45) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s21) | trans(s99, s32) | trans(s99, s50) | trans(s99, s51) | trans(s99, s39) | trans(s99, s75) | trans(s99, s72) | trans(s99, s74) | trans(s99, s73) | trans(s99, s69) | trans(s99, s68) | trans(s99, s67) | trans(s99, s66) | trans(s99, s65) | trans(s99, s64) | trans(s99, s61) | trans(s99, s76) | trans(s99, s62) | trans(s99, s60) | trans(s99, s56) | trans(s99, s54) | trans(s99, s55) | trans(s99, s53) | trans(s99, s57) | trans(s99, s59) | trans(s99, s58) | trans(s99, s63) | trans(s99, s44) | trans(s99, s85) | trans(s99, s83) | trans(s99, s84) | trans(s99, s81) | trans(s99, s82) | trans(s99, s79) | trans(s99, s80) | trans(s99, s78) | trans(s99, s86) | trans(s99, s70) | trans(s99, s71) | trans(s99, s87) | trans(s99, s90) | trans(s99, s91) | trans(s99, s88) | trans(s99, s89) | trans(s99, s95) | trans(s99, s96) | trans(s99, s94) | trans(s99, s92) | trans(s99, s93)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.70 tff(15565,plain,
% 36.87/24.70 ($false),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15564, 15308, 15297, 14704, 15286, 14593, 15285, 15275, 15265, 15264, 15254, 15244, 14534, 15234, 14532, 15224, 15214, 15204, 15194, 14535, 14533, 15184, 14531, 14523, 14518, 15174, 15164, 15154, 15144, 14530, 15134, 14529, 15124, 14528, 15114, 14527, 14526, 14525, 14524, 15104, 15094, 14505, 15084, 15074, 14522, 14521, 14520, 14519, 14536, 15064, 15054, 15044, 14517, 15034, 15024, 14735, 15023, 15013, 14516, 15003, 14993, 14983, 14973, 14963, 14515, 14953, 14943, 14933, 14923, 14514, 14913, 14513, 14903, 14893, 14512, 14511, 14883, 14873, 14872, 14871, 14870, 14869, 14868, 14867, 14510, 14509, 14866, 14508, 14507, 14856, 14845, 14835, 14834, 14506, 14793, 13838, 14734])).
% 36.87/24.70 tff(15566,plain,(always5(s94) | trans(s99, s97) | trans(s99, s91) | trans(s99, s89) | trans(s99, s90) | trans(s99, s18) | trans(s99, s13) | trans(s99, s17) | trans(s99, s15) | trans(s99, s10) | trans(s99, s9) | trans(s99, s8) | trans(s99, s27) | trans(s99, s41) | trans(s99, s43) | trans(s99, s42) | trans(s99, s36) | trans(s99, s38) | trans(s99, s47) | trans(s99, s5) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s3) | trans(s99, s39) | trans(s99, s83) | always5(s77) | trans(s99, s68) | trans(s99, s76) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s44) | trans(s99, s85) | trans(s99, s84) | trans(s99, s81) | trans(s99, s82) | trans(s99, s79) | trans(s99, s80) | trans(s99, s78) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s75) | trans(s99, s88) | trans(s99, s95) | trans(s99, s96)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.70 tff(15567,plain,
% 36.87/24.70 ($false),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15566, 14724, 14723, 14713, 14593, 14704, 14536, 14596, 14535, 14534, 14533, 14532, 14531, 14530, 14529, 14528, 14527, 14526, 14525, 14524, 14523, 14522, 14521, 14520, 14519, 14518, 14517, 14703, 14702, 14516, 14515, 14514, 14513, 14512, 14511, 14692, 14682, 14672, 14662, 14652, 14642, 14632, 14510, 14509, 14508, 14507, 14612, 14506, 14505])).
% 36.87/24.70 tff(15568,plain,(always5(s96) | trans(s99, s89) | trans(s99, s97) | trans(s99, s3) | trans(s99, s17) | trans(s99, s18) | trans(s99, s15) | trans(s99, s13) | trans(s99, s10) | trans(s99, s27) | trans(s99, s41) | trans(s99, s43) | trans(s99, s42) | trans(s99, s36) | trans(s99, s38) | trans(s99, s47) | trans(s99, s9) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s8) | trans(s99, s39) | trans(s99, s68) | trans(s99, s76) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s44) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s75) | trans(s99, s95) | trans(s99, s5)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.70 tff(15569,plain,
% 36.87/24.70 (always5(s96)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15568, 14593, 14592, 14536, 14535, 14534, 14533, 14532, 14531, 14530, 14529, 14528, 14527, 14526, 14525, 14524, 14523, 14522, 14521, 14520, 14519, 14518, 14517, 14516, 14515, 14514, 14513, 14512, 14511, 14510, 14509, 14508, 14507, 14506, 14505])).
% 36.87/24.70 tff(15570,plain,
% 36.87/24.70 (always5(s97)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[47, 15569])).
% 36.87/24.70 tff(15571,plain,
% 36.87/24.70 (~m_counter_cell_v_carry_out(c_bit2, s97)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[61, 58, 15570])).
% 36.87/24.70 tff(15572,plain,
% 36.87/24.70 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s96)) | (~m_counter_cell_v_carry_out(c_bit2, s96)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s96)) | (~m_counter_cell_v_carry_out(c_bit2, s96)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15573,plain,
% 36.87/24.70 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s96)) | (~m_counter_cell_v_carry_out(c_bit2, s96)))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15574,plain,
% 36.87/24.70 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s96)) | (~m_counter_cell_v_carry_out(c_bit2, s96))),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15573, 15572])).
% 36.87/24.70 tff(15575,plain,
% 36.87/24.70 (~m_counter_cell_v_carry_out(c_bit2, s96)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15574, 58, 15569])).
% 36.87/24.70 tff(15576,plain,
% 36.87/24.70 (~always5(s92)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8702, 15288])).
% 36.87/24.70 tff(15577,plain,
% 36.87/24.70 (~always5(s91)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8710, 15576])).
% 36.87/24.70 tff(15578,plain,
% 36.87/24.70 (~always5(s90)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8718, 15577])).
% 36.87/24.70 tff(15579,plain,
% 36.87/24.70 (~always5(s89)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8726, 15578])).
% 36.87/24.70 tff(15580,plain,
% 36.87/24.70 (~always5(s88)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8734, 15579])).
% 36.87/24.70 tff(15581,plain,
% 36.87/24.70 (~trans(s99, s88)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14611, 15580])).
% 36.87/24.70 tff(15582,plain,
% 36.87/24.70 (~always5(s87)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8742, 15580])).
% 36.87/24.70 tff(15583,plain,
% 36.87/24.70 (~always5(s86)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8750, 15582])).
% 36.87/24.70 tff(15584,plain,
% 36.87/24.70 (~always5(s85)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8758, 15583])).
% 36.87/24.70 tff(15585,plain,
% 36.87/24.70 (~always5(s84)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8766, 15584])).
% 36.87/24.70 tff(15586,plain,
% 36.87/24.70 (~always5(s83)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8774, 15585])).
% 36.87/24.70 tff(15587,plain,
% 36.87/24.70 (~always5(s82)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8782, 15586])).
% 36.87/24.70 tff(15588,plain,
% 36.87/24.70 (~always5(s81)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8790, 15587])).
% 36.87/24.70 tff(15589,plain,
% 36.87/24.70 (~always5(s80)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8798, 15588])).
% 36.87/24.70 tff(15590,plain,
% 36.87/24.70 (~always5(s79)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8806, 15589])).
% 36.87/24.70 tff(15591,plain,
% 36.87/24.70 (~always5(s78)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8814, 15590])).
% 36.87/24.70 tff(15592,plain,
% 36.87/24.70 (~trans(s99, s78)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14631, 15591])).
% 36.87/24.70 tff(15593,plain,
% 36.87/24.70 (~trans(s99, s80)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14641, 15589])).
% 36.87/24.70 tff(15594,plain,
% 36.87/24.70 (~trans(s99, s81)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14651, 15588])).
% 36.87/24.70 tff(15595,plain,
% 36.87/24.70 (~trans(s99, s82)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14661, 15587])).
% 36.87/24.70 tff(15596,plain,
% 36.87/24.70 (~trans(s99, s83)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14671, 15586])).
% 36.87/24.70 tff(15597,plain,
% 36.87/24.70 (~trans(s99, s84)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14681, 15585])).
% 36.87/24.70 tff(15598,plain,
% 36.87/24.70 (~trans(s99, s85)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14691, 15584])).
% 36.87/24.70 tff(15599,plain,
% 36.87/24.70 (~trans(s99, s90)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14701, 15578])).
% 36.87/24.70 tff(15600,plain,
% 36.87/24.70 (~trans(s99, s79)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[14722, 15590])).
% 36.87/24.70 tff(15601,plain,
% 36.87/24.70 (always5(s94)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15566, 15600, 14735, 14593, 14592, 14536, 13838, 14535, 14534, 14533, 14532, 14531, 14530, 14529, 14528, 14527, 14526, 14525, 14524, 14523, 14522, 14521, 14520, 14519, 14518, 14517, 15286, 15599, 14516, 14515, 14514, 14513, 14512, 14511, 15598, 15597, 15596, 15595, 15594, 15593, 15592, 14510, 14509, 14508, 14507, 15581, 14506, 14505])).
% 36.87/24.70 tff(15602,plain,
% 36.87/24.70 (always5(s95)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8686, 15601])).
% 36.87/24.70 tff(15603,plain,
% 36.87/24.70 (~m_counter_cell_v_carry_out(c_bit2, s95)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[65, 58, 15602])).
% 36.87/24.70 tff(15604,plain,
% 36.87/24.70 (~node4(c_bit1, s98)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8600, 3076, 14443])).
% 36.87/24.70 tff(15605,plain,
% 36.87/24.70 (~m_counter_cell_v_carry_out(c_bit1, s98)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8604, 2887, 15604])).
% 36.87/24.70 tff(15606,plain,
% 36.87/24.70 (~m_counter_cell_v_carry_in(c_bit2, s98)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8608, 3167, 15605])).
% 36.87/24.70 tff(15607,assumption,(node3(c_bit0, s99, s1)), introduced(assumption)).
% 36.87/24.70 tff(15608,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s1)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s1)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s1)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15609,plain,
% 36.87/24.70 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s1)) | (~m_counter_cell_v_value(c_bit0, s1))) <=> ((~m_counter_cell_v_value(c_bit0, s1)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s1)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15610,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s1)) | (~m_counter_cell_v_value(c_bit0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s1)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s1))))),
% 36.87/24.70 inference(monotonicity,[status(thm)],[15609])).
% 36.87/24.70 tff(15611,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s1)) | (~m_counter_cell_v_value(c_bit0, s1)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s1)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s1)))),
% 36.87/24.70 inference(transitivity,[status(thm)],[15610, 15608])).
% 36.87/24.70 tff(15612,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s1)) | (~m_counter_cell_v_value(c_bit0, s1)))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15613,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s1)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s1))),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15612, 15611])).
% 36.87/24.70 tff(15614,plain,
% 36.87/24.70 ($false),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15613, 234, 14545, 207, 15607])).
% 36.87/24.70 tff(15615,plain,((~node3(c_bit0, s99, s1)) | node2(c_bit0, s99)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.70 tff(15616,plain,
% 36.87/24.70 (~node3(c_bit0, s99, s1)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15615, 14543])).
% 36.87/24.70 tff(15617,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s1)) | node3(c_bit0, s99, s1))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s1)) | node3(c_bit0, s99, s1))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15618,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s1)) | node3(c_bit0, s99, s1))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15619,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s1)) | node3(c_bit0, s99, s1)),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15618, 15617])).
% 36.87/24.70 tff(15620,plain,
% 36.87/24.70 ((~trans(s99, s1)) | node3(c_bit0, s99, s1)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15619, 81])).
% 36.87/24.70 tff(15621,plain,
% 36.87/24.70 (~trans(s99, s1)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15620, 15616])).
% 36.87/24.70 tff(15622,plain,
% 36.87/24.70 (~trans(s99, s92)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15307, 15576])).
% 36.87/24.70 tff(15623,assumption,(node3(c_bit0, s99, s31)), introduced(assumption)).
% 36.87/24.70 tff(15624,assumption,(m_counter_cell_v_value(c_bit0, s31)), introduced(assumption)).
% 36.87/24.70 tff(15625,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s31)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15626,plain,
% 36.87/24.70 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s31)) | (~m_counter_cell_v_value(c_bit0, s31))) <=> ((~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s31)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15627,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s31)) | (~m_counter_cell_v_value(c_bit0, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s31))))),
% 36.87/24.70 inference(monotonicity,[status(thm)],[15626])).
% 36.87/24.70 tff(15628,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s31)) | (~m_counter_cell_v_value(c_bit0, s31)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s31)))),
% 36.87/24.70 inference(transitivity,[status(thm)],[15627, 15625])).
% 36.87/24.70 tff(15629,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s31)) | (~m_counter_cell_v_value(c_bit0, s31)))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15630,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s31))),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15629, 15628])).
% 36.87/24.70 tff(15631,plain,
% 36.87/24.70 ($false),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15630, 234, 15624, 14545, 15623])).
% 36.87/24.70 tff(15632,plain,((~node3(c_bit0, s99, s31)) | (~m_counter_cell_v_value(c_bit0, s31)) | node2(c_bit0, s99)), inference(lemma,lemma(discharge,[]))).
% 36.87/24.70 tff(15633,plain,
% 36.87/24.70 ((~node3(c_bit0, s99, s31)) | node2(c_bit0, s99)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15632, 1029])).
% 36.87/24.70 tff(15634,plain,
% 36.87/24.70 (~node3(c_bit0, s99, s31)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15633, 14543])).
% 36.87/24.70 tff(15635,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s31)) | node3(c_bit0, s99, s31))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s31)) | node3(c_bit0, s99, s31))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15636,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s31)) | node3(c_bit0, s99, s31))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15637,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s31)) | node3(c_bit0, s99, s31)),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15636, 15635])).
% 36.87/24.70 tff(15638,plain,
% 36.87/24.70 ((~trans(s99, s31)) | node3(c_bit0, s99, s31)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15637, 81])).
% 36.87/24.70 tff(15639,plain,
% 36.87/24.70 (~trans(s99, s31)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15638, 15634])).
% 36.87/24.70 tff(15640,plain,
% 36.87/24.70 (~trans(s99, s33)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15562, 14779])).
% 36.87/24.70 tff(15641,plain,
% 36.87/24.70 (~trans(s99, s93)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15296, 15288])).
% 36.87/24.70 tff(15642,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s94) | (~node3(c_bit0, s94, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15643,plain,
% 36.87/24.70 ((node2(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | (~m_counter_cell_v_value(c_bit0, s95))) <=> ((~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15644,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | (~m_counter_cell_v_value(c_bit0, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s94) | (~node3(c_bit0, s94, s95))))),
% 36.87/24.70 inference(monotonicity,[status(thm)],[15643])).
% 36.87/24.70 tff(15645,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | (~m_counter_cell_v_value(c_bit0, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s94) | (~node3(c_bit0, s94, s95)))),
% 36.87/24.70 inference(transitivity,[status(thm)],[15644, 15642])).
% 36.87/24.70 tff(15646,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s94) | (~node3(c_bit0, s94, s95)) | (~m_counter_cell_v_value(c_bit0, s95)))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15647,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s94) | (~node3(c_bit0, s94, s95))),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15646, 15645])).
% 36.87/24.70 tff(15648,plain,
% 36.87/24.70 ((~m_counter_cell_v_value(c_bit0, s95)) | node2(c_bit0, s94)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15647, 234, 8270])).
% 36.87/24.70 tff(15649,plain,
% 36.87/24.70 (node2(c_bit0, s94)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15648, 14502])).
% 36.87/24.70 tff(15650,plain,
% 36.87/24.70 (((~![I0: $i, X: $i] : ((~m_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, s94)) | (~m_counter_cell_v_value(c_bit0, s94)) | (~node2(c_bit0, s94)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s94)) | (~m_counter_cell_v_value(c_bit0, s94)) | (~node2(c_bit0, s94)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15651,plain,
% 36.87/24.70 ((~![I0: $i, X: $i] : ((~m_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, s94)) | (~m_counter_cell_v_value(c_bit0, s94)) | (~node2(c_bit0, s94)))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15652,plain,
% 36.87/24.70 ((~![I0: $i, X: $i] : ((~m_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, s94)) | (~m_counter_cell_v_value(c_bit0, s94)) | (~node2(c_bit0, s94))),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15651, 15650])).
% 36.87/24.70 tff(15653,plain,
% 36.87/24.70 ((~m_counter_cell_v_value(c_bit0, s94)) | (~node2(c_bit0, s94))),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15652, 219, 8258])).
% 36.87/24.70 tff(15654,plain,
% 36.87/24.70 (~m_counter_cell_v_value(c_bit0, s94)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15653, 15649])).
% 36.87/24.70 tff(15655,plain,
% 36.87/24.70 (((~![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_bit0, s94) | node1(c_bit0, s93) | (~node3(c_bit0, s93, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s94) | node1(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15656,plain,
% 36.87/24.70 ((node1(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | m_counter_cell_v_value(c_bit0, s94)) <=> (m_counter_cell_v_value(c_bit0, s94) | node1(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15657,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | m_counter_cell_v_value(c_bit0, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s94) | node1(c_bit0, s93) | (~node3(c_bit0, s93, s94))))),
% 36.87/24.70 inference(monotonicity,[status(thm)],[15656])).
% 36.87/24.70 tff(15658,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | m_counter_cell_v_value(c_bit0, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s94) | node1(c_bit0, s93) | (~node3(c_bit0, s93, s94)))),
% 36.87/24.70 inference(transitivity,[status(thm)],[15657, 15655])).
% 36.87/24.70 tff(15659,plain,
% 36.87/24.70 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s93) | (~node3(c_bit0, s93, s94)) | m_counter_cell_v_value(c_bit0, s94))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15660,plain,
% 36.87/24.70 ((~![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_bit0, s94) | node1(c_bit0, s93) | (~node3(c_bit0, s93, s94))),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15659, 15658])).
% 36.87/24.70 tff(15661,plain,
% 36.87/24.70 (m_counter_cell_v_value(c_bit0, s94) | node1(c_bit0, s93)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15660, 199, 2860])).
% 36.87/24.70 tff(15662,plain,
% 36.87/24.70 (node1(c_bit0, s93)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15661, 15654])).
% 36.87/24.70 tff(15663,plain,
% 36.87/24.70 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93) | (~node1(c_bit0, s93)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93) | (~node1(c_bit0, s93)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15664,plain,
% 36.87/24.70 (((~node1(c_bit0, s93)) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93) | (~node1(c_bit0, s93)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15665,plain,
% 36.87/24.70 (((~![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, s93)) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93) | (~node1(c_bit0, s93))))),
% 36.87/24.70 inference(monotonicity,[status(thm)],[15664])).
% 36.87/24.70 tff(15666,plain,
% 36.87/24.70 (((~![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, s93)) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93) | (~node1(c_bit0, s93)))),
% 36.87/24.70 inference(transitivity,[status(thm)],[15665, 15663])).
% 36.87/24.70 tff(15667,plain,
% 36.87/24.70 ((~![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, s93)) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93))),
% 36.87/24.70 inference(quant_inst,[status(thm)],[])).
% 36.87/24.70 tff(15668,plain,
% 36.87/24.70 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s93)) | m_counter_cell_v_value(c_bit0, s93) | (~node1(c_bit0, s93))),
% 36.87/24.70 inference(modus_ponens,[status(thm)],[15667, 15666])).
% 36.87/24.70 tff(15669,plain,
% 36.87/24.70 (m_counter_cell_v_value(c_bit0, s93) | (~node1(c_bit0, s93))),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15668, 170, 2844])).
% 36.87/24.70 tff(15670,plain,
% 36.87/24.70 (m_counter_cell_v_value(c_bit0, s93)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[15669, 15662])).
% 36.87/24.70 tff(15671,plain,
% 36.87/24.70 (node2(c_bit0, s92)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8208, 15670])).
% 36.87/24.70 tff(15672,plain,
% 36.87/24.70 (~m_counter_cell_v_value(c_bit0, s92)),
% 36.87/24.70 inference(unit_resolution,[status(thm)],[8200, 15671])).
% 36.87/24.70 tff(15673,plain,
% 36.87/24.70 (((~![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_bit0, s92) | node1(c_bit0, s91) | (~node3(c_bit0, s91, s92)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s92) | node1(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15674,plain,
% 36.87/24.70 ((node1(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | m_counter_cell_v_value(c_bit0, s92)) <=> (m_counter_cell_v_value(c_bit0, s92) | node1(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 36.87/24.70 inference(rewrite,[status(thm)],[])).
% 36.87/24.70 tff(15675,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | m_counter_cell_v_value(c_bit0, s92))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s92) | node1(c_bit0, s91) | (~node3(c_bit0, s91, s92))))),
% 36.87/24.70 inference(monotonicity,[status(thm)],[15674])).
% 36.87/24.70 tff(15676,plain,
% 36.87/24.70 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | m_counter_cell_v_value(c_bit0, s92))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s92) | node1(c_bit0, s91) | (~node3(c_bit0, s91, s92)))),
% 36.87/24.70 inference(transitivity,[status(thm)],[15675, 15673])).
% 36.87/24.71 tff(15677,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s91) | (~node3(c_bit0, s91, s92)) | m_counter_cell_v_value(c_bit0, s92))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15678,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s92) | node1(c_bit0, s91) | (~node3(c_bit0, s91, s92))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15677, 15676])).
% 36.87/24.71 tff(15679,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s92) | node1(c_bit0, s91)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15678, 199, 2801])).
% 36.87/24.71 tff(15680,plain,
% 36.87/24.71 (node1(c_bit0, s91)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15679, 15672])).
% 36.87/24.71 tff(15681,plain,
% 36.87/24.71 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91) | (~node1(c_bit0, s91)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91) | (~node1(c_bit0, s91)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15682,plain,
% 36.87/24.71 (((~node1(c_bit0, s91)) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91) | (~node1(c_bit0, s91)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15683,plain,
% 36.87/24.71 (((~![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, s91)) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91) | (~node1(c_bit0, s91))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15682])).
% 36.87/24.71 tff(15684,plain,
% 36.87/24.71 (((~![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, s91)) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91) | (~node1(c_bit0, s91)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15683, 15681])).
% 36.87/24.71 tff(15685,plain,
% 36.87/24.71 ((~![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, s91)) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15686,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s91)) | m_counter_cell_v_value(c_bit0, s91) | (~node1(c_bit0, s91))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15685, 15684])).
% 36.87/24.71 tff(15687,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s91) | (~node1(c_bit0, s91))),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15686, 170, 2785])).
% 36.87/24.71 tff(15688,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s91)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15687, 15680])).
% 36.87/24.71 tff(15689,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s91)) | node2(c_bit0, s90) | (~node3(c_bit0, s90, s91)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s91)) | node2(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15690,plain,
% 36.87/24.71 ((node2(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | (~m_counter_cell_v_value(c_bit0, s91))) <=> ((~m_counter_cell_v_value(c_bit0, s91)) | node2(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15691,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | (~m_counter_cell_v_value(c_bit0, s91)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s91)) | node2(c_bit0, s90) | (~node3(c_bit0, s90, s91))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15690])).
% 36.87/24.71 tff(15692,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | (~m_counter_cell_v_value(c_bit0, s91)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s91)) | node2(c_bit0, s90) | (~node3(c_bit0, s90, s91)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15691, 15689])).
% 36.87/24.71 tff(15693,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s90) | (~node3(c_bit0, s90, s91)) | (~m_counter_cell_v_value(c_bit0, s91)))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15694,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s91)) | node2(c_bit0, s90) | (~node3(c_bit0, s90, s91))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15693, 15692])).
% 36.87/24.71 tff(15695,plain,
% 36.87/24.71 ((~m_counter_cell_v_value(c_bit0, s91)) | node2(c_bit0, s90)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15694, 234, 2775])).
% 36.87/24.71 tff(15696,plain,
% 36.87/24.71 (node2(c_bit0, s90)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15695, 15688])).
% 36.87/24.71 tff(15697,plain,
% 36.87/24.71 (((~![I0: $i, X: $i] : ((~m_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, s90)) | (~m_counter_cell_v_value(c_bit0, s90)) | (~node2(c_bit0, s90)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s90)) | (~m_counter_cell_v_value(c_bit0, s90)) | (~node2(c_bit0, s90)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15698,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~m_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, s90)) | (~m_counter_cell_v_value(c_bit0, s90)) | (~node2(c_bit0, s90)))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15699,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~m_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, s90)) | (~m_counter_cell_v_value(c_bit0, s90)) | (~node2(c_bit0, s90))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15698, 15697])).
% 36.87/24.71 tff(15700,plain,
% 36.87/24.71 ((~m_counter_cell_v_value(c_bit0, s90)) | (~node2(c_bit0, s90))),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15699, 219, 2756])).
% 36.87/24.71 tff(15701,plain,
% 36.87/24.71 (~m_counter_cell_v_value(c_bit0, s90)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15700, 15696])).
% 36.87/24.71 tff(15702,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s90) | node1(c_bit0, s89) | (~node3(c_bit0, s89, s90)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s90) | node1(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15703,plain,
% 36.87/24.71 ((node1(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | m_counter_cell_v_value(c_bit0, s90)) <=> (m_counter_cell_v_value(c_bit0, s90) | node1(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15704,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | m_counter_cell_v_value(c_bit0, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s90) | node1(c_bit0, s89) | (~node3(c_bit0, s89, s90))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15703])).
% 36.87/24.71 tff(15705,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | m_counter_cell_v_value(c_bit0, s90))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s90) | node1(c_bit0, s89) | (~node3(c_bit0, s89, s90)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15704, 15702])).
% 36.87/24.71 tff(15706,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s89) | (~node3(c_bit0, s89, s90)) | m_counter_cell_v_value(c_bit0, s90))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15707,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s90) | node1(c_bit0, s89) | (~node3(c_bit0, s89, s90))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15706, 15705])).
% 36.87/24.71 tff(15708,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s90) | node1(c_bit0, s89)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15707, 199, 2746])).
% 36.87/24.71 tff(15709,plain,
% 36.87/24.71 (node1(c_bit0, s89)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15708, 15701])).
% 36.87/24.71 tff(15710,plain,
% 36.87/24.71 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89) | (~node1(c_bit0, s89)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89) | (~node1(c_bit0, s89)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15711,plain,
% 36.87/24.71 (((~node1(c_bit0, s89)) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89) | (~node1(c_bit0, s89)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15712,plain,
% 36.87/24.71 (((~![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, s89)) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89) | (~node1(c_bit0, s89))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15711])).
% 36.87/24.71 tff(15713,plain,
% 36.87/24.71 (((~![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, s89)) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89) | (~node1(c_bit0, s89)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15712, 15710])).
% 36.87/24.71 tff(15714,plain,
% 36.87/24.71 ((~![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, s89)) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15715,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s89)) | m_counter_cell_v_value(c_bit0, s89) | (~node1(c_bit0, s89))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15714, 15713])).
% 36.87/24.71 tff(15716,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s89) | (~node1(c_bit0, s89))),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15715, 170, 2730])).
% 36.87/24.71 tff(15717,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s89)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15716, 15709])).
% 36.87/24.71 tff(15718,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s89)) | node2(c_bit0, s88) | (~node3(c_bit0, s88, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s89)) | node2(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15719,plain,
% 36.87/24.71 ((node2(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | (~m_counter_cell_v_value(c_bit0, s89))) <=> ((~m_counter_cell_v_value(c_bit0, s89)) | node2(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15720,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | (~m_counter_cell_v_value(c_bit0, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s89)) | node2(c_bit0, s88) | (~node3(c_bit0, s88, s89))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15719])).
% 36.87/24.71 tff(15721,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | (~m_counter_cell_v_value(c_bit0, s89)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s89)) | node2(c_bit0, s88) | (~node3(c_bit0, s88, s89)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15720, 15718])).
% 36.87/24.71 tff(15722,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s88) | (~node3(c_bit0, s88, s89)) | (~m_counter_cell_v_value(c_bit0, s89)))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15723,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s89)) | node2(c_bit0, s88) | (~node3(c_bit0, s88, s89))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15722, 15721])).
% 36.87/24.71 tff(15724,plain,
% 36.87/24.71 ((~m_counter_cell_v_value(c_bit0, s89)) | node2(c_bit0, s88)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15723, 234, 2718])).
% 36.87/24.71 tff(15725,plain,
% 36.87/24.71 (node2(c_bit0, s88)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15724, 15717])).
% 36.87/24.71 tff(15726,plain,
% 36.87/24.71 (((~![I0: $i, X: $i] : ((~m_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, s88)) | (~m_counter_cell_v_value(c_bit0, s88)) | (~node2(c_bit0, s88)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s88)) | (~m_counter_cell_v_value(c_bit0, s88)) | (~node2(c_bit0, s88)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15727,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~m_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, s88)) | (~m_counter_cell_v_value(c_bit0, s88)) | (~node2(c_bit0, s88)))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15728,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~m_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, s88)) | (~m_counter_cell_v_value(c_bit0, s88)) | (~node2(c_bit0, s88))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15727, 15726])).
% 36.87/24.71 tff(15729,plain,
% 36.87/24.71 ((~m_counter_cell_v_value(c_bit0, s88)) | (~node2(c_bit0, s88))),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15728, 219, 2699])).
% 36.87/24.71 tff(15730,plain,
% 36.87/24.71 (~m_counter_cell_v_value(c_bit0, s88)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15729, 15725])).
% 36.87/24.71 tff(15731,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s88) | node1(c_bit0, s87) | (~node3(c_bit0, s87, s88)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s88) | node1(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15732,plain,
% 36.87/24.71 ((node1(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | m_counter_cell_v_value(c_bit0, s88)) <=> (m_counter_cell_v_value(c_bit0, s88) | node1(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15733,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | m_counter_cell_v_value(c_bit0, s88))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s88) | node1(c_bit0, s87) | (~node3(c_bit0, s87, s88))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15732])).
% 36.87/24.71 tff(15734,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | m_counter_cell_v_value(c_bit0, s88))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s88) | node1(c_bit0, s87) | (~node3(c_bit0, s87, s88)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15733, 15731])).
% 36.87/24.71 tff(15735,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s87) | (~node3(c_bit0, s87, s88)) | m_counter_cell_v_value(c_bit0, s88))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15736,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s88) | node1(c_bit0, s87) | (~node3(c_bit0, s87, s88))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15735, 15734])).
% 36.87/24.71 tff(15737,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s88) | node1(c_bit0, s87)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15736, 199, 2687])).
% 36.87/24.71 tff(15738,plain,
% 36.87/24.71 (node1(c_bit0, s87)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15737, 15730])).
% 36.87/24.71 tff(15739,plain,
% 36.87/24.71 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87) | (~node1(c_bit0, s87)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87) | (~node1(c_bit0, s87)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15740,plain,
% 36.87/24.71 (((~node1(c_bit0, s87)) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87) | (~node1(c_bit0, s87)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15741,plain,
% 36.87/24.71 (((~![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, s87)) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87) | (~node1(c_bit0, s87))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15740])).
% 36.87/24.71 tff(15742,plain,
% 36.87/24.71 (((~![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, s87)) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87) | (~node1(c_bit0, s87)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15741, 15739])).
% 36.87/24.71 tff(15743,plain,
% 36.87/24.71 ((~![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, s87)) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15744,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s87)) | m_counter_cell_v_value(c_bit0, s87) | (~node1(c_bit0, s87))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15743, 15742])).
% 36.87/24.71 tff(15745,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s87) | (~node1(c_bit0, s87))),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15744, 170, 2671])).
% 36.87/24.71 tff(15746,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s87)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15745, 15738])).
% 36.87/24.71 tff(15747,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s87)) | node2(c_bit0, s86) | (~node3(c_bit0, s86, s87)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s87)) | node2(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15748,plain,
% 36.87/24.71 ((node2(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | (~m_counter_cell_v_value(c_bit0, s87))) <=> ((~m_counter_cell_v_value(c_bit0, s87)) | node2(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15749,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | (~m_counter_cell_v_value(c_bit0, s87)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s87)) | node2(c_bit0, s86) | (~node3(c_bit0, s86, s87))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15748])).
% 36.87/24.71 tff(15750,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | (~m_counter_cell_v_value(c_bit0, s87)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s87)) | node2(c_bit0, s86) | (~node3(c_bit0, s86, s87)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15749, 15747])).
% 36.87/24.71 tff(15751,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s86) | (~node3(c_bit0, s86, s87)) | (~m_counter_cell_v_value(c_bit0, s87)))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15752,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s87)) | node2(c_bit0, s86) | (~node3(c_bit0, s86, s87))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15751, 15750])).
% 36.87/24.71 tff(15753,plain,
% 36.87/24.71 ((~m_counter_cell_v_value(c_bit0, s87)) | node2(c_bit0, s86)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15752, 234, 2659])).
% 36.87/24.71 tff(15754,plain,
% 36.87/24.71 (node2(c_bit0, s86)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15753, 15746])).
% 36.87/24.71 tff(15755,plain,
% 36.87/24.71 (((~![I0: $i, X: $i] : ((~m_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, s86)) | (~m_counter_cell_v_value(c_bit0, s86)) | (~node2(c_bit0, s86)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s86)) | (~m_counter_cell_v_value(c_bit0, s86)) | (~node2(c_bit0, s86)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15756,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~m_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, s86)) | (~m_counter_cell_v_value(c_bit0, s86)) | (~node2(c_bit0, s86)))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15757,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~m_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, s86)) | (~m_counter_cell_v_value(c_bit0, s86)) | (~node2(c_bit0, s86))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15756, 15755])).
% 36.87/24.71 tff(15758,plain,
% 36.87/24.71 ((~m_counter_cell_v_value(c_bit0, s86)) | (~node2(c_bit0, s86))),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15757, 219, 2640])).
% 36.87/24.71 tff(15759,plain,
% 36.87/24.71 (~m_counter_cell_v_value(c_bit0, s86)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15758, 15754])).
% 36.87/24.71 tff(15760,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s86) | node1(c_bit0, s85) | (~node3(c_bit0, s85, s86)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s86) | node1(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15761,plain,
% 36.87/24.71 ((node1(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | m_counter_cell_v_value(c_bit0, s86)) <=> (m_counter_cell_v_value(c_bit0, s86) | node1(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15762,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | m_counter_cell_v_value(c_bit0, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s86) | node1(c_bit0, s85) | (~node3(c_bit0, s85, s86))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15761])).
% 36.87/24.71 tff(15763,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | m_counter_cell_v_value(c_bit0, s86))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s86) | node1(c_bit0, s85) | (~node3(c_bit0, s85, s86)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15762, 15760])).
% 36.87/24.71 tff(15764,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s85) | (~node3(c_bit0, s85, s86)) | m_counter_cell_v_value(c_bit0, s86))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15765,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s86) | node1(c_bit0, s85) | (~node3(c_bit0, s85, s86))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15764, 15763])).
% 36.87/24.71 tff(15766,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s86) | node1(c_bit0, s85)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15765, 199, 2628])).
% 36.87/24.71 tff(15767,plain,
% 36.87/24.71 (node1(c_bit0, s85)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15766, 15759])).
% 36.87/24.71 tff(15768,plain,
% 36.87/24.71 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85) | (~node1(c_bit0, s85)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85) | (~node1(c_bit0, s85)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15769,plain,
% 36.87/24.71 (((~node1(c_bit0, s85)) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85) | (~node1(c_bit0, s85)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15770,plain,
% 36.87/24.71 (((~![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, s85)) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85) | (~node1(c_bit0, s85))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15769])).
% 36.87/24.71 tff(15771,plain,
% 36.87/24.71 (((~![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, s85)) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85) | (~node1(c_bit0, s85)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15770, 15768])).
% 36.87/24.71 tff(15772,plain,
% 36.87/24.71 ((~![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, s85)) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15773,plain,
% 36.87/24.71 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s85)) | m_counter_cell_v_value(c_bit0, s85) | (~node1(c_bit0, s85))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15772, 15771])).
% 36.87/24.71 tff(15774,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s85) | (~node1(c_bit0, s85))),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15773, 170, 2612])).
% 36.87/24.71 tff(15775,plain,
% 36.87/24.71 (m_counter_cell_v_value(c_bit0, s85)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15774, 15767])).
% 36.87/24.71 tff(15776,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s84) | (~node3(c_bit0, s84, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15777,plain,
% 36.87/24.71 ((node2(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | (~m_counter_cell_v_value(c_bit0, s85))) <=> ((~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 36.87/24.71 inference(rewrite,[status(thm)],[])).
% 36.87/24.71 tff(15778,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | (~m_counter_cell_v_value(c_bit0, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s84) | (~node3(c_bit0, s84, s85))))),
% 36.87/24.71 inference(monotonicity,[status(thm)],[15777])).
% 36.87/24.71 tff(15779,plain,
% 36.87/24.71 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | (~m_counter_cell_v_value(c_bit0, s85)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s84) | (~node3(c_bit0, s84, s85)))),
% 36.87/24.71 inference(transitivity,[status(thm)],[15778, 15776])).
% 36.87/24.71 tff(15780,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s84) | (~node3(c_bit0, s84, s85)) | (~m_counter_cell_v_value(c_bit0, s85)))),
% 36.87/24.71 inference(quant_inst,[status(thm)],[])).
% 36.87/24.71 tff(15781,plain,
% 36.87/24.71 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s84) | (~node3(c_bit0, s84, s85))),
% 36.87/24.71 inference(modus_ponens,[status(thm)],[15780, 15779])).
% 36.87/24.71 tff(15782,plain,
% 36.87/24.71 ((~m_counter_cell_v_value(c_bit0, s85)) | node2(c_bit0, s84)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15781, 234, 2600])).
% 36.87/24.71 tff(15783,plain,
% 36.87/24.71 (node2(c_bit0, s84)),
% 36.87/24.71 inference(unit_resolution,[status(thm)],[15782, 15775])).
% 36.87/24.71 tff(15784,plain,
% 36.87/24.71 (((~![I0: $i, X: $i] : ((~m_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, s84)) | (~m_counter_cell_v_value(c_bit0, s84)) | (~node2(c_bit0, s84)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s84)) | (~m_counter_cell_v_value(c_bit0, s84)) | (~node2(c_bit0, s84)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15785,plain,
% 36.87/24.72 ((~![I0: $i, X: $i] : ((~m_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, s84)) | (~m_counter_cell_v_value(c_bit0, s84)) | (~node2(c_bit0, s84)))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15786,plain,
% 36.87/24.72 ((~![I0: $i, X: $i] : ((~m_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, s84)) | (~m_counter_cell_v_value(c_bit0, s84)) | (~node2(c_bit0, s84))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15785, 15784])).
% 36.87/24.72 tff(15787,plain,
% 36.87/24.72 ((~m_counter_cell_v_value(c_bit0, s84)) | (~node2(c_bit0, s84))),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15786, 219, 2581])).
% 36.87/24.72 tff(15788,plain,
% 36.87/24.72 (~m_counter_cell_v_value(c_bit0, s84)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15787, 15783])).
% 36.87/24.72 tff(15789,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s84) | node1(c_bit0, s83) | (~node3(c_bit0, s83, s84)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s84) | node1(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15790,plain,
% 36.87/24.72 ((node1(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | m_counter_cell_v_value(c_bit0, s84)) <=> (m_counter_cell_v_value(c_bit0, s84) | node1(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15791,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | m_counter_cell_v_value(c_bit0, s84))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s84) | node1(c_bit0, s83) | (~node3(c_bit0, s83, s84))))),
% 36.87/24.72 inference(monotonicity,[status(thm)],[15790])).
% 36.87/24.72 tff(15792,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | m_counter_cell_v_value(c_bit0, s84))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s84) | node1(c_bit0, s83) | (~node3(c_bit0, s83, s84)))),
% 36.87/24.72 inference(transitivity,[status(thm)],[15791, 15789])).
% 36.87/24.72 tff(15793,plain,
% 36.87/24.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s83) | (~node3(c_bit0, s83, s84)) | m_counter_cell_v_value(c_bit0, s84))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15794,plain,
% 36.87/24.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s84) | node1(c_bit0, s83) | (~node3(c_bit0, s83, s84))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15793, 15792])).
% 36.87/24.72 tff(15795,plain,
% 36.87/24.72 (m_counter_cell_v_value(c_bit0, s84) | node1(c_bit0, s83)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15794, 199, 2569])).
% 36.87/24.72 tff(15796,plain,
% 36.87/24.72 (node1(c_bit0, s83)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15795, 15788])).
% 36.87/24.72 tff(15797,plain,
% 36.87/24.72 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83) | (~node1(c_bit0, s83)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83) | (~node1(c_bit0, s83)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15798,plain,
% 36.87/24.72 (((~node1(c_bit0, s83)) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83) | (~node1(c_bit0, s83)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15799,plain,
% 36.87/24.72 (((~![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, s83)) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83) | (~node1(c_bit0, s83))))),
% 36.87/24.72 inference(monotonicity,[status(thm)],[15798])).
% 36.87/24.72 tff(15800,plain,
% 36.87/24.72 (((~![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, s83)) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83) | (~node1(c_bit0, s83)))),
% 36.87/24.72 inference(transitivity,[status(thm)],[15799, 15797])).
% 36.87/24.72 tff(15801,plain,
% 36.87/24.72 ((~![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, s83)) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15802,plain,
% 36.87/24.72 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s83)) | m_counter_cell_v_value(c_bit0, s83) | (~node1(c_bit0, s83))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15801, 15800])).
% 36.87/24.72 tff(15803,plain,
% 36.87/24.72 (m_counter_cell_v_value(c_bit0, s83) | (~node1(c_bit0, s83))),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15802, 170, 2553])).
% 36.87/24.72 tff(15804,plain,
% 36.87/24.72 (m_counter_cell_v_value(c_bit0, s83)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15803, 15796])).
% 36.87/24.72 tff(15805,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s83)) | node2(c_bit0, s82) | (~node3(c_bit0, s82, s83)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s83)) | node2(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15806,plain,
% 36.87/24.72 ((node2(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | (~m_counter_cell_v_value(c_bit0, s83))) <=> ((~m_counter_cell_v_value(c_bit0, s83)) | node2(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15807,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | (~m_counter_cell_v_value(c_bit0, s83)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s83)) | node2(c_bit0, s82) | (~node3(c_bit0, s82, s83))))),
% 36.87/24.72 inference(monotonicity,[status(thm)],[15806])).
% 36.87/24.72 tff(15808,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | (~m_counter_cell_v_value(c_bit0, s83)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s83)) | node2(c_bit0, s82) | (~node3(c_bit0, s82, s83)))),
% 36.87/24.72 inference(transitivity,[status(thm)],[15807, 15805])).
% 36.87/24.72 tff(15809,plain,
% 36.87/24.72 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s82) | (~node3(c_bit0, s82, s83)) | (~m_counter_cell_v_value(c_bit0, s83)))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15810,plain,
% 36.87/24.72 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s83)) | node2(c_bit0, s82) | (~node3(c_bit0, s82, s83))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15809, 15808])).
% 36.87/24.72 tff(15811,plain,
% 36.87/24.72 ((~m_counter_cell_v_value(c_bit0, s83)) | node2(c_bit0, s82)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15810, 234, 2541])).
% 36.87/24.72 tff(15812,plain,
% 36.87/24.72 (node2(c_bit0, s82)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15811, 15804])).
% 36.87/24.72 tff(15813,plain,
% 36.87/24.72 (((~![I0: $i, X: $i] : ((~m_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, s82)) | (~m_counter_cell_v_value(c_bit0, s82)) | (~node2(c_bit0, s82)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s82)) | (~m_counter_cell_v_value(c_bit0, s82)) | (~node2(c_bit0, s82)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15814,plain,
% 36.87/24.72 ((~![I0: $i, X: $i] : ((~m_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, s82)) | (~m_counter_cell_v_value(c_bit0, s82)) | (~node2(c_bit0, s82)))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15815,plain,
% 36.87/24.72 ((~![I0: $i, X: $i] : ((~m_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, s82)) | (~m_counter_cell_v_value(c_bit0, s82)) | (~node2(c_bit0, s82))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15814, 15813])).
% 36.87/24.72 tff(15816,plain,
% 36.87/24.72 ((~m_counter_cell_v_value(c_bit0, s82)) | (~node2(c_bit0, s82))),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15815, 219, 2522])).
% 36.87/24.72 tff(15817,plain,
% 36.87/24.72 (~m_counter_cell_v_value(c_bit0, s82)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15816, 15812])).
% 36.87/24.72 tff(15818,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s82) | node1(c_bit0, s81) | (~node3(c_bit0, s81, s82)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s82) | node1(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15819,plain,
% 36.87/24.72 ((node1(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | m_counter_cell_v_value(c_bit0, s82)) <=> (m_counter_cell_v_value(c_bit0, s82) | node1(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15820,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | m_counter_cell_v_value(c_bit0, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s82) | node1(c_bit0, s81) | (~node3(c_bit0, s81, s82))))),
% 36.87/24.72 inference(monotonicity,[status(thm)],[15819])).
% 36.87/24.72 tff(15821,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | m_counter_cell_v_value(c_bit0, s82))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s82) | node1(c_bit0, s81) | (~node3(c_bit0, s81, s82)))),
% 36.87/24.72 inference(transitivity,[status(thm)],[15820, 15818])).
% 36.87/24.72 tff(15822,plain,
% 36.87/24.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s81) | (~node3(c_bit0, s81, s82)) | m_counter_cell_v_value(c_bit0, s82))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15823,plain,
% 36.87/24.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s82) | node1(c_bit0, s81) | (~node3(c_bit0, s81, s82))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15822, 15821])).
% 36.87/24.72 tff(15824,plain,
% 36.87/24.72 (m_counter_cell_v_value(c_bit0, s82) | node1(c_bit0, s81)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15823, 199, 2510])).
% 36.87/24.72 tff(15825,plain,
% 36.87/24.72 (node1(c_bit0, s81)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15824, 15817])).
% 36.87/24.72 tff(15826,plain,
% 36.87/24.72 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81) | (~node1(c_bit0, s81)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81) | (~node1(c_bit0, s81)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15827,plain,
% 36.87/24.72 (((~node1(c_bit0, s81)) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81) | (~node1(c_bit0, s81)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15828,plain,
% 36.87/24.72 (((~![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, s81)) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81) | (~node1(c_bit0, s81))))),
% 36.87/24.72 inference(monotonicity,[status(thm)],[15827])).
% 36.87/24.72 tff(15829,plain,
% 36.87/24.72 (((~![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, s81)) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81) | (~node1(c_bit0, s81)))),
% 36.87/24.72 inference(transitivity,[status(thm)],[15828, 15826])).
% 36.87/24.72 tff(15830,plain,
% 36.87/24.72 ((~![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, s81)) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15831,plain,
% 36.87/24.72 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s81)) | m_counter_cell_v_value(c_bit0, s81) | (~node1(c_bit0, s81))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15830, 15829])).
% 36.87/24.72 tff(15832,plain,
% 36.87/24.72 (m_counter_cell_v_value(c_bit0, s81) | (~node1(c_bit0, s81))),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15831, 170, 2494])).
% 36.87/24.72 tff(15833,plain,
% 36.87/24.72 (m_counter_cell_v_value(c_bit0, s81)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15832, 15825])).
% 36.87/24.72 tff(15834,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s81)) | node2(c_bit0, s80) | (~node3(c_bit0, s80, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s81)) | node2(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15835,plain,
% 36.87/24.72 ((node2(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | (~m_counter_cell_v_value(c_bit0, s81))) <=> ((~m_counter_cell_v_value(c_bit0, s81)) | node2(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15836,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | (~m_counter_cell_v_value(c_bit0, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s81)) | node2(c_bit0, s80) | (~node3(c_bit0, s80, s81))))),
% 36.87/24.72 inference(monotonicity,[status(thm)],[15835])).
% 36.87/24.72 tff(15837,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | (~m_counter_cell_v_value(c_bit0, s81)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s81)) | node2(c_bit0, s80) | (~node3(c_bit0, s80, s81)))),
% 36.87/24.72 inference(transitivity,[status(thm)],[15836, 15834])).
% 36.87/24.72 tff(15838,plain,
% 36.87/24.72 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s80) | (~node3(c_bit0, s80, s81)) | (~m_counter_cell_v_value(c_bit0, s81)))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15839,plain,
% 36.87/24.72 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s81)) | node2(c_bit0, s80) | (~node3(c_bit0, s80, s81))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15838, 15837])).
% 36.87/24.72 tff(15840,plain,
% 36.87/24.72 ((~m_counter_cell_v_value(c_bit0, s81)) | node2(c_bit0, s80)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15839, 234, 2482])).
% 36.87/24.72 tff(15841,plain,
% 36.87/24.72 (node2(c_bit0, s80)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15840, 15833])).
% 36.87/24.72 tff(15842,plain,
% 36.87/24.72 (((~![I0: $i, X: $i] : ((~m_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, s80)) | (~m_counter_cell_v_value(c_bit0, s80)) | (~node2(c_bit0, s80)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s80)) | (~m_counter_cell_v_value(c_bit0, s80)) | (~node2(c_bit0, s80)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15843,plain,
% 36.87/24.72 ((~![I0: $i, X: $i] : ((~m_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, s80)) | (~m_counter_cell_v_value(c_bit0, s80)) | (~node2(c_bit0, s80)))),
% 36.87/24.72 inference(quant_inst,[status(thm)],[])).
% 36.87/24.72 tff(15844,plain,
% 36.87/24.72 ((~![I0: $i, X: $i] : ((~m_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, s80)) | (~m_counter_cell_v_value(c_bit0, s80)) | (~node2(c_bit0, s80))),
% 36.87/24.72 inference(modus_ponens,[status(thm)],[15843, 15842])).
% 36.87/24.72 tff(15845,plain,
% 36.87/24.72 ((~m_counter_cell_v_value(c_bit0, s80)) | (~node2(c_bit0, s80))),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15844, 219, 2463])).
% 36.87/24.72 tff(15846,plain,
% 36.87/24.72 (~m_counter_cell_v_value(c_bit0, s80)),
% 36.87/24.72 inference(unit_resolution,[status(thm)],[15845, 15841])).
% 36.87/24.72 tff(15847,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s80) | node1(c_bit0, s79) | (~node3(c_bit0, s79, s80)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s80) | node1(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15848,plain,
% 36.87/24.72 ((node1(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | m_counter_cell_v_value(c_bit0, s80)) <=> (m_counter_cell_v_value(c_bit0, s80) | node1(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 36.87/24.72 inference(rewrite,[status(thm)],[])).
% 36.87/24.72 tff(15849,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | m_counter_cell_v_value(c_bit0, s80))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit0, s80) | node1(c_bit0, s79) | (~node3(c_bit0, s79, s80))))),
% 36.87/24.72 inference(monotonicity,[status(thm)],[15848])).
% 36.87/24.72 tff(15850,plain,
% 36.87/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | m_counter_cell_v_value(c_bit0, s80))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s80) | node1(c_bit0, s79) | (~node3(c_bit0, s79, s80)))),
% 36.92/24.72 inference(transitivity,[status(thm)],[15849, 15847])).
% 36.92/24.72 tff(15851,plain,
% 36.92/24.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s79) | (~node3(c_bit0, s79, s80)) | m_counter_cell_v_value(c_bit0, s80))),
% 36.92/24.72 inference(quant_inst,[status(thm)],[])).
% 36.92/24.72 tff(15852,plain,
% 36.92/24.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit0, s80) | node1(c_bit0, s79) | (~node3(c_bit0, s79, s80))),
% 36.92/24.72 inference(modus_ponens,[status(thm)],[15851, 15850])).
% 36.92/24.72 tff(15853,plain,
% 36.92/24.72 (m_counter_cell_v_value(c_bit0, s80) | node1(c_bit0, s79)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15852, 199, 2451])).
% 36.92/24.72 tff(15854,plain,
% 36.92/24.72 (node1(c_bit0, s79)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15853, 15846])).
% 36.92/24.72 tff(15855,plain,
% 36.92/24.72 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79) | (~node1(c_bit0, s79)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79) | (~node1(c_bit0, s79)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15856,plain,
% 36.92/24.72 (((~node1(c_bit0, s79)) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79)) <=> ((~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79) | (~node1(c_bit0, s79)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15857,plain,
% 36.92/24.72 (((~![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, s79)) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79) | (~node1(c_bit0, s79))))),
% 36.92/24.72 inference(monotonicity,[status(thm)],[15856])).
% 36.92/24.72 tff(15858,plain,
% 36.92/24.72 (((~![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, s79)) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79) | (~node1(c_bit0, s79)))),
% 36.92/24.72 inference(transitivity,[status(thm)],[15857, 15855])).
% 36.92/24.72 tff(15859,plain,
% 36.92/24.72 ((~![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, s79)) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79))),
% 36.92/24.72 inference(quant_inst,[status(thm)],[])).
% 36.92/24.72 tff(15860,plain,
% 36.92/24.72 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit0, s79)) | m_counter_cell_v_value(c_bit0, s79) | (~node1(c_bit0, s79))),
% 36.92/24.72 inference(modus_ponens,[status(thm)],[15859, 15858])).
% 36.92/24.72 tff(15861,plain,
% 36.92/24.72 (m_counter_cell_v_value(c_bit0, s79) | (~node1(c_bit0, s79))),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15860, 170, 2435])).
% 36.92/24.72 tff(15862,plain,
% 36.92/24.72 (m_counter_cell_v_value(c_bit0, s79)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15861, 15854])).
% 36.92/24.72 tff(15863,plain,
% 36.92/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s79)) | node2(c_bit0, s78) | (~node3(c_bit0, s78, s79)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s79)) | node2(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15864,plain,
% 36.92/24.72 ((node2(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | (~m_counter_cell_v_value(c_bit0, s79))) <=> ((~m_counter_cell_v_value(c_bit0, s79)) | node2(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15865,plain,
% 36.92/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | (~m_counter_cell_v_value(c_bit0, s79)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s79)) | node2(c_bit0, s78) | (~node3(c_bit0, s78, s79))))),
% 36.92/24.72 inference(monotonicity,[status(thm)],[15864])).
% 36.92/24.72 tff(15866,plain,
% 36.92/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | (~m_counter_cell_v_value(c_bit0, s79)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s79)) | node2(c_bit0, s78) | (~node3(c_bit0, s78, s79)))),
% 36.92/24.72 inference(transitivity,[status(thm)],[15865, 15863])).
% 36.92/24.72 tff(15867,plain,
% 36.92/24.72 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s78) | (~node3(c_bit0, s78, s79)) | (~m_counter_cell_v_value(c_bit0, s79)))),
% 36.92/24.72 inference(quant_inst,[status(thm)],[])).
% 36.92/24.72 tff(15868,plain,
% 36.92/24.72 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s79)) | node2(c_bit0, s78) | (~node3(c_bit0, s78, s79))),
% 36.92/24.72 inference(modus_ponens,[status(thm)],[15867, 15866])).
% 36.92/24.72 tff(15869,plain,
% 36.92/24.72 ((~m_counter_cell_v_value(c_bit0, s79)) | node2(c_bit0, s78)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15868, 234, 2423])).
% 36.92/24.72 tff(15870,plain,
% 36.92/24.72 (node2(c_bit0, s78)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15869, 15862])).
% 36.92/24.72 tff(15871,plain,
% 36.92/24.72 (((~![I0: $i, X: $i] : ((~m_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, s78)) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node2(c_bit0, s78)))) <=> ((~![I0: $i, X: $i] : ((~m_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, s78)) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node2(c_bit0, s78)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15872,plain,
% 36.92/24.72 ((~![I0: $i, X: $i] : ((~m_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, s78)) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node2(c_bit0, s78)))),
% 36.92/24.72 inference(quant_inst,[status(thm)],[])).
% 36.92/24.72 tff(15873,plain,
% 36.92/24.72 ((~![I0: $i, X: $i] : ((~m_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, s78)) | (~m_counter_cell_v_value(c_bit0, s78)) | (~node2(c_bit0, s78))),
% 36.92/24.72 inference(modus_ponens,[status(thm)],[15872, 15871])).
% 36.92/24.72 tff(15874,plain,
% 36.92/24.72 ((~m_counter_cell_v_value(c_bit0, s78)) | (~node2(c_bit0, s78))),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15873, 219, 2404])).
% 36.92/24.72 tff(15875,plain,
% 36.92/24.72 (~m_counter_cell_v_value(c_bit0, s78)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15874, 15870])).
% 36.92/24.72 tff(15876,plain,
% 36.92/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s77) | m_counter_cell_v_value(c_bit0, s78) | (~node3(c_bit0, s77, s78)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s77) | m_counter_cell_v_value(c_bit0, s78) | (~node3(c_bit0, s77, s78)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15877,plain,
% 36.92/24.72 ((node1(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | m_counter_cell_v_value(c_bit0, s78)) <=> (node1(c_bit0, s77) | m_counter_cell_v_value(c_bit0, s78) | (~node3(c_bit0, s77, s78)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15878,plain,
% 36.92/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | m_counter_cell_v_value(c_bit0, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s77) | m_counter_cell_v_value(c_bit0, s78) | (~node3(c_bit0, s77, s78))))),
% 36.92/24.72 inference(monotonicity,[status(thm)],[15877])).
% 36.92/24.72 tff(15879,plain,
% 36.92/24.72 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | m_counter_cell_v_value(c_bit0, s78))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s77) | m_counter_cell_v_value(c_bit0, s78) | (~node3(c_bit0, s77, s78)))),
% 36.92/24.72 inference(transitivity,[status(thm)],[15878, 15876])).
% 36.92/24.72 tff(15880,plain,
% 36.92/24.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit0, s77) | (~node3(c_bit0, s77, s78)) | m_counter_cell_v_value(c_bit0, s78))),
% 36.92/24.72 inference(quant_inst,[status(thm)],[])).
% 36.92/24.72 tff(15881,plain,
% 36.92/24.72 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | node1(c_bit0, s77) | m_counter_cell_v_value(c_bit0, s78) | (~node3(c_bit0, s77, s78))),
% 36.92/24.72 inference(modus_ponens,[status(thm)],[15880, 15879])).
% 36.92/24.72 tff(15882,plain,
% 36.92/24.72 (node1(c_bit0, s77) | m_counter_cell_v_value(c_bit0, s78)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15881, 199, 2392])).
% 36.92/24.72 tff(15883,plain,
% 36.92/24.72 (node1(c_bit0, s77)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15882, 15875])).
% 36.92/24.72 tff(15884,plain,
% 36.92/24.72 (((~![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, s77)) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | m_counter_cell_v_value(c_bit0, s77))) <=> ((~![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, s77)) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | m_counter_cell_v_value(c_bit0, s77))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15885,plain,
% 36.92/24.72 ((~![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, s77)) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | m_counter_cell_v_value(c_bit0, s77))),
% 36.92/24.72 inference(quant_inst,[status(thm)],[])).
% 36.92/24.72 tff(15886,plain,
% 36.92/24.72 ((~![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, s77)) | (~m_counter_cell_v_carry_in(c_bit0, s77)) | m_counter_cell_v_value(c_bit0, s77)),
% 36.92/24.72 inference(modus_ponens,[status(thm)],[15885, 15884])).
% 36.92/24.72 tff(15887,plain,
% 36.92/24.72 ((~node1(c_bit0, s77)) | m_counter_cell_v_value(c_bit0, s77)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15886, 170, 2376])).
% 36.92/24.72 tff(15888,plain,
% 36.92/24.72 (m_counter_cell_v_value(c_bit0, s77)),
% 36.92/24.72 inference(unit_resolution,[status(thm)],[15887, 15883])).
% 36.92/24.72 tff(15889,assumption,(node3(c_bit0, s99, s77)), introduced(assumption)).
% 36.92/24.72 tff(15890,assumption,(m_counter_cell_v_value(c_bit0, s77)), introduced(assumption)).
% 36.92/24.72 tff(15891,plain,
% 36.92/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s77)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s77)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s77)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15892,plain,
% 36.92/24.72 ((node2(c_bit0, s99) | (~node3(c_bit0, s99, s77)) | (~m_counter_cell_v_value(c_bit0, s77))) <=> ((~m_counter_cell_v_value(c_bit0, s77)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s77)))),
% 36.92/24.72 inference(rewrite,[status(thm)],[])).
% 36.92/24.72 tff(15893,plain,
% 36.92/24.72 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s77)) | (~m_counter_cell_v_value(c_bit0, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit0, s77)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s77))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[15892])).
% 36.92/24.73 tff(15894,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s77)) | (~m_counter_cell_v_value(c_bit0, s77)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s77)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s77)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[15893, 15891])).
% 36.92/24.73 tff(15895,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit0, s99) | (~node3(c_bit0, s99, s77)) | (~m_counter_cell_v_value(c_bit0, s77)))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15896,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit0, s77)) | node2(c_bit0, s99) | (~node3(c_bit0, s99, s77))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15895, 15894])).
% 36.92/24.73 tff(15897,plain,
% 36.92/24.73 ($false),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15896, 234, 15890, 14545, 15889])).
% 36.92/24.73 tff(15898,plain,((~node3(c_bit0, s99, s77)) | (~m_counter_cell_v_value(c_bit0, s77)) | node2(c_bit0, s99)), inference(lemma,lemma(discharge,[]))).
% 36.92/24.73 tff(15899,plain,
% 36.92/24.73 (~node3(c_bit0, s99, s77)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15898, 15888, 14543])).
% 36.92/24.73 tff(15900,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s77)) | node3(c_bit0, s99, s77))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s77)) | node3(c_bit0, s99, s77))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15901,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s77)) | node3(c_bit0, s99, s77))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15902,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s77)) | node3(c_bit0, s99, s77)),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15901, 15900])).
% 36.92/24.73 tff(15903,plain,
% 36.92/24.73 ((~trans(s99, s77)) | node3(c_bit0, s99, s77)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15902, 81])).
% 36.92/24.73 tff(15904,plain,
% 36.92/24.73 (~trans(s99, s77)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15903, 15899])).
% 36.92/24.73 tff(15905,plain,
% 36.92/24.73 (trans(s99, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15552, 15600, 14592, 15904, 14593, 14856, 15286, 13838, 15641, 15376, 15640, 15639, 15254, 15244, 14534, 15224, 15234, 15214, 15194, 14535, 14533, 15184, 14532, 14523, 14531, 15264, 15204, 15154, 15144, 14530, 15134, 14529, 15124, 14528, 15114, 14527, 14526, 14525, 14524, 15104, 15094, 15174, 15084, 15074, 14522, 14521, 14520, 14519, 14518, 15064, 15054, 15044, 14517, 14505, 15164, 15034, 15023, 15013, 14516, 15003, 14993, 14983, 14973, 14963, 15622, 14953, 14943, 14933, 14923, 14514, 14913, 14513, 14903, 14893, 14512, 14511, 15599, 14883, 14507, 15597, 14515, 15598, 15596, 15595, 15594, 14510, 14509, 14866, 14508, 15593, 15285, 14845, 15581, 14536, 14506, 15592, 15621, 15275])).
% 36.92/24.73 tff(15906,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s94)) | node3(c_bit2, s99, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s94)) | node3(c_bit2, s99, s94))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15907,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s94)) | node3(c_bit2, s99, s94))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15908,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s94)) | node3(c_bit2, s99, s94)),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15907, 15906])).
% 36.92/24.73 tff(15909,plain,
% 36.92/24.73 ((~trans(s99, s94)) | node3(c_bit2, s99, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15908, 81])).
% 36.92/24.73 tff(15910,plain,
% 36.92/24.73 (node3(c_bit2, s99, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15909, 15905])).
% 36.92/24.73 tff(15911,assumption,(~m_counter_cell_v_value(c_bit1, s94)), introduced(assumption)).
% 36.92/24.73 tff(15912,plain,
% 36.92/24.73 (((~![I0: $i, X: $i] : (m_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, s94) | m_counter_cell_v_value(c_bit1, s94) | (~node2(c_bit1, s94)))) <=> ((~![I0: $i, X: $i] : (m_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, s94) | m_counter_cell_v_value(c_bit1, s94) | (~node2(c_bit1, s94)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15913,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : (m_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, s94) | m_counter_cell_v_value(c_bit1, s94) | (~node2(c_bit1, s94)))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15914,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : (m_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, s94) | m_counter_cell_v_value(c_bit1, s94) | (~node2(c_bit1, s94))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15913, 15912])).
% 36.92/24.73 tff(15915,plain,
% 36.92/24.73 (~node2(c_bit1, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15914, 3291, 15911, 14473])).
% 36.92/24.73 tff(15916,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s95)) | node2(c_bit1, s94) | (~node3(c_bit1, s94, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s95)) | node2(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15917,plain,
% 36.92/24.73 ((node2(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | (~m_counter_cell_v_value(c_bit1, s95))) <=> ((~m_counter_cell_v_value(c_bit1, s95)) | node2(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15918,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | (~m_counter_cell_v_value(c_bit1, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s95)) | node2(c_bit1, s94) | (~node3(c_bit1, s94, s95))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[15917])).
% 36.92/24.73 tff(15919,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | (~m_counter_cell_v_value(c_bit1, s95)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s95)) | node2(c_bit1, s94) | (~node3(c_bit1, s94, s95)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[15918, 15916])).
% 36.92/24.73 tff(15920,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s94) | (~node3(c_bit1, s94, s95)) | (~m_counter_cell_v_value(c_bit1, s95)))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15921,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s95)) | node2(c_bit1, s94) | (~node3(c_bit1, s94, s95))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15920, 15919])).
% 36.92/24.73 tff(15922,plain,
% 36.92/24.73 ((~m_counter_cell_v_value(c_bit1, s95)) | node2(c_bit1, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15921, 234, 8246])).
% 36.92/24.73 tff(15923,plain,
% 36.92/24.73 (~m_counter_cell_v_value(c_bit1, s95)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15922, 15915])).
% 36.92/24.73 tff(15924,plain,
% 36.92/24.73 (~node1(c_bit1, s95)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[8450, 15923])).
% 36.92/24.73 tff(15925,plain,
% 36.92/24.73 (m_counter_cell_v_value(c_bit1, s96)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[8458, 15924])).
% 36.92/24.73 tff(15926,assumption,(~m_counter_cell_v_carry_in(c_bit2, s98)), introduced(assumption)).
% 36.92/24.73 tff(15927,assumption,(node3(c_bit2, s99, s94)), introduced(assumption)).
% 36.92/24.73 tff(15928,plain,
% 36.92/24.73 (((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s94) | (~node4(c_bit1, s94)))) <=> ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s94) | (~node4(c_bit1, s94)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15929,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | (m_counter_cell_v_value(c_bit1, s94) | (~node4(c_bit1, s94)))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15930,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : (m_counter_cell_v_value(I0, X) | (~node4(I0, X)))) | m_counter_cell_v_value(c_bit1, s94) | (~node4(c_bit1, s94))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15929, 15928])).
% 36.92/24.73 tff(15931,plain,
% 36.92/24.73 (~node4(c_bit1, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15930, 2875, 15911])).
% 36.92/24.73 tff(15932,plain,
% 36.92/24.73 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s94)) | node4(c_bit1, s94))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s94)) | node4(c_bit1, s94))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15933,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | ((~m_counter_cell_v_carry_out(c_bit1, s94)) | node4(c_bit1, s94))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15934,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_out(I0, X)) | node4(I0, X))) | (~m_counter_cell_v_carry_out(c_bit1, s94)) | node4(c_bit1, s94)),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15933, 15932])).
% 36.92/24.73 tff(15935,plain,
% 36.92/24.73 (~m_counter_cell_v_carry_out(c_bit1, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15934, 2887, 15931])).
% 36.92/24.73 tff(15936,plain,
% 36.92/24.73 (((~![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, s94)) | m_counter_cell_v_carry_out(c_bit1, s94))) <=> ((~![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, s94)) | m_counter_cell_v_carry_out(c_bit1, s94))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15937,plain,
% 36.92/24.73 ((~![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, s94)) | m_counter_cell_v_carry_out(c_bit1, s94))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15938,plain,
% 36.92/24.73 ((~![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, s94)) | m_counter_cell_v_carry_out(c_bit1, s94)),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15937, 15936])).
% 36.92/24.73 tff(15939,plain,
% 36.92/24.73 (~m_counter_cell_v_carry_in(c_bit2, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15938, 3167, 15935])).
% 36.92/24.73 tff(15940,assumption,(m_counter_cell_v_carry_in(c_bit2, s97)), introduced(assumption)).
% 36.92/24.73 tff(15941,plain,
% 36.92/24.73 (~m_counter_cell_v_value(c_bit2, s97)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[8492, 15940])).
% 36.92/24.73 tff(15942,plain,
% 36.92/24.73 (((~![I0: $i, X: $i] : ((~node1(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, s97)) | m_counter_cell_v_value(c_bit2, s97) | (~node1(c_bit2, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s97)) | m_counter_cell_v_value(c_bit2, s97) | (~node1(c_bit2, s97)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15943,plain,
% 36.92/24.73 (((~node1(c_bit2, s97)) | (~m_counter_cell_v_carry_in(c_bit2, s97)) | m_counter_cell_v_value(c_bit2, s97)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s97)) | m_counter_cell_v_value(c_bit2, s97) | (~node1(c_bit2, s97)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15944,plain,
% 36.92/24.73 (((~![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, s97)) | (~m_counter_cell_v_carry_in(c_bit2, s97)) | m_counter_cell_v_value(c_bit2, s97))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s97)) | m_counter_cell_v_value(c_bit2, s97) | (~node1(c_bit2, s97))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[15943])).
% 36.92/24.73 tff(15945,plain,
% 36.92/24.73 (((~![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, s97)) | (~m_counter_cell_v_carry_in(c_bit2, s97)) | m_counter_cell_v_value(c_bit2, s97))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s97)) | m_counter_cell_v_value(c_bit2, s97) | (~node1(c_bit2, s97)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[15944, 15942])).
% 36.92/24.73 tff(15946,plain,
% 36.92/24.73 ((~![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, s97)) | (~m_counter_cell_v_carry_in(c_bit2, s97)) | m_counter_cell_v_value(c_bit2, s97))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15947,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : ((~node1(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, s97)) | m_counter_cell_v_value(c_bit2, s97) | (~node1(c_bit2, s97))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15946, 15945])).
% 36.92/24.73 tff(15948,plain,
% 36.92/24.73 (~node1(c_bit2, s97)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15947, 170, 15940, 15941])).
% 36.92/24.73 tff(15949,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit2, s97, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit2, s97, s98))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15950,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit2, s97, s98))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15951,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit2, s97, s98)),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15950, 15949])).
% 36.92/24.73 tff(15952,plain,
% 36.92/24.73 (node3(c_bit2, s97, s98)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15951, 81, 8565])).
% 36.92/24.73 tff(15953,plain,
% 36.92/24.73 (((~![Y: $i, 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, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)))) <=> ((~![Y: $i, 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, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15954,plain,
% 36.92/24.73 ((node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)) | m_counter_cell_v_value(c_bit2, s98)) <=> (m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15955,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)) | m_counter_cell_v_value(c_bit2, s98))) <=> ((~![Y: $i, 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, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[15954])).
% 36.92/24.73 tff(15956,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)) | m_counter_cell_v_value(c_bit2, s98))) <=> ((~![Y: $i, 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, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[15955, 15953])).
% 36.92/24.73 tff(15957,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s97) | (~node3(c_bit2, s97, s98)) | m_counter_cell_v_value(c_bit2, s98))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15958,plain,
% 36.92/24.73 ((~![Y: $i, 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, s98) | node1(c_bit2, s97) | (~node3(c_bit2, s97, s98))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15957, 15956])).
% 36.92/24.73 tff(15959,plain,
% 36.92/24.73 (m_counter_cell_v_value(c_bit2, s98) | node1(c_bit2, s97)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15958, 199, 15952])).
% 36.92/24.73 tff(15960,plain,
% 36.92/24.73 (m_counter_cell_v_value(c_bit2, s98)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15959, 15948])).
% 36.92/24.73 tff(15961,plain,
% 36.92/24.73 (((~![I0: $i, X: $i] : ((~node1(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, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15962,plain,
% 36.92/24.73 (((~node1(c_bit2, s98)) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98))) <=> (m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15963,plain,
% 36.92/24.73 (((~![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, s98)) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[15962])).
% 36.92/24.73 tff(15964,plain,
% 36.92/24.73 (((~![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, s98)) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[15963, 15961])).
% 36.92/24.73 tff(15965,plain,
% 36.92/24.73 ((~![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, s98)) | m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98)))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15966,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : ((~node1(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, s98) | (~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15965, 15964])).
% 36.92/24.73 tff(15967,plain,
% 36.92/24.73 ((~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98))),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15966, 3359, 15926])).
% 36.92/24.73 tff(15968,plain,
% 36.92/24.73 (~node1(c_bit2, s98)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15967, 15960])).
% 36.92/24.73 tff(15969,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit2, s98, s99))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit2, s98, s99))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15970,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s98, s99)) | node3(c_bit2, s98, s99))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15971,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s98, s99)) | node3(c_bit2, s98, s99)),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15970, 15969])).
% 36.92/24.73 tff(15972,plain,
% 36.92/24.73 (node3(c_bit2, s98, s99)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15971, 81, 8629])).
% 36.92/24.73 tff(15973,plain,
% 36.92/24.73 (((~![Y: $i, 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, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)))) <=> ((~![Y: $i, 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, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15974,plain,
% 36.92/24.73 ((node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)) | m_counter_cell_v_value(c_bit2, s99)) <=> (m_counter_cell_v_value(c_bit2, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15975,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)) | m_counter_cell_v_value(c_bit2, s99))) <=> ((~![Y: $i, 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, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[15974])).
% 36.92/24.73 tff(15976,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)) | m_counter_cell_v_value(c_bit2, s99))) <=> ((~![Y: $i, 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, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[15975, 15973])).
% 36.92/24.73 tff(15977,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s98) | (~node3(c_bit2, s98, s99)) | m_counter_cell_v_value(c_bit2, s99))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15978,plain,
% 36.92/24.73 ((~![Y: $i, 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, s99) | node1(c_bit2, s98) | (~node3(c_bit2, s98, s99))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15977, 15976])).
% 36.92/24.73 tff(15979,plain,
% 36.92/24.73 (m_counter_cell_v_value(c_bit2, s99) | node1(c_bit2, s98)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15978, 199, 15972])).
% 36.92/24.73 tff(15980,plain,
% 36.92/24.73 (m_counter_cell_v_value(c_bit2, s99)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15979, 15968])).
% 36.92/24.73 tff(15981,plain,
% 36.92/24.73 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s99)) | (~m_counter_cell_v_carry_out(c_bit2, s99)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s99)) | (~m_counter_cell_v_carry_out(c_bit2, s99)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15982,plain,
% 36.92/24.73 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s99)) | (~m_counter_cell_v_carry_out(c_bit2, s99)))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15983,plain,
% 36.92/24.73 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s99)) | (~m_counter_cell_v_carry_out(c_bit2, s99))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15982, 15981])).
% 36.92/24.73 tff(15984,plain,
% 36.92/24.73 (~m_counter_cell_v_carry_out(c_bit2, s99)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15983, 58, 13749])).
% 36.92/24.73 tff(15985,plain,
% 36.92/24.73 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit2, s99)) | m_counter_cell_v_carry_out(c_bit2, s99))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit2, s99)) | m_counter_cell_v_carry_out(c_bit2, s99))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15986,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit2, s99)) | m_counter_cell_v_carry_out(c_bit2, s99))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15987,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit2, s99)) | m_counter_cell_v_carry_out(c_bit2, s99)),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15986, 15985])).
% 36.92/24.73 tff(15988,plain,
% 36.92/24.73 ((~m_counter_cell_v_carry_in(c_bit2, s99)) | (~m_counter_cell_v_value(c_bit2, s99))),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15987, 3031, 15984])).
% 36.92/24.73 tff(15989,plain,
% 36.92/24.73 (~m_counter_cell_v_carry_in(c_bit2, s99)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15988, 15980])).
% 36.92/24.73 tff(15990,plain,
% 36.92/24.73 (((~![I0: $i, X: $i] : ((~node1(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, s99) | (~m_counter_cell_v_value(c_bit2, s99)) | (~node1(c_bit2, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s99) | (~m_counter_cell_v_value(c_bit2, s99)) | (~node1(c_bit2, s99)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15991,plain,
% 36.92/24.73 (((~node1(c_bit2, s99)) | m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_value(c_bit2, s99))) <=> (m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_value(c_bit2, s99)) | (~node1(c_bit2, s99)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15992,plain,
% 36.92/24.73 (((~![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, s99)) | m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_value(c_bit2, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s99) | (~m_counter_cell_v_value(c_bit2, s99)) | (~node1(c_bit2, s99))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[15991])).
% 36.92/24.73 tff(15993,plain,
% 36.92/24.73 (((~![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, s99)) | m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_value(c_bit2, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s99) | (~m_counter_cell_v_value(c_bit2, s99)) | (~node1(c_bit2, s99)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[15992, 15990])).
% 36.92/24.73 tff(15994,plain,
% 36.92/24.73 ((~![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, s99)) | m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_value(c_bit2, s99)))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(15995,plain,
% 36.92/24.73 ((~![I0: $i, X: $i] : ((~node1(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, s99) | (~m_counter_cell_v_value(c_bit2, s99)) | (~node1(c_bit2, s99))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[15994, 15993])).
% 36.92/24.73 tff(15996,plain,
% 36.92/24.73 (~node1(c_bit2, s99)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[15995, 3359, 15989, 15980])).
% 36.92/24.73 tff(15997,plain,
% 36.92/24.73 (((~![Y: $i, 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, s94) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s94)))) <=> ((~![Y: $i, 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, s94) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s94)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15998,plain,
% 36.92/24.73 ((node1(c_bit2, s99) | (~node3(c_bit2, s99, s94)) | m_counter_cell_v_value(c_bit2, s94)) <=> (m_counter_cell_v_value(c_bit2, s94) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s94)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(15999,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s94)) | m_counter_cell_v_value(c_bit2, s94))) <=> ((~![Y: $i, 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, s94) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s94))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[15998])).
% 36.92/24.73 tff(16000,plain,
% 36.92/24.73 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s94)) | m_counter_cell_v_value(c_bit2, s94))) <=> ((~![Y: $i, 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, s94) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s94)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[15999, 15997])).
% 36.92/24.73 tff(16001,plain,
% 36.92/24.73 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s94)) | m_counter_cell_v_value(c_bit2, s94))),
% 36.92/24.73 inference(quant_inst,[status(thm)],[])).
% 36.92/24.73 tff(16002,plain,
% 36.92/24.73 ((~![Y: $i, 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, s94) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s94))),
% 36.92/24.73 inference(modus_ponens,[status(thm)],[16001, 16000])).
% 36.92/24.73 tff(16003,plain,
% 36.92/24.73 (m_counter_cell_v_value(c_bit2, s94) | node1(c_bit2, s99)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[16002, 199, 15927])).
% 36.92/24.73 tff(16004,plain,
% 36.92/24.73 (m_counter_cell_v_value(c_bit2, s94)),
% 36.92/24.73 inference(unit_resolution,[status(thm)],[16003, 15996])).
% 36.92/24.73 tff(16005,assumption,(~m_counter_cell_v_carry_in(c_bit2, s94)), introduced(assumption)).
% 36.92/24.73 tff(16006,plain,
% 36.92/24.73 (((~![I0: $i, X: $i] : ((~node1(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, s94) | (~m_counter_cell_v_value(c_bit2, s94)) | (~node1(c_bit2, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s94) | (~m_counter_cell_v_value(c_bit2, s94)) | (~node1(c_bit2, s94)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(16007,plain,
% 36.92/24.73 (((~node1(c_bit2, s94)) | m_counter_cell_v_carry_in(c_bit2, s94) | (~m_counter_cell_v_value(c_bit2, s94))) <=> (m_counter_cell_v_carry_in(c_bit2, s94) | (~m_counter_cell_v_value(c_bit2, s94)) | (~node1(c_bit2, s94)))),
% 36.92/24.73 inference(rewrite,[status(thm)],[])).
% 36.92/24.73 tff(16008,plain,
% 36.92/24.73 (((~![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, s94)) | m_counter_cell_v_carry_in(c_bit2, s94) | (~m_counter_cell_v_value(c_bit2, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s94) | (~m_counter_cell_v_value(c_bit2, s94)) | (~node1(c_bit2, s94))))),
% 36.92/24.73 inference(monotonicity,[status(thm)],[16007])).
% 36.92/24.73 tff(16009,plain,
% 36.92/24.73 (((~![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, s94)) | m_counter_cell_v_carry_in(c_bit2, s94) | (~m_counter_cell_v_value(c_bit2, s94)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s94) | (~m_counter_cell_v_value(c_bit2, s94)) | (~node1(c_bit2, s94)))),
% 36.92/24.73 inference(transitivity,[status(thm)],[16008, 16006])).
% 36.92/24.73 tff(16010,plain,
% 36.92/24.73 ((~![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, s94)) | m_counter_cell_v_carry_in(c_bit2, s94) | (~m_counter_cell_v_value(c_bit2, s94)))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16011,plain,
% 36.92/24.74 ((~![I0: $i, X: $i] : ((~node1(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, s94) | (~m_counter_cell_v_value(c_bit2, s94)) | (~node1(c_bit2, s94))),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16010, 16009])).
% 36.92/24.74 tff(16012,plain,
% 36.92/24.74 ((~m_counter_cell_v_value(c_bit2, s94)) | (~node1(c_bit2, s94))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16011, 3359, 16005])).
% 36.92/24.74 tff(16013,plain,
% 36.92/24.74 (~node1(c_bit2, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16012, 16004])).
% 36.92/24.74 tff(16014,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit2, s94, s95))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit2, s94, s95))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16015,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s94, s95)) | node3(c_bit2, s94, s95))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16016,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s94, s95)) | node3(c_bit2, s94, s95)),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16015, 16014])).
% 36.92/24.74 tff(16017,plain,
% 36.92/24.74 (node3(c_bit2, s94, s95)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16016, 81, 8242])).
% 36.92/24.74 tff(16018,plain,
% 36.92/24.74 (((~![Y: $i, 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, s95) | node1(c_bit2, s94) | (~node3(c_bit2, s94, s95)))) <=> ((~![Y: $i, 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, s95) | node1(c_bit2, s94) | (~node3(c_bit2, s94, s95)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16019,plain,
% 36.92/24.74 ((node1(c_bit2, s94) | (~node3(c_bit2, s94, s95)) | m_counter_cell_v_value(c_bit2, s95)) <=> (m_counter_cell_v_value(c_bit2, s95) | node1(c_bit2, s94) | (~node3(c_bit2, s94, s95)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16020,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s94) | (~node3(c_bit2, s94, s95)) | m_counter_cell_v_value(c_bit2, s95))) <=> ((~![Y: $i, 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, s95) | node1(c_bit2, s94) | (~node3(c_bit2, s94, s95))))),
% 36.92/24.74 inference(monotonicity,[status(thm)],[16019])).
% 36.92/24.74 tff(16021,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s94) | (~node3(c_bit2, s94, s95)) | m_counter_cell_v_value(c_bit2, s95))) <=> ((~![Y: $i, 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, s95) | node1(c_bit2, s94) | (~node3(c_bit2, s94, s95)))),
% 36.92/24.74 inference(transitivity,[status(thm)],[16020, 16018])).
% 36.92/24.74 tff(16022,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s94) | (~node3(c_bit2, s94, s95)) | m_counter_cell_v_value(c_bit2, s95))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16023,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s95) | node1(c_bit2, s94) | (~node3(c_bit2, s94, s95))),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16022, 16021])).
% 36.92/24.74 tff(16024,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s95) | node1(c_bit2, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16023, 199, 16017])).
% 36.92/24.74 tff(16025,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s95)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16024, 16013])).
% 36.92/24.74 tff(16026,plain,
% 36.92/24.74 (~node1(c_bit2, s95)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8407, 16025, 8391])).
% 36.92/24.74 tff(16027,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8419, 16026])).
% 36.92/24.74 tff(16028,plain,
% 36.92/24.74 (~m_counter_cell_v_carry_in(c_bit2, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8425, 16027])).
% 36.92/24.74 tff(16029,plain,
% 36.92/24.74 (node1(c_bit2, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8486, 15941])).
% 36.92/24.74 tff(16030,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit2, s96) | (~m_counter_cell_v_value(c_bit2, s96))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8474, 3359, 16029])).
% 36.92/24.74 tff(16031,plain,
% 36.92/24.74 ($false),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16030, 16028, 16027])).
% 36.92/24.74 tff(16032,plain,((~m_counter_cell_v_carry_in(c_bit2, s97)) | m_counter_cell_v_carry_out(c_bit2, s96) | m_counter_cell_v_carry_out(c_bit2, s95) | m_counter_cell_v_carry_in(c_bit2, s94) | (~node3(c_bit2, s99, s94)) | m_counter_cell_v_carry_in(c_bit2, s98) | m_counter_cell_v_carry_out(c_bit2, s97)), inference(lemma,lemma(discharge,[]))).
% 36.92/24.74 tff(16033,plain,
% 36.92/24.74 (~m_counter_cell_v_carry_in(c_bit2, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16032, 15939, 8391, 8421, 15927, 15926, 8488])).
% 36.92/24.74 tff(16034,plain,
% 36.92/24.74 (~m_counter_cell_v_carry_out(c_bit1, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8500, 16033])).
% 36.92/24.74 tff(16035,plain,
% 36.92/24.74 (~m_counter_cell_v_value(c_bit1, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8508, 16034, 8468])).
% 36.92/24.74 tff(16036,plain,
% 36.92/24.74 (node1(c_bit1, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8520, 16035])).
% 36.92/24.74 tff(16037,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit1, s96) | (~node1(c_bit1, s96))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8527, 3359, 15925])).
% 36.92/24.74 tff(16038,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit1, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16037, 16036])).
% 36.92/24.74 tff(16039,plain,
% 36.92/24.74 (m_counter_cell_v_carry_out(c_bit1, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8466, 16038, 15925])).
% 36.92/24.74 tff(16040,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit2, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8432, 16039])).
% 36.92/24.74 tff(16041,plain,
% 36.92/24.74 (~m_counter_cell_v_value(c_bit2, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8425, 16040])).
% 36.92/24.74 tff(16042,plain,
% 36.92/24.74 (((~![I0: $i, X: $i] : ((~node1(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, s96)) | m_counter_cell_v_value(c_bit2, s96) | (~node1(c_bit2, s96)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s96)) | m_counter_cell_v_value(c_bit2, s96) | (~node1(c_bit2, s96)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16043,plain,
% 36.92/24.74 (((~node1(c_bit2, s96)) | (~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_value(c_bit2, s96)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_value(c_bit2, s96) | (~node1(c_bit2, s96)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16044,plain,
% 36.92/24.74 (((~![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, s96)) | (~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s96)) | m_counter_cell_v_value(c_bit2, s96) | (~node1(c_bit2, s96))))),
% 36.92/24.74 inference(monotonicity,[status(thm)],[16043])).
% 36.92/24.74 tff(16045,plain,
% 36.92/24.74 (((~![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, s96)) | (~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s96)) | m_counter_cell_v_value(c_bit2, s96) | (~node1(c_bit2, s96)))),
% 36.92/24.74 inference(transitivity,[status(thm)],[16044, 16042])).
% 36.92/24.74 tff(16046,plain,
% 36.92/24.74 ((~![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, s96)) | (~m_counter_cell_v_carry_in(c_bit2, s96)) | m_counter_cell_v_value(c_bit2, s96))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16047,plain,
% 36.92/24.74 ((~![I0: $i, X: $i] : ((~node1(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, s96)) | m_counter_cell_v_value(c_bit2, s96) | (~node1(c_bit2, s96))),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16046, 16045])).
% 36.92/24.74 tff(16048,plain,
% 36.92/24.74 (~node1(c_bit2, s96)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16047, 170, 16041, 16040])).
% 36.92/24.74 tff(16049,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8486, 16048])).
% 36.92/24.74 tff(16050,plain,
% 36.92/24.74 (((~![I0: $i, X: $i] : ((~node1(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, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16051,plain,
% 36.92/24.74 (((~node1(c_bit2, s97)) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97))) <=> (m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16052,plain,
% 36.92/24.74 (((~![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, s97)) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97))))),
% 36.92/24.74 inference(monotonicity,[status(thm)],[16051])).
% 36.92/24.74 tff(16053,plain,
% 36.92/24.74 (((~![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, s97)) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97)))),
% 36.92/24.74 inference(transitivity,[status(thm)],[16052, 16050])).
% 36.92/24.74 tff(16054,plain,
% 36.92/24.74 ((~![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, s97)) | m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97)))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16055,plain,
% 36.92/24.74 ((~![I0: $i, X: $i] : ((~node1(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, s97) | (~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97))),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16054, 16053])).
% 36.92/24.74 tff(16056,plain,
% 36.92/24.74 ((~m_counter_cell_v_value(c_bit2, s97)) | (~node1(c_bit2, s97))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16055, 3359, 16033])).
% 36.92/24.74 tff(16057,plain,
% 36.92/24.74 (~node1(c_bit2, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16056, 16049])).
% 36.92/24.74 tff(16058,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s98)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15959, 16057])).
% 36.92/24.74 tff(16059,plain,
% 36.92/24.74 (~node1(c_bit2, s98)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15967, 16058])).
% 36.92/24.74 tff(16060,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15979, 16059])).
% 36.92/24.74 tff(16061,plain,
% 36.92/24.74 (~m_counter_cell_v_carry_in(c_bit2, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15988, 16060])).
% 36.92/24.74 tff(16062,plain,
% 36.92/24.74 (node1(c_bit2, s95)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8419, 16041])).
% 36.92/24.74 tff(16063,plain,
% 36.92/24.74 (~m_counter_cell_v_value(c_bit2, s95)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8407, 16062, 8391])).
% 36.92/24.74 tff(16064,plain,
% 36.92/24.74 (node1(c_bit2, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16024, 16063])).
% 36.92/24.74 tff(16065,plain,
% 36.92/24.74 ((~m_counter_cell_v_value(c_bit2, s94)) | (~node1(c_bit2, s94))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16011, 3359, 15939])).
% 36.92/24.74 tff(16066,plain,
% 36.92/24.74 (~m_counter_cell_v_value(c_bit2, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16065, 16064])).
% 36.92/24.74 tff(16067,plain,
% 36.92/24.74 (node1(c_bit2, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16003, 16066])).
% 36.92/24.74 tff(16068,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_value(c_bit2, s99))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15995, 3359, 16067])).
% 36.92/24.74 tff(16069,plain,
% 36.92/24.74 ($false),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16068, 16061, 16060])).
% 36.92/24.74 tff(16070,plain,(m_counter_cell_v_value(c_bit1, s94) | m_counter_cell_v_carry_in(c_bit2, s98) | (~node3(c_bit2, s99, s94)) | m_counter_cell_v_carry_out(c_bit2, s95) | m_counter_cell_v_carry_out(c_bit2, s96) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_carry_out(c_bit2, s97) | (~m_counter_cell_v_carry_in(c_bit1, s95)) | m_counter_cell_v_carry_in(c_bit1, s94)), inference(lemma,lemma(discharge,[]))).
% 36.92/24.74 tff(16071,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit1, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16070, 15910, 15606, 15603, 15575, 14472, 15571, 14504, 14473])).
% 36.92/24.74 tff(16072,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s94)) | node3(c_bit1, s99, s94))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s94)) | node3(c_bit1, s99, s94))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16073,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s94)) | node3(c_bit1, s99, s94))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16074,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s94)) | node3(c_bit1, s99, s94)),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16073, 16072])).
% 36.92/24.74 tff(16075,plain,
% 36.92/24.74 ((~trans(s99, s94)) | node3(c_bit1, s99, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16074, 81])).
% 36.92/24.74 tff(16076,plain,
% 36.92/24.74 (node3(c_bit1, s99, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16075, 15905])).
% 36.92/24.74 tff(16077,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s94)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s94)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s94)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16078,plain,
% 36.92/24.74 ((node2(c_bit1, s99) | (~node3(c_bit1, s99, s94)) | (~m_counter_cell_v_value(c_bit1, s94))) <=> ((~m_counter_cell_v_value(c_bit1, s94)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s94)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16079,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s94)) | (~m_counter_cell_v_value(c_bit1, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | ((~m_counter_cell_v_value(c_bit1, s94)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s94))))),
% 36.92/24.74 inference(monotonicity,[status(thm)],[16078])).
% 36.92/24.74 tff(16080,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s94)) | (~m_counter_cell_v_value(c_bit1, s94)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s94)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s94)))),
% 36.92/24.74 inference(transitivity,[status(thm)],[16079, 16077])).
% 36.92/24.74 tff(16081,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (node2(c_bit1, s99) | (~node3(c_bit1, s99, s94)) | (~m_counter_cell_v_value(c_bit1, s94)))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16082,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : (node2(I0, X) | (~node3(I0, X, Y)) | (~m_counter_cell_v_value(I0, Y)))) | (~m_counter_cell_v_value(c_bit1, s94)) | node2(c_bit1, s99) | (~node3(c_bit1, s99, s94))),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16081, 16080])).
% 36.92/24.74 tff(16083,plain,
% 36.92/24.74 ((~m_counter_cell_v_value(c_bit1, s94)) | node2(c_bit1, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16082, 234, 16076])).
% 36.92/24.74 tff(16084,plain,
% 36.92/24.74 (node2(c_bit1, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16083, 16071])).
% 36.92/24.74 tff(16085,plain,
% 36.92/24.74 (m_counter_cell_v_carry_out(c_bit0, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8649, 14538])).
% 36.92/24.74 tff(16086,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit1, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8653, 3046, 16085])).
% 36.92/24.74 tff(16087,plain,
% 36.92/24.74 ((~m_counter_cell_v_value(c_bit1, s99)) | (~node2(c_bit1, s99))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15520, 219, 16086])).
% 36.92/24.74 tff(16088,plain,
% 36.92/24.74 (~m_counter_cell_v_value(c_bit1, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16087, 16084])).
% 36.92/24.74 tff(16089,plain,
% 36.92/24.74 (node1(c_bit1, s98)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15477, 16088])).
% 36.92/24.74 tff(16090,plain,
% 36.92/24.74 ((~m_counter_cell_v_value(c_bit1, s98)) | (~node1(c_bit1, s98))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15513, 3359, 14443])).
% 36.92/24.74 tff(16091,plain,
% 36.92/24.74 (~m_counter_cell_v_value(c_bit1, s98)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16090, 16089])).
% 36.92/24.74 tff(16092,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit1, s97, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit1, s97, s98))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16093,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s97, s98)) | node3(c_bit1, s97, s98))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16094,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s97, s98)) | node3(c_bit1, s97, s98)),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16093, 16092])).
% 36.92/24.74 tff(16095,plain,
% 36.92/24.74 (node3(c_bit1, s97, s98)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16094, 81, 8565])).
% 36.92/24.74 tff(16096,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16097,plain,
% 36.92/24.74 ((node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)) | m_counter_cell_v_value(c_bit1, s98)) <=> (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16098,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)) | m_counter_cell_v_value(c_bit1, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98))))),
% 36.92/24.74 inference(monotonicity,[status(thm)],[16097])).
% 36.92/24.74 tff(16099,plain,
% 36.92/24.74 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)) | m_counter_cell_v_value(c_bit1, s98))) <=> ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)))),
% 36.92/24.74 inference(transitivity,[status(thm)],[16098, 16096])).
% 36.92/24.74 tff(16100,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit1, s97) | (~node3(c_bit1, s97, s98)) | m_counter_cell_v_value(c_bit1, s98))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16101,plain,
% 36.92/24.74 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97) | (~node3(c_bit1, s97, s98))),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16100, 16099])).
% 36.92/24.74 tff(16102,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit1, s98) | node1(c_bit1, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16101, 199, 16095])).
% 36.92/24.74 tff(16103,plain,
% 36.92/24.74 (node1(c_bit1, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16102, 16091])).
% 36.92/24.74 tff(16104,assumption,(~m_counter_cell_v_value(c_bit1, s97)), introduced(assumption)).
% 36.92/24.74 tff(16105,assumption,(node1(c_bit1, s97)), introduced(assumption)).
% 36.92/24.74 tff(16106,plain,
% 36.92/24.74 (((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16107,plain,
% 36.92/24.74 (((~node1(c_bit1, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97)) <=> ((~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16108,plain,
% 36.92/24.74 (((~![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, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | ((~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97))))),
% 36.92/24.74 inference(monotonicity,[status(thm)],[16107])).
% 36.92/24.74 tff(16109,plain,
% 36.92/24.74 (((~![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, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97))) <=> ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)))),
% 36.92/24.74 inference(transitivity,[status(thm)],[16108, 16106])).
% 36.92/24.74 tff(16110,plain,
% 36.92/24.74 ((~![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, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16111,plain,
% 36.92/24.74 ((~![I0: $i, X: $i] : ((~node1(I0, X)) | (~m_counter_cell_v_carry_in(I0, X)) | m_counter_cell_v_value(I0, X))) | (~m_counter_cell_v_carry_in(c_bit1, s97)) | m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97))),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16110, 16109])).
% 36.92/24.74 tff(16112,plain,
% 36.92/24.74 ($false),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16111, 170, 16105, 8468, 16104])).
% 36.92/24.74 tff(16113,plain,(m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97)) | (~m_counter_cell_v_carry_in(c_bit1, s97))), inference(lemma,lemma(discharge,[]))).
% 36.92/24.74 tff(16114,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit1, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16113, 16103, 14472])).
% 36.92/24.74 tff(16115,plain,
% 36.92/24.74 (m_counter_cell_v_carry_out(c_bit1, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8508, 16114, 14472])).
% 36.92/24.74 tff(16116,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit2, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8500, 16115])).
% 36.92/24.74 tff(16117,plain,
% 36.92/24.74 ((~m_counter_cell_v_carry_in(c_bit2, s97)) | (~m_counter_cell_v_value(c_bit2, s97))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[8491, 3031, 15571])).
% 36.92/24.74 tff(16118,plain,
% 36.92/24.74 (~m_counter_cell_v_value(c_bit2, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16117, 16116])).
% 36.92/24.74 tff(16119,plain,
% 36.92/24.74 (~node1(c_bit2, s97)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15947, 170, 16116, 16118])).
% 36.92/24.74 tff(16120,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s98)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15959, 16119])).
% 36.92/24.74 tff(16121,plain,
% 36.92/24.74 ((~m_counter_cell_v_value(c_bit2, s98)) | (~node1(c_bit2, s98))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15966, 3359, 15606])).
% 36.92/24.74 tff(16122,plain,
% 36.92/24.74 (~node1(c_bit2, s98)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16121, 16120])).
% 36.92/24.74 tff(16123,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15979, 16122])).
% 36.92/24.74 tff(16124,plain,
% 36.92/24.74 (~m_counter_cell_v_carry_in(c_bit2, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15988, 16123])).
% 36.92/24.74 tff(16125,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit2, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16032, 16116, 15603, 15575, 15910, 15606, 15571])).
% 36.92/24.74 tff(16126,plain,
% 36.92/24.74 (((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s94)) | (~m_counter_cell_v_carry_out(c_bit2, s94)))) <=> ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s94)) | (~m_counter_cell_v_carry_out(c_bit2, s94)))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16127,plain,
% 36.92/24.74 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | ((~always5(s94)) | (~m_counter_cell_v_carry_out(c_bit2, s94)))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16128,plain,
% 36.92/24.74 ((~![X: $i] : ((~always5(X)) | (~m_counter_cell_v_carry_out(c_bit2, X)))) | (~always5(s94)) | (~m_counter_cell_v_carry_out(c_bit2, s94))),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16127, 16126])).
% 36.92/24.74 tff(16129,plain,
% 36.92/24.74 (~m_counter_cell_v_carry_out(c_bit2, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16128, 58, 15601])).
% 36.92/24.74 tff(16130,plain,
% 36.92/24.74 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s94)) | (~m_counter_cell_v_value(c_bit2, s94)) | m_counter_cell_v_carry_out(c_bit2, s94))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s94)) | (~m_counter_cell_v_value(c_bit2, s94)) | m_counter_cell_v_carry_out(c_bit2, s94))),
% 36.92/24.74 inference(rewrite,[status(thm)],[])).
% 36.92/24.74 tff(16131,plain,
% 36.92/24.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s94)) | (~m_counter_cell_v_value(c_bit2, s94)) | m_counter_cell_v_carry_out(c_bit2, s94))),
% 36.92/24.74 inference(quant_inst,[status(thm)],[])).
% 36.92/24.74 tff(16132,plain,
% 36.92/24.74 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(I0, X)) | (~m_counter_cell_v_value(I0, X)) | m_counter_cell_v_carry_out(I0, X))) | (~m_counter_cell_v_carry_in(c_bit2, s94)) | (~m_counter_cell_v_value(c_bit2, s94)) | m_counter_cell_v_carry_out(c_bit2, s94)),
% 36.92/24.74 inference(modus_ponens,[status(thm)],[16131, 16130])).
% 36.92/24.74 tff(16133,plain,
% 36.92/24.74 ((~m_counter_cell_v_carry_in(c_bit2, s94)) | (~m_counter_cell_v_value(c_bit2, s94))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16132, 3031, 16129])).
% 36.92/24.74 tff(16134,plain,
% 36.92/24.74 (~m_counter_cell_v_value(c_bit2, s94)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16133, 16125])).
% 36.92/24.74 tff(16135,plain,
% 36.92/24.74 (m_counter_cell_v_value(c_bit2, s94) | node1(c_bit2, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16002, 199, 15910])).
% 36.92/24.74 tff(16136,plain,
% 36.92/24.74 (node1(c_bit2, s99)),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16135, 16134])).
% 36.92/24.74 tff(16137,plain,
% 36.92/24.74 (m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_value(c_bit2, s99))),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[15995, 3359, 16136])).
% 36.92/24.74 tff(16138,plain,
% 36.92/24.74 ($false),
% 36.92/24.74 inference(unit_resolution,[status(thm)],[16137, 16124, 16123])).
% 36.92/24.74 tff(16139,plain,(always5(s93) | m_counter_cell_v_carry_in(c_bit1, s98) | m_counter_cell_v_carry_in(c_bit1, s94) | trans(s99, s89) | trans(s99, s91) | trans(s99, s96) | trans(s99, s18) | trans(s99, s17) | trans(s99, s15) | trans(s99, s13) | trans(s99, s9) | trans(s99, s10) | trans(s99, s27) | trans(s99, s41) | trans(s99, s43) | trans(s99, s42) | trans(s99, s36) | trans(s99, s38) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s8) | trans(s99, s39) | trans(s99, s5) | trans(s99, s68) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s44) | trans(s99, s75) | trans(s99, s76) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s3) | trans(s99, s95) | always5(s77)), inference(lemma,lemma(discharge,[]))).
% 36.94/24.75 tff(16140,plain,
% 36.94/24.75 (always5(s93) | m_counter_cell_v_carry_in(c_bit1, s94) | trans(s99, s89) | trans(s99, s91) | trans(s99, s96) | trans(s99, s18) | trans(s99, s17) | trans(s99, s15) | trans(s99, s13) | trans(s99, s9) | trans(s99, s10) | trans(s99, s27) | trans(s99, s41) | trans(s99, s43) | trans(s99, s42) | trans(s99, s36) | trans(s99, s38) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s8) | trans(s99, s39) | trans(s99, s5) | trans(s99, s68) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s44) | trans(s99, s75) | trans(s99, s76) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s3) | trans(s99, s95) | always5(s77)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16139, 8597])).
% 36.94/24.75 tff(16141,plain,
% 36.94/24.75 (always5(s93) | m_counter_cell_v_carry_in(c_bit1, s94) | trans(s99, s89) | trans(s99, s91) | trans(s99, s96) | trans(s99, s18) | trans(s99, s17) | trans(s99, s15) | trans(s99, s13) | trans(s99, s9) | trans(s99, s10) | trans(s99, s27) | trans(s99, s41) | trans(s99, s43) | trans(s99, s42) | trans(s99, s36) | trans(s99, s38) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s8) | trans(s99, s39) | trans(s99, s68) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s44) | trans(s99, s75) | trans(s99, s76) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s95) | always5(s77)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16140, 14442, 14432])).
% 36.94/24.75 tff(16142,plain,
% 36.94/24.75 (always5(s93) | trans(s99, s89) | trans(s99, s91) | trans(s99, s96) | trans(s99, s18) | trans(s99, s17) | trans(s99, s15) | trans(s99, s13) | trans(s99, s9) | trans(s99, s10) | trans(s99, s27) | trans(s99, s41) | trans(s99, s43) | trans(s99, s42) | trans(s99, s36) | trans(s99, s38) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s8) | trans(s99, s39) | trans(s99, s68) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s44) | trans(s99, s75) | trans(s99, s76) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s95) | always5(s77)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16141, 2907])).
% 36.94/24.75 tff(16143,plain,
% 36.94/24.75 (always5(s93) | trans(s99, s89) | trans(s99, s91) | trans(s99, s96) | trans(s99, s18) | trans(s99, s17) | trans(s99, s27) | trans(s99, s41) | trans(s99, s43) | trans(s99, s42) | trans(s99, s36) | trans(s99, s38) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s39) | trans(s99, s68) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s44) | trans(s99, s75) | trans(s99, s76) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s95) | always5(s77)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16142, 14409, 14400, 14390, 14380, 14369])).
% 36.94/24.75 tff(16144,plain,
% 36.94/24.75 (always5(s93) | trans(s99, s89) | trans(s99, s91) | trans(s99, s96) | trans(s99, s41) | trans(s99, s43) | trans(s99, s42) | trans(s99, s47) | trans(s99, s48) | trans(s99, s49) | trans(s99, s46) | trans(s99, s52) | trans(s99, s68) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s44) | trans(s99, s75) | trans(s99, s76) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s95) | always5(s77)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16143, 14338, 14327, 14302, 14280, 14268, 14257])).
% 36.94/24.75 tff(16145,plain,
% 36.94/24.75 (always5(s93) | trans(s99, s89) | trans(s99, s91) | trans(s99, s96) | trans(s99, s48) | trans(s99, s49) | trans(s99, s52) | trans(s99, s68) | trans(s99, s55) | trans(s99, s57) | trans(s99, s63) | trans(s99, s75) | trans(s99, s76) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s95) | always5(s77)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16144, 14238, 14227, 14217, 14205, 14195, 14185])).
% 36.94/24.75 tff(16146,plain,
% 36.94/24.75 (always5(s93) | trans(s99, s89) | trans(s99, s91) | trans(s99, s96) | trans(s99, s68) | trans(s99, s57) | trans(s99, s63) | trans(s99, s75) | trans(s99, s76) | trans(s99, s86) | trans(s99, s70) | trans(s99, s87) | trans(s99, s95) | always5(s77)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16145, 14163, 14152, 14139, 14126])).
% 36.94/24.75 tff(16147,plain,
% 36.94/24.75 (trans(s99, s57)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16146, 13848, 13838, 8695, 13837, 13828, 13818, 13808, 13798, 13788, 13778, 13768, 13758, 8823])).
% 36.94/24.75 tff(16148,assumption,(~always5(s57)), introduced(assumption)).
% 36.94/24.75 tff(16149,plain,
% 36.94/24.75 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s57) | (~trans(s99, s57)))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s57) | (~trans(s99, s57)))),
% 36.94/24.75 inference(rewrite,[status(thm)],[])).
% 36.94/24.75 tff(16150,plain,
% 36.94/24.75 (((~always5(s99)) | (~trans(s99, s57)) | always5(s57)) <=> ((~always5(s99)) | always5(s57) | (~trans(s99, s57)))),
% 36.94/24.75 inference(rewrite,[status(thm)],[])).
% 36.94/24.75 tff(16151,plain,
% 36.94/24.75 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s57)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | always5(s57) | (~trans(s99, s57))))),
% 36.94/24.75 inference(monotonicity,[status(thm)],[16150])).
% 36.94/24.75 tff(16152,plain,
% 36.94/24.75 (((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s57)) | always5(s57))) <=> ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s57) | (~trans(s99, s57)))),
% 36.94/24.75 inference(transitivity,[status(thm)],[16151, 16149])).
% 36.94/24.75 tff(16153,plain,
% 36.94/24.75 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | ((~always5(s99)) | (~trans(s99, s57)) | always5(s57))),
% 36.94/24.75 inference(quant_inst,[status(thm)],[])).
% 36.94/24.75 tff(16154,plain,
% 36.94/24.75 ((~![Y: $i, X: $i] : ((~always5(X)) | (~trans(X, Y)) | always5(Y))) | (~always5(s99)) | always5(s57) | (~trans(s99, s57))),
% 36.94/24.75 inference(modus_ponens,[status(thm)],[16153, 16152])).
% 36.94/24.75 tff(16155,plain,
% 36.94/24.75 ($false),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16154, 11913, 25, 13749, 16148])).
% 36.94/24.75 tff(16156,plain,((~trans(s99, s57)) | always5(s57)), inference(lemma,lemma(discharge,[]))).
% 36.94/24.75 tff(16157,plain,
% 36.94/24.75 (always5(s57)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16156, 16147])).
% 36.94/24.75 tff(16158,plain,
% 36.94/24.75 (always5(s58)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[9038, 16157])).
% 36.94/24.75 tff(16159,plain,
% 36.94/24.75 ($false),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[9030, 16158, 8967])).
% 36.94/24.75 tff(16160,plain,(always5(s95) | trans(s99, s96)), inference(lemma,lemma(discharge,[]))).
% 36.94/24.75 tff(16161,plain,
% 36.94/24.75 (always5(s95)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16160, 8678])).
% 36.94/24.75 tff(16162,plain,
% 36.94/24.75 (always5(s96)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[32, 16161])).
% 36.94/24.75 tff(16163,plain,
% 36.94/24.75 (always5(s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[47, 16162])).
% 36.94/24.75 tff(16164,plain,
% 36.94/24.75 (~m_counter_cell_v_carry_out(c_bit2, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[61, 58, 16163])).
% 36.94/24.75 tff(16165,plain,
% 36.94/24.75 (~m_counter_cell_v_carry_out(c_bit2, s95)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[65, 58, 16161])).
% 36.94/24.75 tff(16166,plain,
% 36.94/24.75 (~m_counter_cell_v_value(c_bit2, s95)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8531, 16165, 16164])).
% 36.94/24.75 tff(16167,plain,
% 36.94/24.75 (~node1(c_bit2, s95)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8542, 16166])).
% 36.94/24.75 tff(16168,plain,
% 36.94/24.75 (m_counter_cell_v_value(c_bit2, s96)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8419, 16167])).
% 36.94/24.75 tff(16169,plain,
% 36.94/24.75 (~node1(c_bit2, s96)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8551, 16168])).
% 36.94/24.75 tff(16170,plain,
% 36.94/24.75 (m_counter_cell_v_value(c_bit2, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8486, 16169])).
% 36.94/24.75 tff(16171,plain,
% 36.94/24.75 (node1(c_bit1, s98)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[15477, 8610])).
% 36.94/24.75 tff(16172,plain,
% 36.94/24.75 (~m_counter_cell_v_value(c_bit1, s98)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[15513, 3359, 16171, 8597])).
% 36.94/24.75 tff(16173,plain,
% 36.94/24.75 (node1(c_bit1, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16102, 16172])).
% 36.94/24.75 tff(16174,plain,
% 36.94/24.75 (m_counter_cell_v_value(c_bit1, s97) | (~node1(c_bit1, s97))),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16113, 8390])).
% 36.94/24.75 tff(16175,plain,
% 36.94/24.75 (m_counter_cell_v_value(c_bit1, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16174, 16173])).
% 36.94/24.75 tff(16176,plain,
% 36.94/24.75 (m_counter_cell_v_carry_out(c_bit1, s97) | (~m_counter_cell_v_value(c_bit1, s97))),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8508, 8390])).
% 36.94/24.75 tff(16177,plain,
% 36.94/24.75 (m_counter_cell_v_carry_out(c_bit1, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16176, 16175])).
% 36.94/24.75 tff(16178,plain,
% 36.94/24.75 (m_counter_cell_v_carry_in(c_bit2, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8500, 16177])).
% 36.94/24.75 tff(16179,plain,
% 36.94/24.75 ($false),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8491, 3031, 16178, 16170, 16164])).
% 36.94/24.75 tff(16180,plain,(m_counter_cell_v_value(c_bit1, s99)), inference(lemma,lemma(discharge,[]))).
% 36.94/24.75 tff(16181,plain,
% 36.94/24.75 (((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99))) <=> ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99))),
% 36.94/24.75 inference(rewrite,[status(thm)],[])).
% 36.94/24.75 tff(16182,plain,
% 36.94/24.75 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99))),
% 36.94/24.75 inference(quant_inst,[status(thm)],[])).
% 36.94/24.75 tff(16183,plain,
% 36.94/24.75 ((~![I0: $i, X: $i] : ((~m_counter_cell_v_carry_in(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, s99)) | (~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99)),
% 36.94/24.75 inference(modus_ponens,[status(thm)],[16182, 16181])).
% 36.94/24.75 tff(16184,plain,
% 36.94/24.75 ((~m_counter_cell_v_value(c_bit1, s99)) | m_counter_cell_v_carry_out(c_bit1, s99)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16183, 3031, 8654])).
% 36.94/24.75 tff(16185,plain,
% 36.94/24.75 (m_counter_cell_v_carry_out(c_bit1, s99)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16184, 16180])).
% 36.94/24.75 tff(16186,assumption,(m_counter_cell_v_carry_out(c_bit1, s99)), introduced(assumption)).
% 36.94/24.75 tff(16187,assumption,(~m_counter_cell_v_carry_in(c_bit2, s99)), introduced(assumption)).
% 36.94/24.75 tff(16188,plain,
% 36.94/24.75 (((~![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, s99)) | m_counter_cell_v_carry_in(c_bit2, s99))) <=> ((~![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, s99)) | m_counter_cell_v_carry_in(c_bit2, s99))),
% 36.94/24.75 inference(rewrite,[status(thm)],[])).
% 36.94/24.75 tff(16189,plain,
% 36.94/24.75 ((~![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, s99)) | m_counter_cell_v_carry_in(c_bit2, s99))),
% 36.94/24.75 inference(quant_inst,[status(thm)],[])).
% 36.94/24.75 tff(16190,plain,
% 36.94/24.75 ((~![X: $i] : ((~m_counter_cell_v_carry_out(c_bit1, X)) | m_counter_cell_v_carry_in(c_bit2, X))) | (~m_counter_cell_v_carry_out(c_bit1, s99)) | m_counter_cell_v_carry_in(c_bit2, s99)),
% 36.94/24.75 inference(modus_ponens,[status(thm)],[16189, 16188])).
% 36.94/24.75 tff(16191,plain,
% 36.94/24.75 ($false),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16190, 4417, 16187, 16186])).
% 36.94/24.75 tff(16192,plain,(m_counter_cell_v_carry_in(c_bit2, s99) | (~m_counter_cell_v_carry_out(c_bit1, s99))), inference(lemma,lemma(discharge,[]))).
% 36.94/24.75 tff(16193,plain,
% 36.94/24.75 (m_counter_cell_v_carry_in(c_bit2, s99)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16192, 16185])).
% 36.94/24.75 tff(16194,plain,
% 36.94/24.75 (~m_counter_cell_v_value(c_bit2, s99)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[15988, 16193])).
% 36.94/24.75 tff(16195,plain,
% 36.94/24.75 (node1(c_bit2, s98)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[15979, 16194])).
% 36.94/24.75 tff(16196,plain,
% 36.94/24.75 (m_counter_cell_v_carry_in(c_bit2, s98) | (~m_counter_cell_v_value(c_bit2, s98))),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[15966, 3359, 16195])).
% 36.94/24.75 tff(16197,plain,
% 36.94/24.75 (~m_counter_cell_v_value(c_bit2, s98)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16196, 8609])).
% 36.94/24.75 tff(16198,plain,
% 36.94/24.75 (node1(c_bit2, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[15959, 16197])).
% 36.94/24.75 tff(16199,plain,
% 36.94/24.75 (m_counter_cell_v_carry_in(c_bit2, s97) | (~m_counter_cell_v_value(c_bit2, s97))),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16055, 3359, 16198])).
% 36.94/24.75 tff(16200,plain,
% 36.94/24.75 (m_counter_cell_v_carry_in(c_bit2, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16199, 8553])).
% 36.94/24.75 tff(16201,plain,
% 36.94/24.75 ($false),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[8491, 3031, 16200, 8553, 62])).
% 36.94/24.75 tff(16202,plain,(~always5(s95)), inference(lemma,lemma(discharge,[]))).
% 36.94/24.75 tff(16203,plain,
% 36.94/24.75 (trans(s99, s96)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[16160, 16202])).
% 36.94/24.75 tff(16204,plain,
% 36.94/24.75 (always5(s96)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[14712, 16203])).
% 36.94/24.75 tff(16205,plain,
% 36.94/24.75 (always5(s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[47, 16204])).
% 36.94/24.75 tff(16206,plain,
% 36.94/24.75 (~m_counter_cell_v_carry_out(c_bit2, s97)),
% 36.94/24.75 inference(unit_resolution,[status(thm)],[61, 58, 16205])).
% 36.94/24.75 tff(16207,plain,
% 36.94/24.75 (((~![I0: $i, X: $i] : ((~node1(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, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99)))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99)))),
% 36.94/24.75 inference(rewrite,[status(thm)],[])).
% 36.94/24.75 tff(16208,plain,
% 36.94/24.75 (((~node1(c_bit2, s99)) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99)) <=> ((~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99)))),
% 36.94/24.75 inference(rewrite,[status(thm)],[])).
% 36.94/24.75 tff(16209,plain,
% 36.94/24.75 (((~![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, s99)) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99))))),
% 36.94/24.75 inference(monotonicity,[status(thm)],[16208])).
% 36.94/24.75 tff(16210,plain,
% 36.94/24.75 (((~![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, s99)) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99))) <=> ((~![I0: $i, X: $i] : ((~node1(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, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99)))),
% 36.94/24.75 inference(transitivity,[status(thm)],[16209, 16207])).
% 36.94/24.75 tff(16211,plain,
% 36.94/24.75 ((~![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, s99)) | (~m_counter_cell_v_carry_in(c_bit2, s99)) | m_counter_cell_v_value(c_bit2, s99))),
% 36.94/24.75 inference(quant_inst,[status(thm)],[])).
% 36.94/24.75 tff(16212,plain,
% 36.94/24.75 ((~![I0: $i, X: $i] : ((~node1(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, s99)) | m_counter_cell_v_value(c_bit2, s99) | (~node1(c_bit2, s99))),
% 36.94/24.76 inference(modus_ponens,[status(thm)],[16211, 16210])).
% 36.94/24.76 tff(16213,plain,
% 36.94/24.76 (~node1(c_bit2, s99)),
% 36.94/24.76 inference(unit_resolution,[status(thm)],[16212, 170, 16193, 16194])).
% 36.94/24.76 tff(16214,plain,
% 36.94/24.76 (((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s96)) | node3(c_bit2, s99, s96))) <=> ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s96)) | node3(c_bit2, s99, s96))),
% 36.94/24.76 inference(rewrite,[status(thm)],[])).
% 36.94/24.76 tff(16215,plain,
% 36.94/24.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | ((~trans(s99, s96)) | node3(c_bit2, s99, s96))),
% 36.94/24.76 inference(quant_inst,[status(thm)],[])).
% 36.94/24.76 tff(16216,plain,
% 36.94/24.76 ((~![Y: $i, I0: $i, X: $i] : ((~trans(X, Y)) | node3(I0, X, Y))) | (~trans(s99, s96)) | node3(c_bit2, s99, s96)),
% 36.94/24.76 inference(modus_ponens,[status(thm)],[16215, 16214])).
% 36.94/24.76 tff(16217,plain,
% 36.94/24.76 ((~trans(s99, s96)) | node3(c_bit2, s99, s96)),
% 36.94/24.76 inference(unit_resolution,[status(thm)],[16216, 81])).
% 36.94/24.76 tff(16218,plain,
% 36.94/24.76 (node3(c_bit2, s99, s96)),
% 36.94/24.76 inference(unit_resolution,[status(thm)],[16217, 16203])).
% 36.94/24.76 tff(16219,plain,
% 36.94/24.76 (((~![Y: $i, 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, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)))) <=> ((~![Y: $i, 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, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)))),
% 36.94/24.76 inference(rewrite,[status(thm)],[])).
% 36.94/24.76 tff(16220,plain,
% 36.94/24.76 ((node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)) | m_counter_cell_v_value(c_bit2, s96)) <=> (m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)))),
% 36.94/24.76 inference(rewrite,[status(thm)],[])).
% 36.94/24.76 tff(16221,plain,
% 36.94/24.76 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![Y: $i, 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, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96))))),
% 36.94/24.76 inference(monotonicity,[status(thm)],[16220])).
% 36.94/24.76 tff(16222,plain,
% 36.94/24.76 (((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)) | m_counter_cell_v_value(c_bit2, s96))) <=> ((~![Y: $i, 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, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)))),
% 36.94/24.76 inference(transitivity,[status(thm)],[16221, 16219])).
% 36.94/24.76 tff(16223,plain,
% 36.94/24.76 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | (node1(c_bit2, s99) | (~node3(c_bit2, s99, s96)) | m_counter_cell_v_value(c_bit2, s96))),
% 36.94/24.76 inference(quant_inst,[status(thm)],[])).
% 36.94/24.76 tff(16224,plain,
% 36.94/24.76 ((~![Y: $i, I0: $i, X: $i] : (node1(I0, X) | (~node3(I0, X, Y)) | m_counter_cell_v_value(I0, Y))) | m_counter_cell_v_value(c_bit2, s96) | node1(c_bit2, s99) | (~node3(c_bit2, s99, s96))),
% 36.94/24.76 inference(modus_ponens,[status(thm)],[16223, 16222])).
% 36.94/24.76 tff(16225,plain,
% 36.94/24.76 (m_counter_cell_v_value(c_bit2, s96)),
% 36.94/24.76 inference(unit_resolution,[status(thm)],[16224, 199, 16218, 16213])).
% 36.94/24.76 tff(16226,plain,
% 36.94/24.76 (~node1(c_bit2, s96)),
% 36.94/24.76 inference(unit_resolution,[status(thm)],[8551, 16225])).
% 36.94/24.76 tff(16227,plain,
% 36.94/24.76 (m_counter_cell_v_value(c_bit2, s97)),
% 36.94/24.76 inference(unit_resolution,[status(thm)],[8486, 16226])).
% 36.94/24.76 tff(16228,plain,
% 36.94/24.76 (m_counter_cell_v_carry_in(c_bit2, s97)),
% 36.94/24.76 inference(unit_resolution,[status(thm)],[16199, 16227])).
% 36.94/24.76 tff(16229,plain,
% 36.94/24.76 ($false),
% 36.94/24.76 inference(unit_resolution,[status(thm)],[8491, 3031, 16228, 16227, 16206])).
% 36.94/24.76 % SZS output end Proof
%------------------------------------------------------------------------------